Solve (8s+3)+(5s^2+7s+7)

$$( 8 s + 3 ) + ( 5 s ^ { 2 } + 7 s + 7 )$$

Evaluate

$$5\left(s+1\right)\left(s+2\right)$$

Solution Steps

Combine 8s and 7s to get 15s.

$$15s+3+5s^{2}+7$$

Add 3 and 7 to get 10.

$$15s+10+5s^{2}$$

Factor

$$5\left(s+1\right)\left(s+2\right)$$

Solution Steps

Multiply and combine like terms.

$$5s^{2}+15s+10$$

Factor out 5.

$$5\left(s^{2}+3s+2\right)$$

Consider s^{2}+3s+2. Factor the expression by grouping. First, the expression needs to be rewritten as s^{2}+as+bs+2. To find a and b, set up a system to be solved.

$$a+b=3 ab=1\times 2=2$$

Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. The only such pair is the system solution.

$$a=1 b=2$$

Rewrite s^{2}+3s+2 as \left(s^{2}+s\right)+\left(2s+2\right).

$$\left(s^{2}+s\right)+\left(2s+2\right)$$

Factor out s in the first and 2 in the second group.

$$s\left(s+1\right)+2\left(s+1\right)$$

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

$$\left(s+1\right)\left(s+2\right)$$

Rewrite the complete factored expression.

$$5\left(s+1\right)\left(s+2\right)$$