Chapter 11: Q15. (page 667)

AREA The area of a rectangle is $x^{2} + 5 x + 6$ . What binomial expressions represent the side lengths of the rectangle?

Short Answer

Expert verified

The length and width of the rectangle are $(x + 3)$ and $(x + 2)$ .

Step by step solution

Step 1. Write the formula for area of rectangle.

Area of rectangle is given by $A = l \times w$ .

Step 2. Find the GCF.

Find the GCF of $x^{2}, 5 x$ and 6.

role="math" localid="1648027471940" $x^{2} = 1 \cdot x \cdot x 5 x = 1 \cdot 5 \cdot x 6 = 1 \cdot 2 \cdot 3$

Therefore, GCF is 1.

Step 3. Apply factoring pattern of ax2+bx+c.

There are two numbers having product of 6 and sum of $5$ . The numbers are $2$ and $3$ .

$x^{2} + m x + n x + 6 = x^{2} + 2 x + 3 x + 6$

Step 4. Group terms with common factors and factor out GCF.

Group terms with common factors and factor out GCF from each grouping.

$(x^{2} + 2 x) + (3 x + 6) = x (x + 2) + 3 (x + 2) = (x + 3) (x + 2)$

The factors of $x^{2} + 5 x + 6$ are $(x + 3) (x + 2)$ . Therefore, length and width of the rectangle are $(x + 3)$ and $(x + 2)$ .

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AREA The area of a rectangle is $x^{2} + 5 x + 6$ . What binomial expressions represent the side lengths of the rectangle?

Short Answer

Step by step solution

Step 1. Write the formula for area of rectangle.

Step 2. Find the GCF.

Step 3. Apply factoring pattern of ax2+bx+c.

Step 4. Group terms with common factors and factor out GCF.

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AREA The area of a rectangle is x2+5x+6. What binomial expressions represent the side lengths of the rectangle?

Short Answer

Step by step solution

Step 1. Write the formula for area of rectangle.

Step 2. Find the GCF.

Step 3. Apply factoring pattern of ax2+bx+c.

Step 4. Group terms with common factors and factor out GCF.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Theoretical and Mathematical Physics

Mechanics Maths

Logic and Functions

Statistics

Calculus

Study anywhere. Anytime. Across all devices.

AREA The area of a rectangle is $x^{2} + 5 x + 6$ . What binomial expressions represent the side lengths of the rectangle?