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# 21 Algebra Problems : Factoring, GCF and Word Problems

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SHOW ALL STEPS WITH SOLUTION. FACTOR OUT THE GCF IN EACH EXPRESSION.

1. 12X^4T + 30X^3T - 24X^2T^2

2. 15X^2Y^2 - 9XY^2 + 6X^2Y

FACTOR EACH POLYNOMIAL

1. 3X^2 + 6X + 3

2. X^3 + X^2 - X - 1

3. 3A - 3B - XA + XB

FACTOR OUT EACH POLYNOMIAL AND FACTOR OUT THE GCF

1. H^2 - 9HS + 9S^2

2. 9W - W^3

3. 8VW^2 + 32VW + 32V

FACTOR EACH TRINOMIAL USING TRIAL AND ERROR

1. 15X^2 - X- 2

2. 15X^2 + 13X - 2

FACTOR EACH POLYNOMIAL COMPLETELY

1. 10X^2Y^2 + XY^2 - 9Y^2

FACTOR EACH POLYNOMIAL COMPLETELY. IF THE POLYNOMIAL IS PRIME, SAY SO

1. 9X^2 + 6X + 1
2. 9X^2 + 6X + 3
3. A^2 - 25A
4. M^4N + MN^4

1. WHEN SIMPLIFYING LIKE TERMS, HOW DO YOU DETERMINE THE LIKE TERMS?

2. HOW DO YOU DETERMINE THE LIKE FACTORS IN A POLYNOMIAL

3. WHAT IS FACTORING BY GROUP

4. WHAT ARE THE PROPER WAYS TO FACTOR POLYNOMIALS AND TO START LOOKING INTO RATIONAL EXPRESSIONS.

5. YOU ARE IN A DRIVING CONTEST AND YOU ARE EXPECTED TO MAINTAIN AN AVERAGE SPEED OF 60MPH FOR TWO MILES. UNFORTUNATELY, YOUR ENGINE DEVELOPS A MISS AND YOU CAN ONLY MAINTAIN 30MPH FOR THE FIRST MILE. HOW FAST MUST YOU DRIVE THE SECOND MILE TO MEET THE OVERALL AVERAGE SPEED REQUIREMENT.

6. WHAT ARE THE PROPER WAYS TO FACTOR POLYNOMIALS AND TO START LOOKING INTO RATIONAL EXPRESSIONS?