Solve 4x^2+16x+2x+14

$$4 { x }^{ 2 } +16x+2x+14$$

Factor

$$2\left(x+1\right)\left(2x+7\right)$$

Solution Steps

Factor out 2.

$$2\left(2x^{2}+8x+x+7\right)$$

Consider 2x^{2}+8x+x+7. Multiply and combine like terms.

$$2x^{2}+9x+7$$

Consider 2x^{2}+9x+7. Factor the expression by grouping. First, the expression needs to be rewritten as 2x^{2}+ax+bx+7. To find a and b, set up a system to be solved.

$$a+b=9 ab=2\times 7=14$$

Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. List all such integer pairs that give product 14.

$$1,14 2,7$$

Calculate the sum for each pair.

$$1+14=15 2+7=9$$

The solution is the pair that gives sum 9.

$$a=2 b=7$$

Rewrite 2x^{2}+9x+7 as \left(2x^{2}+2x\right)+\left(7x+7\right).

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

Factor out 2x in the first and 7 in the second group.

$$2x\left(x+1\right)+7\left(x+1\right)$$

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

$$\left(x+1\right)\left(2x+7\right)$$

Rewrite the complete factored expression.

$$2\left(x+1\right)\left(2x+7\right)$$

Evaluate

$$2\left(x+1\right)\left(2x+7\right)$$

Solution Steps

Combine 16x and 2x to get 18x.

$$4x^{2}+18x+14$$