Practice Factoring Trinomials with Two Variables

Practice Problems

We can identify some trinomials as perfect squares. A perfect square trinomial has the form $$a^2 + 2ab + b^2$$ and $$a^2 -2ab +b^2$$. Because each term is a square, they can be factored into $$(a + b)^2$$ and $$(a - b)^2$$, respectively. It is important to be able to identify trinomials in this form so that we can easily factor them after determining the value of "a" and "b".

Teron and Abigail were each asked to factor the quadratic expression $$-y^2-4y+12$$. Their responses are shown below.

Teron: $$-1(y-6)(y+2)$$

Abigail: $$(-y+6)(y-2)$$

Which student wrote an expression that is equivalent to $$-y^2-4y+12$$?

Choose 1 answer:
1. Only Teron
2. Only Abigail
3. Both Teron and Abigail
4. Neither Teron nor Abigail
The polynomial expressions ‍$$12y^3-5y^2-3y$$ and $$5(3y+1)(2y-3)$$ share a common binomial factor.

What binomial factor do they share?
The quadratic expression ‍$$x^2+Mx+30$$ can be factored as ‍$$(x+a)(x+b)$$, where ‍$$M$$, ‍‍$$a$$, ‍and ‍$$b$$ are integers.

Jusna wrote that ‍$$M$$ could be equal to -13.

Ethan wrote that $$M$$ could be equal to ‍11.

Which student is correct ?

Choose 1 answer:
1. Only Jusna
2. Only Ethan
3. Both Jusna and Ethan
4. Neither Jusna nor Ethan
The rectangle below has an area of $$12ax-28ay+15bx-35by$$ square meters and a width of $$4a+5b$$ meters.

What expression represents the length of the rectangle?

Source: Khan Academy, https://www.khanacademy.org/math/algebra-home/alg-polynomials/alg-factoring-polynomials-quadratic-forms/e/factoring_polynomials_with_two_variables
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