Question

Instructions: Match the quadratic equation to the type of factoring that could be used to solve it.

Answer 1

Recall the following types of factoring:

Difference of squares into a product of conjugate binomials:

$a^2-b^2=(a+b)(a-b)$

Quadratic equation without a constant term into the product by a common factor:

$ax^2+bx=x(ax+b)$

Perfect square trinomial into a binomial squared:

$x^2+2ax+a^2=(x+a)^2$

Notice that the first expression is a difference of the squares of 4x and 3. Then:

$16x^2-9=(4x+3)(4x-3)$

Then, the match for the first equation is Difference of squares.

The second expression has a common factor of 8x:

$8x^2-16x=8x(x-2)$

Then, the match for the second equation is GCF (greatest common factor).

The third expression is a perfect square trinomial:

$x^2+8x+16=(x+4)^2$

Then, the match for the third equation is Perfect Square Trinomial.