Algebraic Fractions & Polynomial Simplification – Core Concepts

25 question-and-answer flashcards covering factoring, combining like terms, common denominators, rational expression operations, FOIL, and simplification techniques relevant to the provided quiz material.

What must two fractions share before you can add or subtract them?

A common (identical) denominator.

When combining like terms, which parts of the terms must be the same?

The variable(s) and their exponents.

What is the Greatest Common Factor (GCF) of 30m and 45m²?

15m.

Factor the expression 5x² – 15x.

5x(x – 3).

Simplify: (n + 7)(n – 2).

n² + 5n – 14.

State the first step when multiplying the rational expressions 3y/4x² · 8x/9y².

Factor numerators and denominators, then cancel common factors before multiplying.

What is the common denominator of 5a/2 and 6a/3a?

6a (because 2 and 3a’s LCM is 6a).

Simplify the rational expression (x² – 9)/(x + 3).

x – 3 (factoring difference of squares and canceling).

Which factoring pattern is used in x² – 49?

Difference of squares: (x – 7)(x + 7).

What restriction must be stated for the expression 4/(x – 3)?

x ≠ 3 (denominator cannot be zero).

Divide: 7x² – 28x by 7x.

x – 4.

Write the reciprocal of 6x/5.

5/(6x).

Simplify completely: (x – 1)(x + 3)/(x + 2)(x – 1).

(x + 3)/(x + 2).

When subtracting (3m)/(4n) – (2m)/(n), what common denominator is needed?

4n.

State the FOIL acronym.

First, Outer, Inner, Last – used to multiply two binomials.

Factor the trinomial x² + 7x + 12.

(x + 3)(x + 4).

Simplify: 8v – 4 – (5v – 2).

3v – 2.

What is the product of (x + 2)(x – 5)?

x² – 3x – 10.

Simplify the complex fraction (5/(2x)) ÷ (x/3).

15/(2x²).

How do you divide two rational expressions?

Multiply the first by the reciprocal of the second, then simplify.

True or False: (x + 1)/(x – 1) + (x – 1)/(x + 1) requires factoring before addition.

True – you need the common denominator (x – 1)(x + 1).

Identify the GCF of 12y³x and 18y²x².

6y²x.

Simplify the expression 36x²/12x³.

3/x.

What is the result of subtracting (3/2x) – (4/3x)?

(1/6x) (after using common denominator 6x).

Explain why x ≠ –2 in the fraction (x + 3)/(x + 2).

Because x = –2 would make the denominator zero, which is undefined.