Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Factor. $\newline$ $16x^2 + 40x + 25$

View step-by-step help

View step-by-step help

Factor quadratics: special cases

Full solution

Q. Factor.

\newline

16x^2 + 40x + 25

Check Perfect Square Trinomial: Determine if the quadratic expression is a perfect square trinomial. $\newline$ A perfect square trinomial is in the form $(ax)^2 + 2abx + b^2$ , which factors to $(ax + b)^2$ . $\newline$ Check if $16x^2 + 40x + 25$ fits this pattern. $\newline$ $16x^2$ is a perfect square, as $16x^2 = (4x)^2$ . $\newline$ $25$ is a perfect square, as $25 = 5^2$ . $\newline$ The middle term, $40x$ , is twice the product of the square roots of the first and last terms, as $2 \times 4x \times 5 = 40x$ . $\newline$ Since all conditions are met, the expression is a perfect square trinomial.
Factor Trinomial: Factor the perfect square trinomial. $\newline$ Since we have established that the expression is a perfect square trinomial, we can factor it as $(ax + b)^2$ . $\newline$ From Step $1$ , we know that $a = 4x$ and $b = 5$ . $\newline$ Therefore, the factored form is $(4x + 5)^2$ .

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 2 months 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 3 months ago

Question

\newline

k^2 + 9k + 18

\newline

Posted 2 months ago

Question

\newline

9j^2 - 16

\newline

Posted 2 months ago

Question

\newline

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

Posted 3 months ago

Question

x^4 + 6x^2 + 9

\newline

All factors in your answer should have integer coefficients.

\newline

Posted 3 months ago

Question

\newline

z^2 + 13z + 22

\newline

Posted 2 months ago

Question

Simplify the expression:

\newline

5x + 9x - 4x - 2x

\newline

Posted 4 months ago

Question

3 - 3^2

Posted 4 months ago

Question

5 - 5^2

Posted 2 months ago