Solve 30x^4+70x^3-120x^2-280x

$$30 x ^ { 4 } + 70 x ^ { 3 } - 120 x ^ { 2 } - 280 x$$

Factor

$$10x\left(x-2\right)\left(x+2\right)\left(3x+7\right)$$

Solution Steps

Factor out 10.

$$10\left(3x^{4}+7x^{3}-12x^{2}-28x\right)$$

Consider 3x^{4}+7x^{3}-12x^{2}-28x. Factor out x.

$$x\left(3x^{3}+7x^{2}-12x-28\right)$$

Consider 3x^{3}+7x^{2}-12x-28. Do the grouping 3x^{3}+7x^{2}-12x-28=\left(3x^{3}+7x^{2}\right)+\left(-12x-28\right), and factor out x^{2} in the first and -4 in the second group.

$$x^{2}\left(3x+7\right)-4\left(3x+7\right)$$

Factor out common term 3x+7 by using distributive property.

$$\left(3x+7\right)\left(x^{2}-4\right)$$

Consider x^{2}-4. Rewrite x^{2}-4 as x^{2}-2^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-2\right)\left(x+2\right)$$

Rewrite the complete factored expression.

$$10x\left(3x+7\right)\left(x-2\right)\left(x+2\right)$$

Evaluate

$$10x\left(3x+7\right)\left(x^{2}-4\right)$$