Warm Up Solutions

Simplify using long division. Write remainders as a fraction.

Note

It is important to know how to divide whole numbers using long division with confidence.

Problems 1–2
Q: Complete the sentence. The remainder must always be ___ than the divisor.
A: smaller

Q: What term or terms are placed in the denominator when a remainder is written as a fraction?
A: The divisor

$11 13672$
$1101242 13672 - 11 26 - 22 47 - 44 32 - 22 10 \frac{10}{11}$

$12 2532$

$120211 2532 - 24 13 - 12 12 - 12 0$

Find the GCF of each column and row. Then write the expression as the product of binomial factors and a quadratic trinomial.

Note

Problems 3–4
Recall that this diagram is one way to find the binomial factors. The terms in the box can be combined to form a quadratic trinomial. See Algebra 1: Principles of Secondary Mathematics Unit 4 to review.

$(x + 4) (3 x + 2) = 3 x^{2} + 14 x + 8$

$(x + 5) (8 x - 1) = 8 x^{2} + 39 x - 5$