Factor completely. 2x^(2)-9x+7 Answer:

Identify Coefficients: Identify the coefficients of the quadratic expression. The quadratic expression is 2x^2 - 9x + 7. Here, a = 2, b = -9, and c = 7.Find Multiplying Numbers: Find two numbers that multiply to ac (a times c) and add up to b. ac = 2 * 7 = 14 We need two numbers that multiply to 14 and add up to -9. The numbers -2 and -7 work because -2 * -7 = 14 and -2 + -7 = -9.Rewrite Middle Term: Rewrite the middle term, -9x, using the two numbers found in the previous step. The expression becomes 2x^2 - 2x - 7x + 7.Factor by Grouping: Factor by grouping. Group the terms as follows: (2x^2 - 2x) + (-7x + 7). Factor out the common factors from each group. From the first group, factor out 2x: 2x(x - 1). From the second group, factor out -7: -7(x - 1).Combine Factored Groups: Combine the factored groups since they have a common factor of (x - 1). The factored form is (2x - 7)(x - 1).

Home

Math Problems

Algebra 1

Factor polynomials

Full solution

Q. Factor completely.

\newline

2 x^{2}-9 x+7

\newline

Answer:

Identify Coefficients: Identify the coefficients of the quadratic expression. $\newline$ The quadratic expression is $2x^2 - 9x + 7$ . $\newline$ Here, $a = 2$ , $b = -9$ , and $c = 7$ .
Find Multiplying Numbers: Find two numbers that multiply to $ac$ ( $a \times c$ ) and add up to $b$ . $\newline$ $ac = 2 \times 7 = 14$ $\newline$ We need two numbers that multiply to $14$ and add up to $-9$ . $\newline$ The numbers $-2$ and $-7$ work because $-2 \times -7 = 14$ and $-2 + -7 = -9$ .
Rewrite Middle Term: Rewrite the middle term, $-9x$ , using the two numbers found in the previous step. $\newline$ The expression becomes $2x^2 - 2x - 7x + 7$ .
Factor by Grouping: Factor by grouping. $\newline$ Group the terms as follows: $2x^2 - 2x$ + $-7x + 7$ . $\newline$ Factor out the common factors from each group. $\newline$ From the first group, factor out $2x$ : $2x(x - 1)$ . $\newline$ From the second group, factor out $-7$ : $-7(x - 1)$ .
Combine Factored Groups: Combine the factored groups since they have a common factor of $(x - 1)$ . $\newline$ The factored form is $(2x - 7)(x - 1)$ .