Question 1

Which of the following is the correct factorization of the polynomial

9a^2 - 25

?

Accepted Answer

(3a - 5)(3a + 5)

Answer

(3a - 5)(3a + 5)

Answer

(3a - 5)(3a + 5)

Answer

(3a - 5)(3a + 5)

Question 2

When factoring the trinomial

9a^2 - 25

, what two numbers must you find that multiply to

12

and add to

-7

?

Accepted Answer

(3a - 5)(3a + 5)

and

-4

Answer

(3a - 5)(3a + 5)

and

-4

Answer

(3a - 5)(3a + 5)

and

-4

Answer

(3a - 5)(3a + 5)

and

-4

Question 3

Which of the following polynomials cannot be factored using the Difference of Squares method?

Accepted Answer

(3a - 5)(3a + 5)

Answer

(3a - 5)(3a + 5)

Answer

(3a - 5)(3a + 5)

Answer

(3a - 5)(3a + 5)

Question 4

What is the result when you multiply the binomials

9a^2 - 25

using the FOIL method?

Accepted Answer

(3a - 5)(3a + 5)

Answer

(3a - 5)(3a + 5)

Answer

(3a - 5)(3a + 5)

Answer

(3a - 5)(3a + 5)

Question 5

What is the result of factoring out the Greatest Common Factor (GCF) from the expression

9a^2 - 25

?

Accepted Answer

(3a - 5)(3a + 5)

Answer

(3a - 5)(3a + 5)

Answer

(3a - 5)(3a + 5)

Answer

(3a - 5)(3a + 5)

Question 6

What is the correct factorization of the polynomial

9a^2 - 25

using the grouping method?

Accepted Answer

(3a - 5)(3a + 5)

Answer

(3a - 5)(3a + 5)

Answer

(3a - 5)(3a + 5)

Answer

(3a - 5)(3a + 5)

Question 7

Which of the following describes the difference between the FOIL method and the Vertical Method of polynomial multiplication?

Accepted Answer

FOIL is restricted to two binomials, while the Vertical Method can multiply any polynomial regardless of its number of terms.

Answer

FOIL requires aligning like terms in columns, while the Vertical Method does not.

Answer

The Vertical Method is always faster than the FOIL method for simple binomial multiplication.

Answer

FOIL is used for polynomials with three or more terms, while the Vertical Method is only for binomials.

Question 8

Which of the following is the first step when using the grouping method to factor the trinomial

9a^2 - 25

?

Accepted Answer

Multiply

9a^2 - 25

and

12

(

-7

)

Answer

Find the square root of

9a^2 - 25

Answer

Square the middle term (

9a^2 - 25

)

Answer

Divide the entire polynomial by

9a^2 - 25

Question 9

Which of the following is the final result of multiplying

9a^2 - 25

using either the FOIL or Vertical Method?

Accepted Answer

(3a - 5)(3a + 5)

Answer

(3a - 5)(3a + 5)

Answer

(3a - 5)(3a + 5)

Answer

(3a - 5)(3a + 5)

Question 10

Which of the following is the most important reminder to check before applying any other factoring method to a polynomial?

Accepted Answer

Check for a Greatest Common Factor (GCF)

Answer

Check if the leading coefficient is equal to 1

Answer

Check if the polynomial is a difference of squares

Answer

Check if the constant term is a perfect square

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