ដោះស្រាយ (x-(-6-i))(x-(-6+i))(x-(-1+3i))(x-(-1+3i))

$$( x - ( - 6 - i ) ) ( x - ( - 6 + i ) ) ( x - ( - 1 + 3 i ) ) ( x - ( - 1 + 3 i ) )$$

វាយតម្លៃ

$$\left(x+\left(6-i\right)\right)\left(x+\left(6+i\right)\right)\left(x+\left(1-3i\right)\right)^{2}$$

ជំហានចម្លើយ

គុណ x-\left(-1+3i\right) និង x-\left(-1+3i\right) ដើម្បីបាន \left(x-\left(-1+3i\right)\right)^{2}។

$$\left(x-\left(-6-i\right)\right)\left(x-\left(-6+i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

ភាពផ្ទុយគ្នានៃ -6-i គឺ 6+i។

$$\left(x+\left(6+i\right)\right)\left(x-\left(-6+i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

ប្រើលក្ខណៈបំបែក​ដើម្បីគុណ x+\left(6+i\right) នឹង x-\left(-6+i\right)។

$$\left(x\left(x-\left(-6+i\right)\right)+\left(6+i\right)\left(x-\left(-6+i\right)\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

ប្រើលក្ខណៈបំបែក​ដើម្បីគុណ x\left(x-\left(-6+i\right)\right)+\left(6+i\right)\left(x-\left(-6+i\right)\right) នឹង \left(x-\left(-1+3i\right)\right)^{2}។

$$x\left(x-\left(-6+i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}+\left(6+i\right)\left(x-\left(-6+i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

គុណ -1 និង -6+i ដើម្បីបាន 6-i។

$$x\left(x+\left(6-i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}+\left(6+i\right)\left(x-\left(-6+i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

គុណ -1 និង -1+3i ដើម្បីបាន 1-3i។

$$x\left(x+\left(6-i\right)\right)\left(x+\left(1-3i\right)\right)^{2}+\left(6+i\right)\left(x-\left(-6+i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

ប្រើទ្រឹស្ដីបទទ្វេរធា \left(a+b\right)^{2}=a^{2}+2ab+b^{2} ដើម្បីពង្រីក \left(x+\left(1-3i\right)\right)^{2}។

$$x\left(x+\left(6-i\right)\right)\left(x^{2}+\left(2-6i\right)x+\left(-8-6i\right)\right)+\left(6+i\right)\left(x-\left(-6+i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

ប្រើលក្ខណៈបំបែក​ដើម្បីគុណ x នឹង x+\left(6-i\right)។

$$\left(x^{2}+\left(6-i\right)x\right)\left(x^{2}+\left(2-6i\right)x+\left(-8-6i\right)\right)+\left(6+i\right)\left(x-\left(-6+i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

អនុវត្ត​លក្ខណៈបំបែកដោយគុណតួនីមួយៗនៃ x^{2}+\left(6-i\right)x នឹងតួនីមួយៗនៃ x^{2}+\left(2-6i\right)x+\left(-8-6i\right)។

$$x^{4}+\left(2-6i\right)x^{3}+\left(-8-6i\right)x^{2}+\left(6-i\right)x^{3}+\left(6-38i\right)x^{2}+\left(-54-28i\right)x+\left(6+i\right)\left(x-\left(-6+i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

បន្សំ \left(2-6i\right)x^{3} និង \left(6-i\right)x^{3} ដើម្បីបាន \left(8-7i\right)x^{3}។

$$x^{4}+\left(8-7i\right)x^{3}+\left(-8-6i\right)x^{2}+\left(6-38i\right)x^{2}+\left(-54-28i\right)x+\left(6+i\right)\left(x-\left(-6+i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

បន្សំ \left(-8-6i\right)x^{2} និង \left(6-38i\right)x^{2} ដើម្បីបាន \left(-2-44i\right)x^{2}។

$$x^{4}+\left(8-7i\right)x^{3}+\left(-2-44i\right)x^{2}+\left(-54-28i\right)x+\left(6+i\right)\left(x-\left(-6+i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

