Factor. 2y^2 + 9y + 10 ____

Identify a, b, c: Identify a, b, and c in the quadratic expression 2y^2 + 9y + 10. Compare 2y^2 + 9y + 10 with ax^2 + bx + c. a = 2 b = 9 c = 10Find two numbers: Find two numbers that multiply to a*c (which is 2*10 = 20) and add up to b (which is 9). The two numbers that satisfy these conditions are 5 and 4, since 5*4 = 20 and 5+4 = 9.Rewrite middle term: Rewrite the middle term of the quadratic expression using the two numbers found in Step 2. 2y^2 + 9y + 10 can be rewritten as 2y^2 + 5y + 4y + 10.Factor by grouping: Factor by grouping. Group the terms: (2y^2 + 5y) + (4y + 10). Factor out the common factor from each group. From the first group, factor out y: y(2y + 5). From the second group, factor out 4: 4(2y + 5).Write factored form: Write the factored form of the expression. Since both groups contain the common factor (2y + 5), factor this out. The factored form is (y + 4)(2y + 5).

Home

Math Problems

Algebra 1

Factor quadratics with other leading coefficients

Full solution

Q. Factor.

\newline

2y^2 + 9y + 10

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $2y^2 + 9y + 10$ . Compare $2y^2 + 9y + 10$ with $ax^2 + bx + c$ . $a = 2$ $b$ $0$ $b$ $1$
Find two numbers: Find two numbers that multiply to $a*c$ (which is $2*10 = 20$ ) and add up to $b$ (which is $9$ ). $\newline$ The two numbers that satisfy these conditions are $5$ and $4$ , since $5*4 = 20$ and $5+4 = 9$ .
Rewrite middle term: Rewrite the middle term of the quadratic expression using the two numbers found in Step $2$ . $\newline$ $2y^2 + 9y + 10$ can be rewritten as $2y^2 + 5y + 4y + 10$ .
Factor by grouping: Factor by grouping. $\newline$ Group the terms: $2y^2 + 5y$ + $4y + 10$ . $\newline$ Factor out the common factor from each group. $\newline$ From the first group, factor out $y$ : $y(2y + 5)$ . $\newline$ From the second group, factor out $4$ : $4(2y + 5)$ .
Write factored form: Write the factored form of the expression. $\newline$ Since both groups contain the common factor $(2y + 5)$ , factor this out. $\newline$ The factored form is $(y + 4)(2y + 5)$ .