Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Factor. $\newline$ $y^2 + 9y + 14$

View step-by-step help

View step-by-step help

Factor quadratics with leading coefficient 1

Full solution

Q. Factor.

\newline

y^2 + 9y + 14

Identify Variables: Identify $a$ , $b$ , and $c$ in the quadratic expression $y^2 + 9y + 14$ . Compare $y^2 + 9y + 14$ with the standard quadratic form $ax^2 + bx + c$ . Here, $a = 1$ , $b = 9$ , and $c = 14$ .
Find Multiplying Numbers: Find two numbers that multiply to $ac$ (which is just $c$ since $a = 1$ ) and add up to $b$ . We need two numbers that multiply to $14$ and add up to $9$ . The numbers $2$ and $7$ satisfy these conditions because: $2 \times 7 = 14$ (product is $c$ ) $c$ $0$ (sum is $b$ )
Rewrite Expression: Write the quadratic expression using the two numbers found in Step $2$ . $\newline$ The expression $y^2 + 9y + 14$ can be rewritten as $y^2 + 2y + 7y + 14$ .
Factor by Grouping: Factor by grouping. $\newline$ Group the terms to factor by common terms: $\newline$ $(y^2 + 2y) + (7y + 14)$ $\newline$ Factor out the common factors from each group: $\newline$ $y(y + 2) + 7(y + 2)$
Factor Common Binomial: Factor out the common binomial factor. $\newline$ Since both groups contain the factor $(y + 2)$ , we can factor it out: $\newline$ $(y + 2)(y + 7)$

More problems from Factor quadratics with leading coefficient 1

Question

Find the greatest common factor.

\newline

9v^3, 6v^3

\newline

\newline

Write your answer as a constant times a product of single variables raised to exponents.

\newline

\underline{\hspace{1cm}}

Posted 1 month ago

Question

Factor out the greatest common factor. If the greatest common factor is

1

, just retype the polynomial.

\newline

6x^3 + 9x^2

\newline

Posted 2 months ago

Question

\newline

k^2 + 9k + 18

\newline

Posted 1 month ago

Question

\newline

9j^2 - 16

\newline

Posted 1 month ago

Question

\newline

j^3 + 2j^2 + 5j + 10

Posted 2 months ago

Question

x^4 + 6x^2 + 9

\newline

All factors in your answer should have integer coefficients.

\newline

Posted 2 months ago

Question

\newline

z^2 + 13z + 22

\newline

Posted 1 month ago

Question

Simplify the expression:

\newline

5x + 9x - 4x - 2x

\newline

Posted 3 months ago

Question

3 - 3^2

Posted 3 months ago

Question

5 - 5^2

Posted 1 month ago