Question 1

Aunt Barbara is sewing a rectangular blanket with dimensions $(x + 4)$ and $(x + 2)$. What is the correct expression for the area of the blanket?

Accepted Answer

$x^2 + 6x + 8$

Question 2

Barb incorrectly finds the area of the blanket as $x^2 + 8$. Which mistake did she most likely make?

Accepted Answer

She multiplied $x$ by $x$ and $4$ by $2$, but forgot the cross terms.

Question 3

Which of the following is the product of $(x - 5)(x + 3)$?

Question 4

Find the product of $(2x + 7)(3x - 1)$.

Accepted Answer

$6x^2 + 19x - 7$

Question 5

What is the result of multiplying $(3r^2 - 2)(r - 9)$?

Accepted Answer

$3r^3 - 27r^2 - 2r + 18$

Question 6

Which of the following represents the product $(-x + 11)(-5x + 8)$?

Question 7

Carla is painting two rectangular skyscraper backdrops. The larger has dimensions $(2x + 5)$ and $(x - 7)$. What is the area of the larger skyscraper?

Question 8

Which method can be used to multiply polynomials such as $(x + 6)(-4x - 5)$?

Accepted Answer

Distributive property (FOIL method)

Question 9

Mark is designing a robot with a head that is a square of side $(x - 5)$ and a body that is a rectangle with dimensions $(4x + 5)$ and $(x + 2)$. What is the total area of cardboard Mark will use?

Accepted Answer

$(x - 5)^2 + (4x + 5)(x + 2)$

Question 10

Which of the following is the simplified product of $(x + 2)(x^2 - 3x + 4)$?

Question 11

A student multiplies $(x^2 - 3)(x + 2)$ and gets $x^3 - 6$. What mistake did the student make?

Accepted Answer

They only multiplied the first terms and constants.

Question 12

Which of the following is the correct product of $(-6x - 1)(4x - 3)$?

Question 13

Which expression represents the area of a triangle with base $(x + 3)$ and height $(2x - 4)$?

Accepted Answer

$2x^2 + 2x - 12$

Question 14

Which of the following is the product of $(h + 9)(5h - 4h^2 - 10)$?

Accepted Answer

$-4h^3 + 5h^2 - 10h - 36h^2 + 45h - 90$

Question 15

Which of the following is the product of $(x + 7)(x - 3)$?

Accepted Answer

$x^2 + 4x - 21$

Question 16

Which of the following is the product of $(x^2 + 8)(-3x + 5)$?

Accepted Answer

$-3x^3 + 5x^2 - 24x + 40$

Question 17

Which of the following is the product of $(6 + 7y)(-3y + 10)$?

Question 18

Which of the following is the product of $(-6h + 5h^2 + 4)(-3h + 2)$?

Accepted Answer

$-15h^3 + 28h^2 - 26h + 8$

Step-by-Step Guidance for Multiplying Polynomials (College Algebra)

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