Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Factor. $\newline$ $9s^2 + 30s + 25$

View step-by-step help

View step-by-step help

Factor quadratics: special cases

Full solution

Q. Factor.

\newline

9s^2 + 30s + 25

Check Perfect Square Trinomial: Determine if the quadratic expression can be factored using the perfect square trinomial formula. $\newline$ A perfect square trinomial is in the form $(a^2 + 2ab + b^2)$ which factors to $(a + b)^2$ . $\newline$ Check if $9s^2 + 30s + 25$ fits this pattern. $\newline$ $9s^2$ is a perfect square, as $(3s)^2 = 9s^2$ . $\newline$ $25$ is a perfect square, as $5^2 = 25$ . $\newline$ The middle term, $30s$ , is twice the product of the square roots of the first and last terms, as $2 \times 3s \times 5 = 30s$ . $\newline$ Since all conditions are met, we can conclude that $9s^2 + 30s + 25$ is a perfect square trinomial.
Identify $a$ and $b$ : Factor the perfect square trinomial using the formula $(a + b)^2 = a^2 + 2ab + b^2$ . Identify $a$ and $b$ from the expression $9s^2 + 30s + 25$ . $a = 3s$ (since $(3s)^2 = 9s^2$ ) $b = 5$ (since $5^2 = 25$ ) Now, factor the expression as $b$ $0$ . $b$ $1$ This matches the original expression, so the factored form is $b$ $2$ .

More problems from Factor quadratics: special cases

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