Solve x^2+10x+2^4

$$x ^ { 2 } + 10 x + 2 ^ { 4 }$$

Factor

$$\left(x+2\right)\left(x+8\right)$$

Solution Steps

Multiply and combine like terms.

$$x^{2}+10x+16$$

Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx+16. To find a and b, set up a system to be solved.

$$a+b=10 ab=1\times 16=16$$

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 16.

$$1,16 2,8 4,4$$

Calculate the sum for each pair.

$$1+16=17 2+8=10 4+4=8$$

The solution is the pair that gives sum 10.

$$a=2 b=8$$

Rewrite x^{2}+10x+16 as \left(x^{2}+2x\right)+\left(8x+16\right).

$$\left(x^{2}+2x\right)+\left(8x+16\right)$$

Factor out x in the first and 8 in the second group.

$$x\left(x+2\right)+8\left(x+2\right)$$

Factor out common term x+2 by using distributive property.

$$\left(x+2\right)\left(x+8\right)$$

Evaluate

$$\left(x+2\right)\left(x+8\right)$$

Solution Steps

Calculate 2 to the power of 4 and get 16.

$$x^{2}+10x+16$$