Solve 17x^2-7+4x-6x^2

$$17 x ^ { 2 } - 7 + 4 x - 6 x ^ { 2 }$$

Factor

$$\left(11x-7\right)\left(x+1\right)$$

Solution Steps

Multiply and combine like terms.

$$11x^{2}+4x-7$$

Factor the expression by grouping. First, the expression needs to be rewritten as 11x^{2}+ax+bx-7. To find a and b, set up a system to be solved.

$$a+b=4 ab=11\left(-7\right)=-77$$

Since ab is negative, a and b have the opposite signs. Since a+b is positive, the positive number has greater absolute value than the negative. List all such integer pairs that give product -77.

$$-1,77 -7,11$$

Calculate the sum for each pair.

$$-1+77=76 -7+11=4$$

The solution is the pair that gives sum 4.

$$a=-7 b=11$$

Rewrite 11x^{2}+4x-7 as \left(11x^{2}-7x\right)+\left(11x-7\right).

$$\left(11x^{2}-7x\right)+\left(11x-7\right)$$

Factor out x in 11x^{2}-7x.

$$x\left(11x-7\right)+11x-7$$

Factor out common term 11x-7 by using distributive property.

$$\left(11x-7\right)\left(x+1\right)$$

Evaluate

$$\left(11x-7\right)\left(x+1\right)$$

Solution Steps

Combine 17x^{2} and -6x^{2} to get 11x^{2}.

$$11x^{2}-7+4x$$