(2) (2x^(2)-11 x-6)/(x-6)

Question

(2)  (2x^(2)-11 x-6)/(x-6)

Bytelearn · Accepted Answer

Identify expression: Identify the expression to be simplified. The expression given is (2x^(2)-11x-6)/(x-6). We need to simplify this expression by performing polynomial division or factoring, if possible.Check for factoring: Check if the numerator can be factored. We will attempt to factor the quadratic expression 2x^2 - 11x - 6. To factor, we need two numbers that multiply to 2*(-6) = -12 and add up to -11.Find factors: Find the factors of the quadratic expression. The factors of -12 that add up to -11 are -12 and +1. So we can rewrite the quadratic expression as 2x^2 - 12x + x - 6.Group terms to factor: Group the terms to factor by grouping. (2x^2 - 12x) + (x - 6) can be grouped to factor out common terms.Factor out common terms: Factor out the common terms from each group. From the first group, we can factor out 2x, and from the second group, we can factor out 1. 2x(x - 6) + 1(x - 6)Factor out binomial factor: Factor out the common binomial factor. We can now factor out the common binomial factor (x - 6) from the expression. (2x + 1)(x - 6)Simplify expression: Simplify the original expression by canceling out the common factors. Now we can cancel the (x - 6) term in the numerator with the (x - 6) term in the denominator. The simplified form is (2x + 1).

( $2$ ) $\frac{2 x^{2}-11 x-6}{x-6}$

Full solution

More problems from Add, subtract, multiply, and divide polynomials

Related topics

(222) 2x2−11x−6x−6 \frac{2 x^{2}-11 x-6}{x-6} x−62x2−11x−6​

( $2$ ) $\frac{2 x^{2}-11 x-6}{x-6}$