Factor the trinomial: 5x^(2)+16 x+3 Answer:

Identify a, b, c: Identify a, b, and c in the trinomial 5x^2 + 16x + 3. Compare 5x^2 + 16x + 3 with ax^2 + bx + c. a = 5 b = 16 c = 3Find Product and Sum: Find two numbers whose product is a*c (5*3=15) and whose sum is b (16). We need to find two numbers that multiply to 15 and add up to 16. After checking possible factors of 15, we find: 1 * 15 = 15 1 + 15 = 16 Two numbers: 1, 15Rewrite Middle Term: Rewrite the middle term 16x using the two numbers found in Step 2. 5x^2 + 16x + 3 becomes 5x^2 + 1x + 15x + 3Factor by Grouping: Factor by grouping. Group the terms: (5x^2 + 1x) + (15x + 3) Factor out the greatest common factor from each group. From the first group, x is the greatest common factor: x(5x + 1) From the second group, 3 is the greatest common factor: 3(5x + 1)Factor out Common Binomial: Factor out the common binomial factor. We now have x(5x + 1) + 3(5x + 1) The common binomial factor is (5x + 1). Factored form: (5x + 1)(x + 3)

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Factor the trinomial:

5x^(2)+16 x+3
Answer:

Factor the trinomial: $\newline$ $5 x^{2}+16 x+3$ $\newline$ Answer:

View step-by-step help

Full solution

Q. Factor the trinomial:

\newline

5 x^{2}+16 x+3

\newline

Answer:

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the trinomial $5x^2 + 16x + 3$ . Compare $5x^2 + 16x + 3$ with $ax^2 + bx + c$ . $a = 5$ $b$ $0$ $b$ $1$
Find Product and Sum: Find two numbers whose product is $a*c$ ( $5*3=15$ ) and whose sum is $b$ ( $16$ ). $\newline$ We need to find two numbers that multiply to $15$ and add up to $16$ . $\newline$ After checking possible factors of $15$ , we find: $\newline$ $1 * 15 = 15$ $\newline$ $1 + 15 = 16$ $\newline$ Two numbers: $1$ , $15$
Rewrite Middle Term: Rewrite the middle term $16x$ using the two numbers found in Step $2$ . $\newline$ $5x^2 + 16x + 3$ becomes $5x^2 + 1x + 15x + 3$
Factor by Grouping: Factor by grouping. $\newline$ Group the terms: $5x^2 + 1x$ + $15x + 3$ $\newline$ Factor out the greatest common factor from each group. $\newline$ From the first group, $x$ is the greatest common factor: $x(5x + 1)$ $\newline$ From the second group, $3$ is the greatest common factor: $3(5x + 1)$
Factor out Common Binomial: Factor out the common binomial factor. $\newline$ We now have $x(5x + 1) + 3(5x + 1)$ $\newline$ The common binomial factor is $(5x + 1)$ . $\newline$ Factored form: $(5x + 1)(x + 3)$