Algebra Questions

A student was asked to sketch the graph below Using the graph determine whether each statement is true or false 0 1 Statement 1 is a zero of the function 0 is a zero of the function 1 is a zero of the function 2 is a zero of the function True False

Which of the following is the factored form of the simplest function with real and rational coefficients of the given zeros 8 8 and 13 A x 8 13 x 8 13 B x 8 x 8 x 13 x 13 C x 8 x 13 x 13

3 2 and 1 i

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

7i and 2

Subtract 9a 6a 5 from 10a 3a 25 Your answer should be a polynomial in standard form

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

8x 27 0 3

A 8 D E 9 10 B 3 C 5 If m 5 51 then m ABC 6 If m2 58 then m 3 and m BCD 7 If m26 60 and ED 10 then the perimeter of ABCD

Write the ploynomial function in factored form with real and rational coefficients with given zeros 3 2 and 1 i

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 en zeros

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

olve the ploynomial equation by finding all roots x 2x x 2 0

Which of the following is the factored form of the simplest function with real and rational coefficients of the given zeros 5 11 and 6i A x 5 x 11 x 11 x 6i x 6i B x 5 x 5 x 11 x 11 x 6i x 6i C x 5 x 11 x 6i

Solve the polynomial equation by finding all roots 8x 27 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

Which of the following is the factored form of the simplest function with real and rational coefficients o the given zeros 0 and 5 A x 5 B x 5 x 5 C x x 5 x 5

Write the row operations you would need in order to finish row reducing this matrix and perform the operations 1 0 4 0 1 0 00 3 7 3 15

etermine which is a factor of the following polynomial h x 6x 7x 9x 2 A x 3 B x 2 C x 6 D x 2

Given p x find p 3 by using synthetic substitution p x x 6x 7x 25

Perform the indicated operation 1 2 5 3 4 8 X 0 10 14 6

Find 2A if A 2 7 3 1 5

4 The graph shows a linear relationship between and y Suppose a represents the number of months Jada plans to make equal payments to her mother for the money she borrowed for a new laptop and y represents the amount of money in dollars she still owes her mother a b C Find and interpret the and y intercept of this line Write an equation of this line Amount owed 30 600 700 600 Kiran s work 3x y 5 3 1 2 5 3 2 5 500 100 Xntercer 6000 15 The point 2 1 is not a solution to the equation 400 Find and interpret the slope of this line 1 intercent 30 300 200 2 20 18 16 Number of month d If Jada has made 12 months of equal payments how much money does she still owe her mother Explain your thinking 250 Since the ordered Peir is 12 250 4 6 8 10 12 14 5 Kiran is determining if the ordered pair 2 1 is a solution to the equation 3x y 5 His work is shown Is he correct Explain your thinking No 6 The ordered pairs 0 5 1 7 5 and 2 10 are solutions to a linear equation What is the linear equation Express your answer in the form Ax By C Show your thinking 21 1

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

Use row reduction to solve the linear system X1 2x2 3x3 6 2x1 3x2 2x3 14 6x1 2x22x3 2

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

Factor each polynomial or identify it as irreducible 2x4 7x 5

And 6x 6x 6 7x 6x 5

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