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. x2– 1 /2 x – 5 /4 C. x – 5 /x + 4 D. x + 5 /x–4
Answer: C

## 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. x2– 1 /2 x – 5 /4

C. x – 5 /x + 4

D. x + 5 /x–4

Answer: C

## Additional Resources:

PDESAS Algebra I Module 4Khan Academy - Polynomials

Khan Academy - Simplifying rational expression