GPS- A.10E

A rectangle has an area represented by  $x^2+14x+24$   square feet. If the length is  $\left(x+12\right)$   feet, what is the width of the rectangle?

•  $\left(x+12\right)$  feet

•  $\left(x+7\right)$   feet

•  $\left(x+2\right)$   feet

•  $\left(x+6\right)$   feet

Tags

CCSS.HSA.APR.D.6

A rectangular pool has a surface area represented by  $2x^2-3x-9$  square meters. Factor the trinomial to represent the length and width of the pool as algebraic expressions.

• length =  $\left(2x+3\right)$  ; width =  $\left(x-3\right)$  

• length =  $\left(2x-3\right)$  ; width =  $\left(x+3\right)$  

• length =  $\left(2x-3\right)$  ; width =  $\left(x-3\right)$  

• length =  $\left(2x+3\right)$  ; width =  $\left(x+3\right)$  

A square photo has an area that is represented by  $n^2-12n+36$  square inches. Write a binomial that represents the area of the photo.

•  $\left(n+6\right)^2$  inches

•  $\left(n-6\right)^2$  inches

•  $\left(n+18\right)^2$  inches

•  $\left(n-4\right)\left(n-3\right)$  square inches

Tags

CCSS.HSA.APR.C.4

Edgar wants to build a rectangular tabletop with a surface area represented by  $2t^2-7t+21$  square feet. Determine the algebraic dimensions that Edgar should use for his table. 

• length =  $\left(2t-3\right)$  ; width =  $\left(t-4\right)$  

• length =  $\left(2t+7\right)$  ; width =  $\left(t+3\right)$  

• length =  $\left(t-6\right)$  ; width =  $\left(2t-7\right)$  

• Edgar cannot build a rectangular table with this algebraic surface area because it cannot be factored to find dimensions.

A garden has an area represented by  $p^2+24p+144$  square meters. Describe the dimensions of the garden.

• The garden is rectangular with dimensions of  $\left(p+72\right)$  meters and  $\left(p+2\right)$  meters.

• The garden is square with side lengths of  $\left(p+12\right)^2$  meters.

• The garden is rectangular with dimensions of  $\left(p+12\right)$  meters and  $\left(p-12\right)$  meters.

• The garden is square with side lengths of  $\left(p-12\right)^2$  meters.

Tags

CCSS.HSA.APR.C.4

A ball is dropped from the top of a building. The polynomial  $25-20t+4t^2$  represents the time, t, in seconds that it took the ball to reach the ground. Which of the following factors also represents this situation?

•  $\left(5-t\right)\left(5+4t\right)$  

•  $\left(5-2t\right)^2$  

•  $\left(5-2t\right)\left(5+2t\right)$  

• None of the above

Henry threw a discus at track practice. The path of the discus can be represented by the trinomial  $-16t^2-40t-24$ . Factor the trinomial completely.

•  $-16\left(t-6\right)\left(t+4\right)$  

•  $-8\left(2t+3\right)\left(t+1\right)$  

•  $-4\left(4t+2\right)\left(t+1\right)$  

•  $-8\left(2t+1\right)\left(t-3\right)$  

Tags

CCSS.HSA.APR.C.4

The trinomial  $h^2-15h+50$  represents the area of a puzzle. Which of the following factor pairs could represent the length and width of the puzzle?

•  $\left(h+25\right)\left(h+2\right)$  

•  $\left(h+10\right)\left(h-5\right)$  

•  $\left(h-10\right)\left(h-5\right)$  

•  $\left(h-10\right)\left(h+10\right)$  

Allen's computer screen has an area that can be represented as  $k^2+k-12$  square inches. Write the length and width of the computer screen as factors of the trinomial. 

•  $\left(k+4\right)\left(k-3\right)$  

•  $\left(k+6\right)\left(k-2\right)$  

•  $\left(k-4\right)\left(k+3\right)$  

• The trinomial cannot be factored.

Mikaela used the algebra tiles to create a polygon with an area of  $3x^2-25x+28$ . Determine which factors she used to create the polygon, and name the polygon. 

•  $\left(3x-7\right)\left(x-4\right)$ ; rectangle

•  $\left(3x+4\right)\left(x+7\right)$ ; square

•  $\left(3x-5\right)^2$ ; square

•  $\left(3x-4\right)\left(x-7\right)$ ; rectangle

Tags

CCSS.HSA.APR.C.4