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Common Core Standard HSA-APR.B.2 Questions

Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).

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Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.B.2
Given that [math]x+3[/math] is factor of polynomial [math]p(x) = ax^3+53x^2+46x-15[/math], what is the value of [math]a ?[/math]
  1. [math]200/9[/math]
  2. [math]-3[/math]
  3. [math]"Not enough information"[/math]
  4. [math]12[/math]
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.B.2
Given a polynomial p(x) such that p(−1) = 5, what is a possible result when p(x) is divided by x + 1?
  1. [math]2x^2 − x + 3 + 5/(x + 1)[/math]
  2. x + 5
  3. [math]5x^2 + 2x + 1[/math]
  4. [math]x^2 + 1 + 5/(x + 1)[/math]
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.B.2
Given a polynomial p(x) such that p(−2) = 0, what is a possible result when p(x) is divided by x + 2?
  1. [math]x^3 + 8[/math]
  2. [math]2x^2 + 3x − 5 + 2/(x + 2)[/math]
  3. [math]x^2 + 4[/math]
  4. x - 2
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.B.2
For polynomial f(x), if f(−4) = 0, which of the following MUST be a factor of f(x)?
  1. x − 4
  2. x + 4
  3. x − 2
  4. x + 2
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.B.2
Given polynomial p(x) such that p(5) = 0, what is a possible result when p(x) is divided by x − 5?
  1. [math]5x^3 + 10[/math]
  2. [math]x^2 − 5x + 2 + 3/(x − 5)[/math]
  3. x − 5
  4. [math]x^2 + 25[/math]
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.B.2
For polynomial r(x), if r(−8) = 0, which of the following MUST be a factor of r(x)?
  1. x + 8
  2. x - 8
  3. x + 4
  4. x
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.B.2
For polynomial [math]f(x)[/math], if [math]f(0)=0[/math], which of the following MUST be a factor of [math]f(x) ?[/math]
  1. [math]x[/math]
  2. [math]x-4[/math]
  3. [math]x-1[/math]
  4. [math]x+1[/math]
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.B.2
For polynomial f(x), if f(2) = 0, which of the following MUST be a factor of f(x)?
  1. x + 2
  2. x - 2
  3. x - 1
  4. x
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.B.2
For polynomial q(x), if q([math]−1/2[/math]) = 0, which of the following MUST be a factor of q(x)?
  1. 2x − 1
  2. 2x + 1
  3. x − 2
  4. x + 2
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.B.2
For polynomial f(x), if f(−3) = 0, which of the following MUST be a factor of f(x)?
  1. x − 3
  2. x + 3
  3. x − 1
  4. x + 1
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.B.2
What is the remainder of [math]2x^4 − 3x^2 + x − 1[/math] divided by x + 1?
  1. -1
  2. -3
  3. -5
  4. -7
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.B.2
For polynomial f(x), if f(1/2) = 0, which of the following MUST be a factor of f(x)?
  1. 2x + 1
  2. x − 2
  3. 2x − 1
  4. x + 2
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.B.2
Given a polynomial p(x) such that p(1) = −4, what is a possible result when p(x) is divided by x − 1?
  1. [math] x^3 + x + 2[/math]
  2. [math]−4x^2 + 3x − 1[/math]
  3. [math]x^2 + 2x − 7 − 4/(x − 1)[/math]
  4. x − 4
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