# Polynomials and Rational Expressions Practice

## CCSS High School Algebra Practice

This quiz illustrates the range of difficulty expected by the following Common Core State (CCS) standards:

 Question Common Core Standard # 1 A.APR.1 2 A.APR.1 3 A.APR.1 4 A.APR.2 5 A.APR.3 6 A.APR.4 7 A.APR.5 + 8 A.APR.2 9 A.APR.2 10 A.APR.6
indicates a modeling standard.
+ indicates a college and career ready standard.

All questions of this quiz illustrate the difficulty of the high school A.APR standards required for all students, including the college and career ready students.

Question 1: Given the polynomials P(x) and Q(x) below, calculate R(x) = P(x) + Q(x).

P(x) = x3 + 3x2 - 1
Q(x) = -2x2 - x + 4

Question 2: Given the polynomials P(x,y) and Q(x,y) below, calculate R(x,y) = P(x,y) - Q(x,y).

P(x,y) = 3x3 + xy2 - xy + 4
Q(x,y) = -2x3 + xy2 - y2 - 5

Question 3: Given the polynomials P(x) and Q(x) below, calculate R(x) = P(x) · Q(x).

P(x) = x2 - x
Q(x) = x - 3

Question 4: Consider the polynomial function:

P(x) = 4x3 - 10x2 - ax + 6,

where a is an unknown real number. If (x-3) is a factor of this polynomial, the value of a is

Question 5: Identify the zeros of the following polynomial:

P(x) = x3 + 8x2 - 9x .

Question 6: Given the polynomials P(x,y,z) and Q(x,y,z) and R(x,y,z) below,

P(x,y,z) = (x + y + z)2
Q(x,y,z) = x2 + y2 + z2
R(x,y,z) = xy + yz + zx

which of the following identities is true?

Question 7: What is the third term in the expansion of (x - 2)10

Questions 8 and 9: Consider the polynomial function:

P(x) = x4 + ax3 - bx2 - 4x + 21,

where a and b are unknown real numbers. If (x-1) and (x+1) are factors of this polynomial, the value of a is and the value of b is .

Question 10: Given the equation:

P(x) = .

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