Factor. 6x^2 - 11x + 3 ______

Identify a, b, c: Identify a, b, and c in the quadratic expression 6x^2 - 11x + 3. Compare 6x^2 - 11x + 3 with ax^2 + bx + c. a = 6 b = -11 c = 3Find two numbers: Find two numbers whose product is a*c (6*3 = 18) and whose sum is b (-11). We need to find two numbers that multiply to 18 and add up to -11. After checking pairs of factors of 18, we find that -9 and -2 satisfy the conditions. -9 * -2 = 18 -9 + -2 = -11Rewrite middle term: Rewrite the middle term -11x using the two numbers found in Step 2. 6x^2 - 9x - 2x + 3 Now we have four terms instead of three, which we can factor by grouping.Factor by grouping: Factor by grouping. Group the first two terms and the last two terms. (6x^2 - 9x) + (-2x + 3) Factor out the greatest common factor from each group. 3x(2x - 3) - 1(2x - 3)Factor out common binomial: Factor out the common binomial factor. Both groups contain the common factor (2x - 3). The factored form is (3x - 1)(2x - 3).

Home

Math Problems

Algebra 1

Factor polynomials

Full solution

Q. Factor.

\newline

6x^2 - 11x + 3

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $6x^2 - 11x + 3$ . Compare $6x^2 - 11x + 3$ with $ax^2 + bx + c$ . $a = 6$ $b$ $0$ $b$ $1$
Find two numbers: Find two numbers whose product is $a*c$ ( $6*3 = 18$ ) and whose sum is $b$ ( $-11$ ). $\newline$ We need to find two numbers that multiply to $18$ and add up to $-11$ . $\newline$ After checking pairs of factors of $18$ , we find that $-9$ and $-2$ satisfy the conditions. $\newline$ $-9 * -2 = 18$ $\newline$ $6*3 = 18$ $0$
Rewrite middle term: Rewrite the middle term $-11x$ using the two numbers found in Step $2$ . $\newline$ $6x^2 - 9x - 2x + 3$ $\newline$ Now we have four terms instead of three, which we can factor by grouping.
Factor by grouping: Factor by grouping. $\newline$ Group the first two terms and the last two terms. $\newline$ $(6x^2 - 9x) + (-2x + 3)$ $\newline$ Factor out the greatest common factor from each group. $\newline$ $3x(2x - 3) - 1(2x - 3)$
Factor out common binomial: Factor out the common binomial factor. $\newline$ Both groups contain the common factor $(2x - 3)$ . $\newline$ The factored form is $(3x - 1)(2x - 3)$ .