SAT Math: Practice Questions-Passport to advanced mathematics-Operations with polynomials

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Question

\(x\)(\(x\)+2)2=\(x\)3+b\(x\)2+c\(x\)

In the equation above, b and c are constants. If the equation is true for all values of \(x\), what is the value of b+c ?

  1. 4
  2. 6
  3. 8
  4. 16
Answer/Explanation

Ans: C

Question

Which of the following is equivalent to the expression \(x\)4-8\(x\)2+16 ?

I. (\(x\)+2)2 (\(x\)-2)2

II. (\(x\)2-4)2

  1. I only
  2. II only
  3. I and II
  4. Neither I nor II
Answer/Explanation

Ans: C

Question

Which expression is equivalent to 12\(x\)3/8\(x\)2 where \(x\) is not equal to 0?

  1. 4/\(x\)
  2. 3\(x\)/2
  3. 4\(x\)
  4. 20\(x\)5
Answer/Explanation

Ans: B

Question

Which expression is equivalent to \(x\)4-18\(x\)2+81? 

  1. (\(x\)-3)4
  2. (\(x\)-3)(\(x\)+3)3
  3. (\(x\)-3)3(\(x\)+3)
  4. (\(x\)-3)2(\(x\)+3)2
Answer/Explanation

Ans: D

Question

(\(x\)-8)3=0

What is the solution to the given equation? 

  1. -8
  2. -2
  3. 2
  4. 8
Answer/Explanation

Ans: D

Question

\(f(x) = x^2+ bx\)

 \(g(x) = 3x^2 – 9x\)
The functions \(f\) and \(g\) are defined above, where \(b\) is a constant. If \(f (x) · g(x) = 3x^4 – 8x^3 – 3x^2\) , what is the value of \(b\) ? 

Answer/Explanation

Ans: 1/3, .333

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