គុណ -1 និង -6+i ដើម្បីបាន 6-i។

$$x^{4}+\left(8-7i\right)x^{3}+\left(-2-44i\right)x^{2}+\left(-54-28i\right)x+\left(6+i\right)\left(x+\left(6-i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

គុណ -1 និង -1+3i ដើម្បីបាន 1-3i។

$$x^{4}+\left(8-7i\right)x^{3}+\left(-2-44i\right)x^{2}+\left(-54-28i\right)x+\left(6+i\right)\left(x+\left(6-i\right)\right)\left(x+\left(1-3i\right)\right)^{2}$$

ប្រើទ្រឹស្ដីបទទ្វេរធា \left(a+b\right)^{2}=a^{2}+2ab+b^{2} ដើម្បីពង្រីក \left(x+\left(1-3i\right)\right)^{2}។

$$x^{4}+\left(8-7i\right)x^{3}+\left(-2-44i\right)x^{2}+\left(-54-28i\right)x+\left(6+i\right)\left(x+\left(6-i\right)\right)\left(x^{2}+\left(2-6i\right)x+\left(-8-6i\right)\right)$$

ប្រើលក្ខណៈបំបែក​ដើម្បីគុណ 6+i នឹង x+\left(6-i\right)។

$$x^{4}+\left(8-7i\right)x^{3}+\left(-2-44i\right)x^{2}+\left(-54-28i\right)x+\left(\left(6+i\right)x+37\right)\left(x^{2}+\left(2-6i\right)x+\left(-8-6i\right)\right)$$

អនុវត្ត​លក្ខណៈបំបែកដោយគុណតួនីមួយៗនៃ \left(6+i\right)x+37 នឹងតួនីមួយៗនៃ x^{2}+\left(2-6i\right)x+\left(-8-6i\right)។

$$x^{4}+\left(8-7i\right)x^{3}+\left(-2-44i\right)x^{2}+\left(-54-28i\right)x+\left(6+i\right)x^{3}+\left(18-34i\right)x^{2}+\left(-42-44i\right)x+37x^{2}+\left(74-222i\right)x+\left(-296-222i\right)$$

បន្សំ \left(18-34i\right)x^{2} និង 37x^{2} ដើម្បីបាន \left(55-34i\right)x^{2}។

$$x^{4}+\left(8-7i\right)x^{3}+\left(-2-44i\right)x^{2}+\left(-54-28i\right)x+\left(6+i\right)x^{3}+\left(55-34i\right)x^{2}+\left(-42-44i\right)x+\left(74-222i\right)x+\left(-296-222i\right)$$

បន្សំ \left(-42-44i\right)x និង \left(74-222i\right)x ដើម្បីបាន \left(32-266i\right)x។

$$x^{4}+\left(8-7i\right)x^{3}+\left(-2-44i\right)x^{2}+\left(-54-28i\right)x+\left(6+i\right)x^{3}+\left(55-34i\right)x^{2}+\left(32-266i\right)x+\left(-296-222i\right)$$

បន្សំ \left(8-7i\right)x^{3} និង \left(6+i\right)x^{3} ដើម្បីបាន \left(14-6i\right)x^{3}។

$$x^{4}+\left(14-6i\right)x^{3}+\left(-2-44i\right)x^{2}+\left(-54-28i\right)x+\left(55-34i\right)x^{2}+\left(32-266i\right)x+\left(-296-222i\right)$$

បន្សំ \left(-2-44i\right)x^{2} និង \left(55-34i\right)x^{2} ដើម្បីបាន \left(53-78i\right)x^{2}។

$$x^{4}+\left(14-6i\right)x^{3}+\left(53-78i\right)x^{2}+\left(-54-28i\right)x+\left(32-266i\right)x+\left(-296-222i\right)$$

បន្សំ \left(-54-28i\right)x និង \left(32-266i\right)x ដើម្បីបាន \left(-22-294i\right)x។

$$x^{4}+\left(14-6i\right)x^{3}+\left(53-78i\right)x^{2}+\left(-22-294i\right)x+\left(-296-222i\right)$$

