A1.1.1.5 - Simplify expressions involving polynomials.

Key Vocabulary:

A1.1.1.5.1 Add, subtract, and/or multiply polynomial expressions (express answers in simplest form). Note: Nothing larger than a binomial multiplied by a trinomial.

A polynomial expression is shown below.
(mx3 + 3) (2x2 + 5x + 2) – (8x5 + 20x4)
The expression is simplified to 8x3 + 6x2 + 15x + 6.
What is the value of m?
A.–8
B. –4
C. 4
D. 8
Answer: D


A1.1.1.5.2 Factor Algebraic expressions, including difference of squares and trinomials. Note: Trinomials are limited to the form ax2 + bx + c where a is equal to 1 after factoring out all monomial factors.

When the expression x2 – 3x – 18 is factored completely, which is one of its factors?
A.(x – 2)
B. (x – 3)
C. (x – 6)
D. (x – 9)
Answer: C


A1.1.1.5.3 Simplify/reduce a rational algebraic expression.

Simplify:
x2 – 3 x – 10 /x2 + 6 x + 8 ; x ≠ –4, –2
A. -1 /2 x – 5/4
B. x21 /2 x – 5 /4
C. x – 5 /x + 4
D. x + 5 /x–4
Answer: C

Additional Resources:

PDESAS Algebra I Module 4
Khan Academy - Polynomials
Khan Academy - Simplifying rational expression