Applications of Polynomials

Find the area of a rectangle with length (x-5) and width (3x+1).

• 3x²+16x-5
• 3x²-14x+5
• 3x²-14x-5

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.A.1

CCSS.HSA.SSE.B.3

Find the perimeter of a rectangle with length (x-5) and width (3x+1).

• 8x-8
• 4x-4
• 8x+8
• 4x+12

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.A.1

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

You are drawing a rectangle with side lengths of (3 – x) inches and (x – 7) inches.

What is the value of x that will maximize this drawing?

What is the maximum area that can be obtained from this drawing?

• x = 3

  max area = 7 in²

• x = 5

  max area = 4 in²

• x = 7

  max area = 3 in²

• x = 4

  max area = 5 in²

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

CCSS.HSA.SSE.A.1

An open box is to be made from a 2-foot by 3-foot rectangular piece of material by cutting equal squares from the corners and turning up the sides. Find the volume of the largest box that can be made in this manner.

• 0.392 ft³

• 2.683 ft³

• 1.056 ft³

• 0.4140 ft³

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.2

CCSS.HSA.REI.B.4

CCSS.HSA.SSE.A.1

CCSS.HSG.GMD.A.3

Find the area of the triangle with height (x+8) and base (2x+4). ( $A=\frac{1}{2}bh$ ) 

• 2x²+20x+32

• x²+10x+16

• 4x²+40x+64

• x²+32x+16

Tags

CCSS.HSA.SSE.A.1

CCSS.HSA.SSE.B.3

CCSS.HSG.GPE.B.7

Find the volume of a rectangular prism with length (x+2), width (x-4), and height (2x+1). 

• $2x^3-3x^2-18x-8$

• $x^2-2x-8$

• $2x^3+5x^2+18x-8y$

• $2x^2+4x+6$

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.A.1

CCSS.HSG.GMD.A.3

Find the width for a rectangle that has an area of 2x² + 6x – 8 and length of 2x – 2

• x + 4
• 2x² + 4x – 6
• x - 4
• x + 4 - 16/(2x-2)

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.4

CCSS.HSA.REI.B.4

CCSS.HSA.SSE.A.1

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

A rectangular sheet of cardboard measures 16cm by 6cm. Equal squares are cut out of each corner and the sides are turned up to form an open rectangular box. What is the maximum volume of the box?

• 59.259 cm³

• 23.361 cm³

• 37.483 cm³

• 43.961 cm³

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

CCSS.HSA.SSE.A.1

CCSS.HSG.GMD.A.3

You want to create a garden in your backyard. Given are the dimensions of the garden and a border. Determine the area of the gray border surrounding the garden bed.

• 8x + 24

• 6x + 32

• 2x² - 8x + 4

• x² + 16x + 16

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.2

CCSS.HSA.SSE.A.1

CCSS.HSA.SSE.B.3

CCSS.HSG.MG.A.1

BONUS QUESTION: The length of your storage crate is 2 meters greater than its width, and its height is 1 meter greater than its width. If the volume if 24 cubic meters, find the width, length, and height.

• width = 2m

  length = 4m

  height = 3m

• width = 1m

  length = 6m

  height = 4m

• width = 2m

  length = 6m

  height = 2m

• width = 3m

  length = 4m

  height = 2m

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.C.6

CCSS.HSA.SSE.A.1

CCSS.HSG.GMD.A.3