Quadratic equations Questions and Answers

Factor each polynomial or identify it as irreducible 3n6 12n4

Simplify the polynomial given the operation Write your answer in standard form 5x4 x 7 9x 2 2x x

Which graph is sketched to the right A g x x x 2 x 1 B g x x x 2 x 1 C g x x x 2 x 1 3 0 2

Which of the following is the factored form of the simplest function with real and rational coefficients of the given zeros 4 2 and 2 A x 4 x 4 x 2 x 2 B x 4 x 2 x 2 C x 4 x 2 x 2

How is the graph of g x x 1 related to the graph of f x x A The graph of g x is a translation of the graph of f x down 1 unit B The graph of g x is a translation of the graph of f x down 1 unit and a reflection across the x axis C The graph of g x is a translation of the graph of f x left 1 unit and a reflection across the y axis

3 2 and 1 i

Solve the polynomial equations by finding all ro x 4x 5x 2 0

7i and 2

1 3 y x 1 5 y 3x 3 Ay 2 y x 2 4 y x 4 15 45 6 y 4 241 fy Ay HE Y

Divide the polynomials The form of your answer should either be p x or p x is a polynomial and k is an integer x 4x 15 3 H I k X 3 where p x

Write the polynomial function in factored form with real and rational coefficients with the given zeros Hint Polynomials with irrational or complex roots MUST come in pairs 0 4 and 3

State which are roots for the following polynomial f x x x 8x 12 12 2 0 Yes 000 C No 000

Solve the polynomial equations by finding all roots x3 4x 5x 2 0

Write the polynomial function in factored form with real and rational coefficients with the given zeros Hint Polynomials with irrational or complex roots MUST come in pairs 2 1 and 3i

Write the polynomial function in factored form with real and rational coefficients with the given zerc 2 3i 4 and 1

Solve the polynomial equations by finding all roots 2x 6x x 3 0

Find the rational zeros of the polynomial function then write the function as a product of factors Make sure to test the possible zeros to find the actual zeros of the function

1 Select all of the ordered pairs x y that are solutions to the soul linear equation 6x 3y 6 A 1 4 B 1 0 C 3 4 A 16 0 B 0 16 C 8 3 2 Select all of the following ordered pairs that make the equation x 8y 16 true 3 The graph shows a linear relationship between z and y Suppose represents the number of paperback books Noah buys at the book fair all at the same price and y represents the amount of money in dollars he has after buying the books a b C Find and interpret the x and y intercepts of this line interpret 30 D 2 2 E 2 2 F 0 2 Find and interpret the slope of this line Xinterpret S Write an equation of this line t sx t30 D 1 3 0 2 F 2 0 Amount of money 35 30 25 20 15 10 5 bal y nogle Tone 0 1 2 3 4 567 Number of paperback boo d If Noah buys 4 paperback books how much money will he have left Explain your thinking Nook hi beyo 18 left

Determine whether the given binomial is a factor of the polynomial p x If it is find the remaining factors of p x x4 4x3 6x 4x 5 x 1 Hint There are four factors 1 1 4 6 45

Use long division to find the quotient and remainder Write the result in the form quotient 4 3 2 9x x 11x 4 x 4 remainder divisor

Given a polynomial p x use synthetic division to divide by x a and obtain the quotient and the nonzero remainder Write the result in the form quotient remainder divisor 4x43x 7x 2 x 1 Find a 4 0 3 7 2 4

Given a polynomial p x use synthetic division to divide by x a and obtain the quotient and t nonzero remainder Write the result in the form quotient remainder divisor 6x 25x 3x 5 x 1

Given a polynomial p x use synthetic division to divide by x nonzero remainder Write the results in the form quotient 2x 6x 5x 7 x 3 a and obtain the quotient and the remainder divisor

Determine whether the given binomial is a factor of the polynomial p x If it is find the remaining factors of p x

Use long division to find the quotient and remainder remainder Write the result in the form quotient divisor 6x4 5x 2x 8 x 2x 5 6x x 2x 5 6x 5x 0x 2x 8 6x 12x 30x 7x 30x 2x 7x 8

9x 25

4x4 4x x 1 3

Factor each 8x 64 polynomial or identify it as irreducible

6x 2x 9x 3

x 12x 32x 3

15x 2

Simplify by performing the following polynomial multiplications 3x 2 2x 3x 1

Factor the polynomial or identify it as irreducible 4x 2x 8x

x3 12x 32x

6x 6x 6 7x 6x 5

Simplify by performing the following polynomial multiplications 2 2x 5x x 4x 2

Factor the polynomial or identify it as irreducible x 27

125x 64

Factor the polynomial or identify it as irreducible x x 20x

The number of items in millions that a company sold from 1998 through 2004 is modeled as N x 0 1x x 3x 4 and the average price per item in dollars as P x 0 2x 5 where x represents the number of years since 1998 Write a polynomial R x that can be used to model the total revenue for 81 this company Hint R x N x P x

actoring the polynomial by group x 3x 3x 9

4x316x 20x

10x 490x

30x6 72x4

Factor the polynomial 3x3 7x 4x or identify it as irreducible

2 12x 21X 8X 14 72x 56x 36x 28

Simplify by performing the following polynomial multiplications 4x 2 6x x 2

A biologist has found that the number of branches on a certain rare tree can be modeled by the polynomial b y 4y y where y is the number of years after the tree reaches a height of 6 feet The number of leaves on each branch can be modeled by the polynomial y 2y 3y y Write a polynomial describing the total number of leaves on the tree

A rectangle has a length of x and a width of 5x 4x What is the polynomial that models the perimeter of the rectangle A 10x 2x 2x 8 B 10x3 8 C 5x4x 4x

Perform the following polynomial multiplications 3 2x 4 7x 5x