### Polynomial Factorization and Finding Zeros#### 3. Factor the Polynomial CompletelyA polynomial and one of its factors is given. Factor the polynomial **completely** given that one of its factors is \(x + 4\).**Given Polynomial:**\[ f(x) = x^7 + 4x^6 + 7x^4 + 28x^3 - 8x - 32 \]**Instructions:**- Factor the polynomial completely.- Your final answer should be in factored form.Your answer: ______________________**Note:** This is a required question.---#### 4. Find All Additional Real ZerosGiven that \( x = 6 \) is a zero of the polynomial, find all additional real zeros of the given polynomial.**Given Polynomial:**\[ f(x) = 4x^7 - 24x^6 - 25x^5 + 150x^4 - 4x^3 + 24x^2 + 25x - 150 \]**Instructions:**- Your final answer should be values of \( x \) that will make the equation true.Your answer: ______________________**Note:** This is a required question.---These exercises require in-depth understanding of polynomial factorization and finding zeros of polynomial equations. Make sure to apply the given factors and zeros accurately to achieve the correct solutions.

We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Answered: A polynomial and one of its factors is…

A polynomial and one of its factors is given. Factor the polynomial OMPLETELY given that one of its factors is x + 4. YOUR FINAL ANSWER SHOULD E IN FACTORED FORM! *

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter8: Polynomials

Section8.2: Multiplying A Polynomial By A Monomial

Problem 44PPS

See similar textbooks

Similar questions

What does it mean to say a polynomial is in factored form?
Building Envelope The building code in a certain town requires that a house be at least 10 ft from the boundaries of the lot. The buildable area or building envelope for the rectangular lot shown in the following figure is given by A=(x20)(y20) a Explain how the expression for A is obtained. b Expand to express A as a polynomial in x and y. c A contractor has a choice of purchasing one of two rectangular lots, each having the same area. One lot measures 100 ft by 400 ft; the other measures 200 ft by 200 ft. Which lot has the larger building envelope?
Too Many Corn Plants per Acre? The more corn a farmer plants per acre, the greater is the yield the farmer can expect. But only up to a point, many plants acre can cause Overcrowding and decrease yields, data give yields per acre for various densities of corn plantings, as found by researchers at a university test farm. (a) Find the quadratic polynormal that best fits the data. (b) Draw a graph of the polynomial from part (a) together with a scatter plot of the data. (c) use your result (b) to estimate the yield for 37000 plants per acre.
Write a fourth degree polynomial function with real coefficients and the given zeros. i,2i
Gift boxes The corners of a 12 in.-by-12 in. piece of cardboard are folded inward and glued to make a box. Write a polynomial that represents the volume of the resulting box.
(a) Give the general form of polynomial function P of degree n. (b) What does it mean to say that c is a zero of P? Give two equivalent conditions that tell us that c is a zero of P.
Explain what it mean to factor a polynomial completely.
DISCOVER: Nested Form of a Polynomial Expand Q to prove that the polynomials P and Q are the same. P(x)=3x45x3+x23x+5 Q(x)=(((3x5)x+1)x3)x+5 Try to evaluate P(2) and Q(2) in your head, using the forms given. Which is easier? Now write the polynomial R(x)=x52x4+3x32x2+3x+4 in nested form, like the polynomial Q. Use the nested form to find R(3) in your head. Do you see how calculating with the nested form follows the same arithmetic steps as calculating the value of a polynomial using synthetic division?
Population The table shows the U.S. populations for the years 1970,1980,1990 and 2000. Source: U.S. Census Bureau Year Population in millions 1970 1980 1990 2000 205 227 249 282 a Find a cubic polynomial that fits the data and use it to estimate the population in 2010. b The actual population in 2010 was 309 million. How does your estimate compare?
Use synthetic division to show that x=3 is a zero of the function f(x)=2x35x26x+15. Use the result to factor the polynomial function completely and list all the zeros of the function.
The polynomial P(x)=5x2(x4)3(x+7) has degree ___________. It has zeros 0, 4, and ______________. The zero has multiplicity _________
Number of Intercepts and Local Extrema How many x-intercepts and how many local extrema does the polynomial P(x)=x34x have? How many x-intercepts and how many local extremadoes the polynomial Q(x)=x3+4x have? If a > 0. bow many x-intercepts and how many local extrema does each Of the polynomials P(x)=x3ax and Q(x)=x3+ax have? Explain your answer.