Solve 12x^2-72x+104-44

$$12 x ^ { 2 } - 72 x + 104 - 44$$

Factor

$$12\left(x-5\right)\left(x-1\right)$$

Solution Steps

Factor out 4.

$$4\left(3x^{2}-18x+15\right)$$

Consider 3x^{2}-18x+26-11. Multiply and combine like terms.

$$3x^{2}-18x+15$$

Consider 3x^{2}-18x+15. Factor out 3.

$$3\left(x^{2}-6x+5\right)$$

Consider x^{2}-6x+5. Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx+5. To find a and b, set up a system to be solved.

$$a+b=-6 ab=1\times 5=5$$

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

$$a=-5 b=-1$$

Rewrite x^{2}-6x+5 as \left(x^{2}-5x\right)+\left(-x+5\right).

$$\left(x^{2}-5x\right)+\left(-x+5\right)$$

Factor out x in the first and -1 in the second group.

$$x\left(x-5\right)-\left(x-5\right)$$

Factor out common term x-5 by using distributive property.

$$\left(x-5\right)\left(x-1\right)$$

Rewrite the complete factored expression.

$$12\left(x-5\right)\left(x-1\right)$$

Evaluate

$$12\left(x-5\right)\left(x-1\right)$$

Solution Steps

Subtract 44 from 104 to get 60.

$$12x^{2}-72x+60$$