Solve 2y^3+5y^2+4y+10

$$2 y ^ { 3 } + 5 y ^ { 2 } + 4 y + 10$$

Factor

$$\left(2y+5\right)\left(y^{2}+2\right)$$

Solution Steps

Do the grouping 2y^{3}+5y^{2}+4y+10=\left(2y^{3}+5y^{2}\right)+\left(4y+10\right), and factor out y^{2} in the first and 2 in the second group.

$$y^{2}\left(2y+5\right)+2\left(2y+5\right)$$

Factor out common term 2y+5 by using distributive property. Polynomial y^{2}+2 is not factored since it does not have any rational roots.

$$\left(2y+5\right)\left(y^{2}+2\right)$$

Evaluate

$$\left(2y+5\right)\left(y^{2}+2\right)$$