Solve -4q^2-22q+12-2q+1

$$- 4 q ^ { 2 } - 22 q + 12 - 2 q + 1$$

Evaluate

$$\left(1-2q\right)\left(2q+13\right)$$

Solution Steps

Combine -22q and -2q to get -24q.

$$-4q^{2}-24q+12+1$$

Add 12 and 1 to get 13.

$$-4q^{2}-24q+13$$

Factor

$$\left(1-2q\right)\left(2q+13\right)$$

Solution Steps

Multiply and combine like terms.

$$-4q^{2}-24q+13$$

Factor the expression by grouping. First, the expression needs to be rewritten as -4q^{2}+aq+bq+13. To find a and b, set up a system to be solved.

$$a+b=-24 ab=-4\times 13=-52$$

Since ab is negative, a and b have the opposite signs. Since a+b is negative, the negative number has greater absolute value than the positive. List all such integer pairs that give product -52.

$$1,-52 2,-26 4,-13$$

Calculate the sum for each pair.

$$1-52=-51 2-26=-24 4-13=-9$$

The solution is the pair that gives sum -24.

$$a=2 b=-26$$

Rewrite -4q^{2}-24q+13 as \left(-4q^{2}+2q\right)+\left(-26q+13\right).

$$\left(-4q^{2}+2q\right)+\left(-26q+13\right)$$

Factor out 2q in the first and 13 in the second group.

$$2q\left(-2q+1\right)+13\left(-2q+1\right)$$

Factor out common term -2q+1 by using distributive property.

$$\left(-2q+1\right)\left(2q+13\right)$$