ពន្លាត

$$x^{4}+\left(14-6i\right)x^{3}+\left(53-78i\right)x^{2}+\left(-22-294i\right)x+\left(-296-222i\right)$$

ជំហានចម្លើយ

គុណ x-\left(-1+3i\right) និង x-\left(-1+3i\right) ដើម្បីបាន \left(x-\left(-1+3i\right)\right)^{2}។

$$\left(x-\left(-6-i\right)\right)\left(x-\left(-6+i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

ភាពផ្ទុយគ្នានៃ -6-i គឺ 6+i។

$$\left(x+\left(6+i\right)\right)\left(x-\left(-6+i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

ប្រើលក្ខណៈបំបែក​ដើម្បីគុណ x+\left(6+i\right) នឹង x-\left(-6+i\right)។

$$\left(x\left(x-\left(-6+i\right)\right)+\left(6+i\right)\left(x-\left(-6+i\right)\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

ប្រើលក្ខណៈបំបែក​ដើម្បីគុណ x\left(x-\left(-6+i\right)\right)+\left(6+i\right)\left(x-\left(-6+i\right)\right) នឹង \left(x-\left(-1+3i\right)\right)^{2}។

$$x\left(x-\left(-6+i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}+\left(6+i\right)\left(x-\left(-6+i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

គុណ -1 និង -6+i ដើម្បីបាន 6-i។

$$x\left(x+\left(6-i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}+\left(6+i\right)\left(x-\left(-6+i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

គុណ -1 និង -1+3i ដើម្បីបាន 1-3i។

$$x\left(x+\left(6-i\right)\right)\left(x+\left(1-3i\right)\right)^{2}+\left(6+i\right)\left(x-\left(-6+i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

ប្រើទ្រឹស្ដីបទទ្វេរធា \left(a+b\right)^{2}=a^{2}+2ab+b^{2} ដើម្បីពង្រីក \left(x+\left(1-3i\right)\right)^{2}។

$$x\left(x+\left(6-i\right)\right)\left(x^{2}+\left(2-6i\right)x+\left(-8-6i\right)\right)+\left(6+i\right)\left(x-\left(-6+i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

ប្រើលក្ខណៈបំបែក​ដើម្បីគុណ x នឹង x+\left(6-i\right)។

$$\left(x^{2}+\left(6-i\right)x\right)\left(x^{2}+\left(2-6i\right)x+\left(-8-6i\right)\right)+\left(6+i\right)\left(x-\left(-6+i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

អនុវត្ត​លក្ខណៈបំបែកដោយគុណតួនីមួយៗនៃ x^{2}+\left(6-i\right)x នឹងតួនីមួយៗនៃ x^{2}+\left(2-6i\right)x+\left(-8-6i\right)។

$$x^{4}+\left(2-6i\right)x^{3}+\left(-8-6i\right)x^{2}+\left(6-i\right)x^{3}+\left(6-38i\right)x^{2}+\left(-54-28i\right)x+\left(6+i\right)\left(x-\left(-6+i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

បន្សំ \left(2-6i\right)x^{3} និង \left(6-i\right)x^{3} ដើម្បីបាន \left(8-7i\right)x^{3}។

$$x^{4}+\left(8-7i\right)x^{3}+\left(-8-6i\right)x^{2}+\left(6-38i\right)x^{2}+\left(-54-28i\right)x+\left(6+i\right)\left(x-\left(-6+i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

បន្សំ \left(-8-6i\right)x^{2} និង \left(6-38i\right)x^{2} ដើម្បីបាន \left(-2-44i\right)x^{2}។

$$x^{4}+\left(8-7i\right)x^{3}+\left(-2-44i\right)x^{2}+\left(-54-28i\right)x+\left(6+i\right)\left(x-\left(-6+i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

