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 $$(x - 5)(x + 3)$$?

Accepted Answer

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 $$(-x + 11)(-5x + 8)$$?

Accepted Answer

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?

Accepted Answer

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 $$(x + 2)(x^2$ - 3x + 4)$$?

Accepted Answer

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 $$(-6x - 1)(4x - 3)$$?

Accepted Answer

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 $$(6 + 7y)(-3y + 10)$$?

Accepted Answer

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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