Solve c^2+2c+7c+14

$$c ^ { 2 } + 2 c + 7 c + 14$$

Factor

$$\left(c+2\right)\left(c+7\right)$$

Solution Steps

Multiply and combine like terms.

$$c^{2}+9c+14$$

Factor the expression by grouping. First, the expression needs to be rewritten as c^{2}+ac+bc+14. To find a and b, set up a system to be solved.

$$a+b=9 ab=1\times 14=14$$

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 c^{2}+9c+14 as \left(c^{2}+2c\right)+\left(7c+14\right).

$$\left(c^{2}+2c\right)+\left(7c+14\right)$$

Factor out c in the first and 7 in the second group.

$$c\left(c+2\right)+7\left(c+2\right)$$

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

$$\left(c+2\right)\left(c+7\right)$$

Evaluate

$$\left(c+2\right)\left(c+7\right)$$

Solution Steps

Combine 2c and 7c to get 9c.

$$c^{2}+9c+14$$