Factor the trinomial: 5x^(2)+18 x+9 Answer:

Identify trinomial: Identify the trinomial to be factored, which is 5x^2 + 18x + 9.Find two numbers: Look for two numbers that multiply to give the product of the coefficient of x^2 term (5) and the constant term (9), which is 5*9 = 45, and add up to the coefficient of the x term (18).Determine numbers: Find the two numbers that meet the criteria from Step 2. The numbers 15 and 3 multiply to give 45 and add up to 18.Rewrite middle term: Rewrite the middle term (18x) using the two numbers found in Step 3 as the sum of two terms: 15x and 3x. The trinomial becomes 5x^2 + 15x + 3x + 9.Factor by grouping: Factor by grouping. Group the first two terms and the last two terms: (5x^2 + 15x) + (3x + 9).Factor out common factor: Factor out the greatest common factor from each group. From the first group, factor out 5x, and from the second group, factor out 3: 5x(x + 3) + 3(x + 3).Final factorization: Since both groups contain the common factor (x + 3), factor it out: (x + 3)(5x + 3).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Factor the trinomial:

5x^(2)+18 x+9
Answer:

Factor the trinomial: $\newline$ $5 x^{2}+18 x+9$ $\newline$ Answer:

View step-by-step help

Full solution

Q. Factor the trinomial:

\newline

5 x^{2}+18 x+9

\newline

Answer:

Identify trinomial: Identify the trinomial to be factored, which is $5x^2 + 18x + 9$ .
Find two numbers: Look for two numbers that multiply to give the product of the coefficient of $x^2$ term $(5)$ and the constant term $(9)$ , which is $5 \times 9 = 45$ , and add up to the coefficient of the $x$ term $(18)$ .
Determine numbers: Find the two numbers that meet the criteria from Step $2$ . The numbers $15$ and $3$ multiply to give $45$ and add up to $18$ .
Rewrite middle term: Rewrite the middle term $18x$ using the two numbers found in Step $3$ as the sum of two terms: $15x$ and $3x$ . The trinomial becomes $5x^2 + 15x + 3x + 9$ .
Factor by grouping: Factor by grouping. Group the first two terms and the last two terms: $(5x^2 + 15x) + (3x + 9)$ .
Factor out common factor: Factor out the greatest common factor from each group. From the first group, factor out $5x$ , and from the second group, factor out $3$ : $5x(x + 3) + 3(x + 3)$ .
Final factorization: Since both groups contain the common factor $(x + 3)$ , factor it out: $(x + 3)(5x + 3)$ .