Solve 7-5x^2-3x+2x^2-x

$$7 - 5 x ^ { 2 } - 3 x + 2 x ^ { 2 } - x$$

Evaluate

$$\left(1-x\right)\left(3x+7\right)$$

Solution Steps

Combine -5x^{2} and 2x^{2} to get -3x^{2}.

$$7-3x^{2}-3x-x$$

Combine -3x and -x to get -4x.

$$7-3x^{2}-4x$$

Factor

$$\left(1-x\right)\left(3x+7\right)$$

Solution Steps

Multiply and combine like terms.

$$-3x^{2}-4x+7$$

Factor the expression by grouping. First, the expression needs to be rewritten as -3x^{2}+ax+bx+7. To find a and b, set up a system to be solved.

$$a+b=-4 ab=-3\times 7=-21$$

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 -21.

$$1,-21 3,-7$$

Calculate the sum for each pair.

$$1-21=-20 3-7=-4$$

The solution is the pair that gives sum -4.

$$a=3 b=-7$$

Rewrite -3x^{2}-4x+7 as \left(-3x^{2}+3x\right)+\left(-7x+7\right).

$$\left(-3x^{2}+3x\right)+\left(-7x+7\right)$$

Factor out 3x in the first and 7 in the second group.

$$3x\left(-x+1\right)+7\left(-x+1\right)$$

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

$$\left(-x+1\right)\left(3x+7\right)$$