Factor. 5w^2 - 8w + 3 ______

Identify a, b, c: Identify a, b, and c in the quadratic expression 5w^2 - 8w + 3. Compare 5w^2 - 8w + 3 with ax^2 + bx + c. a = 5 b = -8 c = 3Find product and sum: Find two numbers whose product is a*c (5*3 = 15) and whose sum is b (-8). We need to find two numbers that multiply to 15 and add up to -8. After checking possible pairs of factors of 15, we find that: -3 * -5 = 15 -3 + -5 = -8 Two numbers: -3, -5Rewrite middle term: Rewrite the middle term -8w using the two numbers found in Step 2. 5w^2 - 3w - 5w + 3Factor by grouping: Factor by grouping. Group the first two terms and the last two terms. (5w^2 - 3w) - (5w - 3)Factor out common factor: Factor out the greatest common factor from each group. w(5w - 3) - 1(5w - 3)Factor out the common binomial factor (5w - 3). (w - 1)(5w - 3)

Home

Math Problems

Algebra 1

Factor polynomials

Full solution

Q. Factor.

\newline

5w^2 - 8w + 3

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $5w^2 - 8w + 3$ . $\newline$ Compare $5w^2 - 8w + 3$ with $ax^2 + bx + c$ . $\newline$ $a = 5$ $\newline$ $b$ $0$ $\newline$ $b$ $1$
Find product and sum: Find two numbers whose product is $a*c$ ( $5*3 = 15$ ) and whose sum is $b$ ( $-8$ ). $\newline$ We need to find two numbers that multiply to $15$ and add up to $-8$ . $\newline$ After checking possible pairs of factors of $15$ , we find that: $\newline$ $-3 * -5 = 15$ $\newline$ $-3 + -5 = -8$ $\newline$ Two numbers: $-3$ , $5*3 = 15$ $0$
Rewrite middle term: Rewrite the middle term $-8w$ using the two numbers found in Step $2$ . $\newline$ $5w^2 - 3w - 5w + 3$
Factor by grouping: Factor by grouping. Group the first two terms and the last two terms. $(5w^2 - 3w) - (5w - 3)$
Factor out common factor: Factor out the greatest common factor from each group. $\newline$ $w(5w - 3) - 1(5w - 3)$
Factor out common factor: Factor out the greatest common factor from each group. $\newline$ $w(5w - 3) - 1(5w - 3)$ Factor out the common binomial factor $(5w - 3)$ . $\newline$ $(w - 1)(5w - 3)$