Factor the trinomial: 3x^(2)+7x+2 Answer:

Identify a, b, c: Identify a, b, and c in the trinomial 3x^2 + 7x + 2. Compare 3x^2 + 7x + 2 with ax^2 + bx + c. a = 3 b = 7 c = 2Find two numbers: Find two numbers whose product is a*c (3*2 = 6) and whose sum is b (7). We need to find two numbers that multiply to 6 and add up to 7. The numbers 6 and 1 satisfy these conditions because: 6 * 1 = 6 6 + 1 = 7Rewrite middle term: Rewrite the middle term (7x) using the two numbers found in Step 2. We can express 7x as 6x + x. So, the trinomial 3x^2 + 7x + 2 can be rewritten as 3x^2 + 6x + x + 2.Factor by grouping: Factor by grouping. Group the terms into two pairs: (3x^2 + 6x) and (x + 2). Factor out the common factor from each pair. From the first pair, we can factor out 3x: 3x(x + 2). From the second pair, we can factor out 1: 1(x + 2). Now we have 3x(x + 2) + 1(x + 2).Factor out common binomial: Factor out the common binomial factor (x + 2). We can now factor out (x + 2) from both terms. The factored form is (x + 2)(3x + 1).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Factor the trinomial:

3x^(2)+7x+2
Answer:

Factor the trinomial: $\newline$ $3 x^{2}+7 x+2$ $\newline$ Answer:

View step-by-step help

Full solution

Q. Factor the trinomial:

\newline

3 x^{2}+7 x+2

\newline

Answer:

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the trinomial $3x^2 + 7x + 2$ . Compare $3x^2 + 7x + 2$ with $ax^2 + bx + c$ . $a = 3$ $b$ $0$ $b$ $1$
Find two numbers: Find two numbers whose product is $a*c$ ( $3*2 = 6$ ) and whose sum is $b$ ( $7$ ). $\newline$ We need to find two numbers that multiply to $6$ and add up to $7$ . $\newline$ The numbers $6$ and $1$ satisfy these conditions because: $\newline$ $6 * 1 = 6$ $\newline$ $6 + 1 = 7$
Rewrite middle term: Rewrite the middle term $7x$ using the two numbers found in Step $2$ . $\newline$ We can express $7x$ as $6x + x$ . $\newline$ So, the trinomial $3x^2 + 7x + 2$ can be rewritten as $3x^2 + 6x + x + 2$ .
Factor by grouping: Factor by grouping. $\newline$ Group the terms into two pairs: $(3x^2 + 6x)$ and $(x + 2)$ . $\newline$ Factor out the common factor from each pair. $\newline$ From the first pair, we can factor out $3x$ : $3x(x + 2)$ . $\newline$ From the second pair, we can factor out $1$ : $1(x + 2)$ . $\newline$ Now we have $3x(x + 2) + 1(x + 2)$ .
Factor out common binomial: Factor out the common binomial factor $(x + 2)$ . $\newline$ We can now factor out $(x + 2)$ from both terms. $\newline$ The factored form is $(x + 2)(3x + 1)$ .