/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 12 Factor each trinomial, or state ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 12

Factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$y^{2}-8 y+7$$

Short Answer

Expert verified
The trinomial \( y^2 - 8y + 7 \) factors out to \( (y - 1)(y - 7) \)

Step by step solution

01

Identify a, b, and c

Firstly, identify the coefficients and the constant in the quadratic equation. The standard form of a quadratic is \( ax^2 + bx + c \) . In this case, 'a' is the coefficient of \( y^2 \), which is 1, 'b' is the coefficient of 'y', which is -8, and 'c' is the constant term, which is 7.
02

Factor

Next, find two numbers that multiply to 'a*c' (which is 7) and add up to 'b' (which is -8). Those numbers are -1 and -7. So, factor the trinomial as: \( (y - 1)(y - 7) \)
03

Checking the factorization using FOIL

Finally, verify that the factoring is correct by multiplying the factors together using the FOIL method. The FOIL method stands for First, Outer, Inner, Last. Multiplying the first terms in each binomial gives \( y^2 \). Multiplying the outer terms gives -7y. Multiplying the inner terms gives -y. Multiplying the last terms gives +7. Adding these together gives \( y^2 - 8y + 7 \), which is the original trinomial, hence confirming the factorization is correct

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Use the \([\mathrm{GRAPH}]\) or \([\mathrm { TABLE }]\) feature of a graphing utility to determine if the polynomial on the left side of each equation has been correctly factored. If not, factor the polynomial correctly and then use your graphing utility to verify the factorization. $$\begin{aligned} &-2 x^{3}+10 x^{2}-2 x-10=2(x+5)\left(x^{2}+1\right) ;[-8,4,1] \text { by }\\\ &[-100,100,10] \end{aligned}$$

Now let's move on to factorizations that may require two or more techniques. Factor completely, or state that the polynomial is prime. Check factorizations using multiplication or a graphing utility. $$-7 y^{3}+21 y^{2}-14 y$$

Factor completely. $$(y+1)^{3}+1$$

The second angle of a triangle measures three times that of the first angle's measure. The third angle measures \(80^{\circ}\) more than the first. Find the measure of each angle.

Contain polynomials in several variables. Factor each polynomial completely and check using multiplication. $$81 x^{4} y-y^{5}$$
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.