គុណ -1 និង -6+i ដើម្បីបាន 6-i។

$$x^{4}+\left(8-7i\right)x^{3}+\left(-2-44i\right)x^{2}+\left(-54-28i\right)x+\left(6+i\right)\left(x+\left(6-i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

គុណ -1 និង -1+3i ដើម្បីបាន 1-3i។

$$x^{4}+\left(8-7i\right)x^{3}+\left(-2-44i\right)x^{2}+\left(-54-28i\right)x+\left(6+i\right)\left(x+\left(6-i\right)\right)\left(x+\left(1-3i\right)\right)^{2}$$

ប្រើទ្រឹស្ដីបទទ្វេរធា \left(a+b\right)^{2}=a^{2}+2ab+b^{2} ដើម្បីពង្រីក \left(x+\left(1-3i\right)\right)^{2}។

$$x^{4}+\left(8-7i\right)x^{3}+\left(-2-44i\right)x^{2}+\left(-54-28i\right)x+\left(6+i\right)\left(x+\left(6-i\right)\right)\left(x^{2}+\left(2-6i\right)x+\left(-8-6i\right)\right)$$

ប្រើលក្ខណៈបំបែក​ដើម្បីគុណ 6+i នឹង x+\left(6-i\right)។

$$x^{4}+\left(8-7i\right)x^{3}+\left(-2-44i\right)x^{2}+\left(-54-28i\right)x+\left(\left(6+i\right)x+37\right)\left(x^{2}+\left(2-6i\right)x+\left(-8-6i\right)\right)$$

អនុវត្ត​លក្ខណៈបំបែកដោយគុណតួនីមួយៗនៃ \left(6+i\right)x+37 នឹងតួនីមួយៗនៃ x^{2}+\left(2-6i\right)x+\left(-8-6i\right)។

$$x^{4}+\left(8-7i\right)x^{3}+\left(-2-44i\right)x^{2}+\left(-54-28i\right)x+\left(6+i\right)x^{3}+\left(18-34i\right)x^{2}+\left(-42-44i\right)x+37x^{2}+\left(74-222i\right)x+\left(-296-222i\right)$$

បន្សំ \left(18-34i\right)x^{2} និង 37x^{2} ដើម្បីបាន \left(55-34i\right)x^{2}។

$$x^{4}+\left(8-7i\right)x^{3}+\left(-2-44i\right)x^{2}+\left(-54-28i\right)x+\left(6+i\right)x^{3}+\left(55-34i\right)x^{2}+\left(-42-44i\right)x+\left(74-222i\right)x+\left(-296-222i\right)$$

បន្សំ \left(-42-44i\right)x និង \left(74-222i\right)x ដើម្បីបាន \left(32-266i\right)x។

$$x^{4}+\left(8-7i\right)x^{3}+\left(-2-44i\right)x^{2}+\left(-54-28i\right)x+\left(6+i\right)x^{3}+\left(55-34i\right)x^{2}+\left(32-266i\right)x+\left(-296-222i\right)$$

បន្សំ \left(8-7i\right)x^{3} និង \left(6+i\right)x^{3} ដើម្បីបាន \left(14-6i\right)x^{3}។

$$x^{4}+\left(14-6i\right)x^{3}+\left(-2-44i\right)x^{2}+\left(-54-28i\right)x+\left(55-34i\right)x^{2}+\left(32-266i\right)x+\left(-296-222i\right)$$

បន្សំ \left(-2-44i\right)x^{2} និង \left(55-34i\right)x^{2} ដើម្បីបាន \left(53-78i\right)x^{2}។

$$x^{4}+\left(14-6i\right)x^{3}+\left(53-78i\right)x^{2}+\left(-54-28i\right)x+\left(32-266i\right)x+\left(-296-222i\right)$$

បន្សំ \left(-54-28i\right)x និង \left(32-266i\right)x ដើម្បីបាន \left(-22-294i\right)x។

$$x^{4}+\left(14-6i\right)x^{3}+\left(53-78i\right)x^{2}+\left(-22-294i\right)x+\left(-296-222i\right)$$