Solve 5x^2-35x+x-7

$$5 x ^ { 2 } - 35 x + x - 7$$

Factor

$$\left(x-7\right)\left(5x+1\right)$$

Solution Steps

Multiply and combine like terms.

$$5x^{2}-34x-7$$

Factor the expression by grouping. First, the expression needs to be rewritten as 5x^{2}+ax+bx-7. To find a and b, set up a system to be solved.

$$a+b=-34 ab=5\left(-7\right)=-35$$

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 -35.

$$1,-35 5,-7$$

Calculate the sum for each pair.

$$1-35=-34 5-7=-2$$

The solution is the pair that gives sum -34.

$$a=-35 b=1$$

Rewrite 5x^{2}-34x-7 as \left(5x^{2}-35x\right)+\left(x-7\right).

$$\left(5x^{2}-35x\right)+\left(x-7\right)$$

Factor out 5x in 5x^{2}-35x.

$$5x\left(x-7\right)+x-7$$

Factor out common term x-7 by using distributive property.

$$\left(x-7\right)\left(5x+1\right)$$

Evaluate

$$\left(x-7\right)\left(5x+1\right)$$

Solution Steps

Combine -35x and x to get -34x.

$$5x^{2}-34x-7$$