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Chapter 11: Q10. (page 699)

Jorge hasx2+8x+15 square yards of carpet. He wants to carpet rooms that have areas ofx2+5x+6 square yards. Write and simplify an expression to show how many rooms he can carpet,

Short Answer

Expert verified

OptionBis the correct answer.

Step by step solution

01

Step 1. Define an expression.

A mathematical expression is a combinations of numbers and variables ordered with mathematical operations.

02

Step 2. Define factorization of the expression x2+x(a+b)+ab.

x2+x(a+b)+ab=(x+a)(x+b)

03

Step 3. Determine the expression for the number of rooms that Jorge can carpet.

Area of the available carpet=(x2+8x+15)square yards

Area of the room=(x2+5x+6)square yards

To find the number of rooms divide the area of the available carpet by the area of the room.

The number of rooms that Jorge can carpet is

=x2+8x+15x2+5x+6

To simplify the expression, Factorise the numerator and the denominator.

=x2+5x+3x+15x2+3x+2x+6=x(x+5)+3(x+5)x(x+3)+2(x+3)=(x+5)(x+3)(x+3)(x+2)=x+5x+2

Hence, the number of rooms that Jorge can carpet islocalid="1648018239552" x+5x+2.

Therefore, optionlocalid="1648018248454" Bis the correct answer.

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