Factor. 5n^2 + 9n + 4 ____

Identify a, b, c: Identify a, b, and c in the quadratic expression 5n^2 + 9n + 4. Compare 5n^2 + 9n + 4 with ax^2 + bx + c. a = 5 b = 9 c = 4Find numbers multiply add: Find two numbers that multiply to a*c (5*4=20) and add up to b (9). We need to find two numbers that multiply to 20 and add up to 9. After checking possible pairs that multiply to 20 (1 and 20, 2 and 10, 4 and 5), we find that 1 and 20 do not add up to 9, 2 and 10 do not add up to 9, but 4 and 5 do add up to 9. So the two numbers are 4 and 5.Rewrite middle term: Rewrite the middle term (9n) using the two numbers found in Step 2. 5n^2 + 9n + 4 can be rewritten as 5n^2 + 4n + 5n + 4.Factor by grouping: Factor by grouping. Group the first two terms and the last two terms: (5n^2 + 4n) + (5n + 4) Factor out the common factor from each group: n(5n + 4) + 1(5n + 4)Factor out common binomial: Factor out the common binomial factor. Since both groups contain the factor (5n + 4), we can factor it out: (5n + 4)(n + 1)

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Factor. $\newline$ $5n^2 + 9n + 4$

View step-by-step help

Home

Math Problems

Algebra 1

Factor quadratics with other leading coefficients

Full solution

Q. Factor.

\newline

5n^2 + 9n + 4

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $5n^2 + 9n + 4$ . Compare $5n^2 + 9n + 4$ with $ax^2 + bx + c$ . $a = 5$ $b$ $0$ $b$ $1$
Find numbers multiply add: Find two numbers that multiply to $a*c$ ( $5*4=20$ ) and add up to $b$ ( $9$ ). $\newline$ We need to find two numbers that multiply to $20$ and add up to $9$ . $\newline$ After checking possible pairs that multiply to $20$ ( $1$ and $20$ , $2$ and $5*4=20$ $0$ , $5*4=20$ $1$ and $5*4=20$ $2$ ), we find that $1$ and $20$ do not add up to $9$ , $2$ and $5*4=20$ $0$ do not add up to $9$ , but $5*4=20$ $1$ and $5*4=20$ $2$ do add up to $9$ . $\newline$ So the two numbers are $5*4=20$ $1$ and $5*4=20$ $2$ .
Rewrite middle term: Rewrite the middle term $9n$ using the two numbers found in Step $2$ . $5n^2 + 9n + 4$ can be rewritten as $5n^2 + 4n + 5n + 4$ .
Factor by grouping: Factor by grouping. $\newline$ Group the first two terms and the last two terms: $\newline$ $(5n^2 + 4n) + (5n + 4)$ $\newline$ Factor out the common factor from each group: $\newline$ $n(5n + 4) + 1(5n + 4)$
Factor out common binomial: Factor out the common binomial factor. $\newline$ Since both groups contain the factor $(5n + 4)$ , we can factor it out: $\newline$ $(5n + 4)(n + 1)$