Application of Factoring

Application of Factoring

Test of Prior Knowledge

Multiple Choice

What is the first step when factoring polynomials?

• Find the GCF

• List all the terms

• Make the X and fill in the top and bottom

• Multiply a and c

Multiple Choice

Factor
x² + 9x - 36

• (x + 12)(x - 3)
• (x + 9)(x - 4)
• (x - 12)(x + 3)
• (x - 9)(x - 4)

Multiple Choice

If a closet has length of
(x + 2) ft and width of
(3x - 7) ft, what is the area of the closet?

• 3x² + x - 14
• 3x² - 13x - 14
• 3x² - x - 14
• 3x² +13x - 14

Multiple Choice

Find the area of the rectangle.

• 9x² - 2x
• 9x² - 2
• 10x - 2
• 20x - 4 

Multiple Choice

The function f(t) = -5t²+20t + 60 models the approximate height of an object t seconds after it is launched. How many seconds does it take the object to hit the ground?

• 4 seconds

• -2 seconds

• 6 seconds

• -3 seconds

Multiple Choice

What is the smallest of 3 consecutive positive integers if the product of the smaller two integers is 5 less than 5 times the largest integer? 

• 10
• -5
• 5
• -10

Multiple Choice

If you square 5 more than a positive number, the result is 88 more than 12 times the number.  Find the numbers.

• -9, 7
• √75
• 9, -7
• 15, -5

Multiple Choice

Find two consecutive odd integers whose product is 35.

• -5,7 and -7,5

• -7,-5 and 5,7

• -7,-5

• 5,7

Multiple Choice

Eight more than the square of a number is the same as six times the number. Find all possible solutions.

• 2,4

• -2,-4

• 2,-4

• -2,4

Multiple Choice

A rectangle has an area of k² -2k - 24, what is the length & width of the rectangle?

• (k+4) & (k-6)

• (k+4) & (k+6)

• (k+6) & (k-1)

• (k-4) & (k+6)

Multiple Choice

The product of two consecutive negative even integers is 24. Find the integers.

• -3, -8

• -24, -1

• -2, -12

• -6, -4

Multiple Choice

If a number is added to twice its square, the result is 6. Find all possible solutions.

• 3,-2

• $-\frac{3}{2}$ ,2

• $\frac{3}{2}$ , -2

• $-\frac{3}{2}$ ,-2

Multiple Choice

The area of a rectangle is (6x²+7x+2) square inches and the length is (3x+2) inches. Which expression represents the rectangle's width?

• (2x+2) inches

• (2x-2) inches

• (2x+1) inches

• (2x-1) inches

Multiple Choice

Factor completely:
 $2p^2-9p-18$  

•  $\left(7p+4\right)\left(p+10\right)$  

•  $\left(2p+3\right)\left(p+6\right)$  

•  $\left(2p+3\right)\left(p-6\right)$  

•  $\left(7p+8\right)\left(p+6\right)$  

Multiple Choice

A rectangle has an area of 24 square units. The width is 5 units less than the length. What is the length, in units, of the rectangle? 

• 6
• 8
• 3
• 19

Multiple Choice

#4) A movie screen has an area of 143 square feet.  The length of the screen is 2 feet more than the width.  What is the length of the screen?

• 10
• 11
• 12
• 13

Multiple Choice

One leg of a right triangle is seven more than the other leg. The hypotenuse is eight more than the shorter leg. Find the lengths of the longest side.

• 5 ft
• 3 ft
• 12 ft
• 13 ft

Multiple Choice

Factor:
2x² + 13x + 15

• (2x + 1)(x + 15)
• (x + 3)(x + 5)
• (2x - 3)(x - 5)
• (2x + 3)(x + 5)

Multiple Choice

A rectangle has an area of 2x² – 19x +45 ft². What are the dimensions of the rectangle?  

• (2x - 9)(x - 5)
• (2x + 9)(x + 5)
• (2x - 5)(x - 9)
• (2x - 5)(x + 9)

Multiple Choice

Solve for the values of x:
(2x - 1)(x + 4) = 0

• { 1/2, -4 }
•  { 1/2, 4 }
• { 2, -4 }
• { -2, 4 }

Multiple Choice

Which of the following is a difference of perfect squares?

• x² - 18
• 4x² + 36 
• 9x² - 100
• x² + 4

Multiple Choice

What are the factors of

25x² - 81?

• (5x - 9)(5x + 9)

• (5x - 9)(5x - 9)

• (5x + 9)(5x + 9)

• Cannot be factored

Multiple Choice

Fully Factor the Following
4x²-16

• (2x-4)(2x+4)
• (4x-4)(4x+4)
• 4(x-2)²
• 4(x-2)(x+2)

Multiple Choice

3x² - 75

• 3( x + 5 ) ( x - 5 ) 
• Prime
• ( x + 5 ) ( x - 5 ) 
• 3( x - 5 ) ( x - 5 )