Solve 6x^2+54x+48/

$$\frac{ 6 { x }^{ 2 } +54x+48 }{ }$$

Factor

$$6\left(x+1\right)\left(x+8\right)$$

Solution Steps

Factor out 6.

$$6\left(x^{2}+9x+8\right)$$

Consider x^{2}+9x+8. Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx+8. To find a and b, set up a system to be solved.

$$a+b=9 ab=1\times 8=8$$

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 8.

$$1,8 2,4$$

Calculate the sum for each pair.

$$1+8=9 2+4=6$$

The solution is the pair that gives sum 9.

$$a=1 b=8$$

Rewrite x^{2}+9x+8 as \left(x^{2}+x\right)+\left(8x+8\right).

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

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

$$x\left(x+1\right)+8\left(x+1\right)$$

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

$$\left(x+1\right)\left(x+8\right)$$

Rewrite the complete factored expression.

$$6\left(x+1\right)\left(x+8\right)$$

Evaluate

$$6\left(x+1\right)\left(x+8\right)$$

Solution Steps

Anything divided by one gives itself.

$$6x^{2}+54x+48$$