Factor. 2t^2 + 11t + 9 ______

Identify a, b, c: Identify a, b, and c in the quadratic expression 2t^2 + 11t + 9. Compare 2t^2 + 11t + 9 with ax^2 + bx + c. a = 2 b = 11 c = 9Find numbers multiply and add: Find two numbers that multiply to a*c (2*9 = 18) and add up to b (11). We need to find two numbers that multiply to 18 and add up to 11. The numbers 2 and 9 satisfy these conditions because 2*9 = 18 and 2+9 = 11.Rewrite middle term: Rewrite the middle term 11t using the two numbers found in Step 2. We can express 11t as the sum of 2t and 9t. So, 2t^2 + 11t + 9 becomes 2t^2 + 2t + 9t + 9.Factor by grouping: Factor by grouping. First, group the terms: (2t^2 + 2t) + (9t + 9). Factor out the common factor from each group. From the first group, we can factor out 2t: 2t(t + 1). From the second group, we can factor out 9: 9(t + 1).Write factored form: Write the factored form of the expression. Since both groups contain the factor (t + 1), we can factor this out. The factored form is (2t + 9)(t + 1).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Factor. $\newline$ $2t^2 + 11t + 9$

View step-by-step help

Home

Math Problems

Algebra 1

Factor quadratics with other leading coefficients

Full solution

Q. Factor.

\newline

2t^2 + 11t + 9

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $2t^2 + 11t + 9$ . Compare $2t^2 + 11t + 9$ with $ax^2 + bx + c$ . $a = 2$ $b$ $0$ $b$ $1$
Find numbers multiply and add: Find two numbers that multiply to $a*c$ ( $2*9 = 18$ ) and add up to $b$ ( $11$ ). $\newline$ We need to find two numbers that multiply to $18$ and add up to $11$ . $\newline$ The numbers $2$ and $9$ satisfy these conditions because $2*9 = 18$ and $2+9 = 11$ .
Rewrite middle term: Rewrite the middle term $11t$ using the two numbers found in Step $2$ . $\newline$ We can express $11t$ as the sum of $2t$ and $9t$ . $\newline$ So, $2t^2 + 11t + 9$ becomes $2t^2 + 2t + 9t + 9$ .
Factor by grouping: Factor by grouping. $\newline$ First, group the terms: $2t^2 + 2t$ + $9t + 9$ . $\newline$ Factor out the common factor from each group. $\newline$ From the first group, we can factor out $2t$ : $2t(t + 1)$ . $\newline$ From the second group, we can factor out $9$ : $9(t + 1)$ .
Write factored form: Write the factored form of the expression. $\newline$ Since both groups contain the factor $(t + 1)$ , we can factor this out. $\newline$ The factored form is $(2t + 9)(t + 1)$ .