Refer a friend and earn $50 when they subscribe to an annual planRefer Now

Get the answer to your homework problem.

Try Numerade Free for 30 Days

Like

Report

In $42-45,$ each polynomial represents the area of a rectangle. Write two binomials that could represent the length and width of the rectangle.$$16 x^{2}-25$$

Length $=4 x+5$Width $=4 x-5$

Algebra

Chapter 1

THE INTEGERS

Section 6

Factoring Polynomials

The Integers

Equations and Inequalities

Polynomials

Campbell University

Baylor University

Idaho State University

Lectures

01:32

In mathematics, the absolu…

01:11

02:24

In $42-45,$ each polynomia…

02:12

01:48

01:01

Algebra A rectangle has a …

01:16

The length of a rectangle …

Write an equation and solv…

01:15

Find the polynomial that r…

02:33

In Exercises $39-40,$ writ…

01:51

For each rectangle, find a…

01:53

So in this question, looking at initially a little confusing to me. But it represents the area of a rectangle this 16 x squared minus 25. And what it wants us to do is to write to binomial that could represent the length and the width, so kind of just looking at its surface level, it suppose that mean? But if we just break it down, let's say we have some sort of rectangle right here. Doesn't matter to find the area of wrecking what, you're going to have a length and you're going to have a with And to find that area, I'm just gonna move in together. So basically this question is asking you to do the bare bones of what we've been doing so far is just to factor this because the fact of this will get a product of two by normals. And of course, we can kind of just say, then one of those terms, in the process, going to be the length the other term is going to be the with. So we can say that 60 next week, minus 25 equals that length times with and we're just factor it so 60 Next. Three minutes 25. Um, this is another question where we can use that, Uh, not even a trick. But we know that we have some, like, extra nice nine. I don't keep using the example. We could write as X minus three times X plus three because it's the term squared minus another term squared or they're just squares off. Something like nine is the square of three. So what we can do is we have a term that, um we could take this word of your mother term with jinx word up. So let's use that. So for the first term would take the squared off, um, the phrase that differently. So for the first term of our product, let's take the squared of the first term Interpol. No meal so scared of 16 X ray is just going to give us four X because of school. Six teams for a sort of experts X, of course, Then we have minus the square of our second term was just sort of 25 is five. Then we have again taking that four x and plus, So now we're gonna set up equals our length times with and, of course, could have written it as it products by no meals. And we're looking for another product. We could just kind of a sign either one, so we could just say this. The lengths of the wit so we're insured will be that the length equals four X minus five. Or you could say, for every side does make a difference and the with equals for X. That's life and that's your answer.

View More Answers From This Book

Find Another Textbook

Numerade Educator

In mathematics, the absolute value or modulus |x| of a real number x is its …

In $42-45,$ each polynomial represents the area of a rectangle. Write two bi…

Algebra A rectangle has a perimeter of $(26 x+16) \mathrm{cm}$ and an area o…

The length of a rectangle is 4 more than twice the width, $x .$ Express the …

Write an equation and solve.The length of a rectangle is 5 in. more than…

Find the polynomial that represents the perimeter of each rectangle.3 w^…

In Exercises $39-40,$ write a polynomial that represents the length of each …

For each rectangle, find a polynomial that represents the missing side. (rec…

03:59

Simplify each expression. In each case, list any values of the variables for…

02:13

In $3-38$ write each expression in simplest form. Variables in the radicand …

01:17

02:05

In $9-26,$ write each expression as the product of two binomials.$$x…

01:08

In $3-38$ , write each radical in simplest radical form. Variables in the ra…

03:42

In $3-14,$ solve and check each inequality.$$3-\frac{2}{a+1}<5

02:11

The area of a rectangle is 25$\sqrt{35}$ square feet and the width is 10$\sq…

02:15

The lengths of the legs of a right triangle are 8 centimeters and 12 centime…

01:31

01:20

92% of Numerade students report better grades.

Try Numerade Free for 30 Days. You can cancel at any time.

Annual

0.00/mo 0.00/mo

Billed annually at 0.00/yr after free trial

Monthly

0.00/mo

Billed monthly at 0.00/mo after free trial

Earn better grades with our study tools:

Textbooks

Video lessons matched directly to the problems in your textbooks.

Ask a Question

Can't find a question? Ask our 30,000+ educators for help.

Courses

Watch full-length courses, covering key principles and concepts.

AI Tutor

Receive weekly guidance from the world’s first A.I. Tutor, Ace.

30 day free trial, then pay 0.00/month

30 day free trial, then pay 0.00/year

You can cancel anytime

OR PAY WITH

Your subscription has started!

The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

Receive weekly guidance from the world's first A.I. Tutor, Ace.

Mount Everest weighs an estimated 357 trillion pounds

Snapshot a problem with the Numerade app, and we'll give you the video solution.

A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.

Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.