Solve g(x)=4x^4-5x^3-39x^2-41x-10/(x^2-3x-5)

$$g ( x ) = \frac { 4 x ^ { 4 } - 5 x ^ { 3 } - 39 x ^ { 2 } - 41 x - 10 } { ( x ^ { 2 } - 3 x - 5 ) }$$

Evaluate

$$4x^{2}+7x+2$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{4\left(x-\left(-\frac{1}{8}\sqrt{17}-\frac{7}{8}\right)\right)\left(x-\left(\frac{1}{8}\sqrt{17}-\frac{7}{8}\right)\right)\left(x-\left(-\frac{1}{2}\sqrt{29}+\frac{3}{2}\right)\right)\left(x-\left(\frac{1}{2}\sqrt{29}+\frac{3}{2}\right)\right)}{\left(x-\left(-\frac{1}{2}\sqrt{29}+\frac{3}{2}\right)\right)\left(x-\left(\frac{1}{2}\sqrt{29}+\frac{3}{2}\right)\right)}$$

Cancel out \left(x-\left(-\frac{1}{2}\sqrt{29}+\frac{3}{2}\right)\right)\left(x-\left(\frac{1}{2}\sqrt{29}+\frac{3}{2}\right)\right) in both numerator and denominator.

$$4\left(x-\left(-\frac{1}{8}\sqrt{17}-\frac{7}{8}\right)\right)\left(x-\left(\frac{1}{8}\sqrt{17}-\frac{7}{8}\right)\right)$$

Expand the expression.

$$4x^{2}+7x+2$$

Expand

$$4x^{2}+7x+2$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{4\left(x-\left(-\frac{1}{8}\sqrt{17}-\frac{7}{8}\right)\right)\left(x-\left(\frac{1}{8}\sqrt{17}-\frac{7}{8}\right)\right)\left(x-\left(-\frac{1}{2}\sqrt{29}+\frac{3}{2}\right)\right)\left(x-\left(\frac{1}{2}\sqrt{29}+\frac{3}{2}\right)\right)}{\left(x-\left(-\frac{1}{2}\sqrt{29}+\frac{3}{2}\right)\right)\left(x-\left(\frac{1}{2}\sqrt{29}+\frac{3}{2}\right)\right)}$$

Cancel out \left(x-\left(-\frac{1}{2}\sqrt{29}+\frac{3}{2}\right)\right)\left(x-\left(\frac{1}{2}\sqrt{29}+\frac{3}{2}\right)\right) in both numerator and denominator.

$$4\left(x-\left(-\frac{1}{8}\sqrt{17}-\frac{7}{8}\right)\right)\left(x-\left(\frac{1}{8}\sqrt{17}-\frac{7}{8}\right)\right)$$

Expand the expression.

$$4x^{2}+7x+2$$