Solve 2x^2+17x+8-27

$$2 x ^ { 2 } + 17 x + 8 - 27$$

Factor

$$\left(x-1\right)\left(2x+19\right)$$

Solution Steps

Multiply and combine like terms.

$$2x^{2}+17x-19$$

Factor the expression by grouping. First, the expression needs to be rewritten as 2x^{2}+ax+bx-19. To find a and b, set up a system to be solved.

$$a+b=17 ab=2\left(-19\right)=-38$$

Since ab is negative, a and b have the opposite signs. Since a+b is positive, the positive number has greater absolute value than the negative. List all such integer pairs that give product -38.

$$-1,38 -2,19$$

Calculate the sum for each pair.

$$-1+38=37 -2+19=17$$

The solution is the pair that gives sum 17.

$$a=-2 b=19$$

Rewrite 2x^{2}+17x-19 as \left(2x^{2}-2x\right)+\left(19x-19\right).

$$\left(2x^{2}-2x\right)+\left(19x-19\right)$$

Factor out 2x in the first and 19 in the second group.

$$2x\left(x-1\right)+19\left(x-1\right)$$

Factor out common term x-1 by using distributive property.

$$\left(x-1\right)\left(2x+19\right)$$

Evaluate

$$\left(x-1\right)\left(2x+19\right)$$

Solution Steps

Subtract 27 from 8 to get -19.

$$2x^{2}+17x-19$$