Solve 28x^4+112x^3-21x^2-84x

$$28 x ^ { 4 } + 112 x ^ { 3 } - 21 x ^ { 2 } - 84 x$$

Factor

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

Solution Steps

Factor out 7.

$$7\left(4x^{4}+16x^{3}-3x^{2}-12x\right)$$

Consider 4x^{4}+16x^{3}-3x^{2}-12x. Factor out x.

$$x\left(4x^{3}+16x^{2}-3x-12\right)$$

Consider 4x^{3}+16x^{2}-3x-12. Do the grouping 4x^{3}+16x^{2}-3x-12=\left(4x^{3}+16x^{2}\right)+\left(-3x-12\right), and factor out 4x^{2} in the first and -3 in the second group.

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

Factor out common term x+4 by using distributive property.

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

Rewrite the complete factored expression. Polynomial 4x^{2}-3 is not factored since it does not have any rational roots.

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

Evaluate

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