Advanced Math practice question

Answer: C. 3

Factor completely: x³ − 4x = x(x² − 4) = x(x − 2)(x + 2), so the zeros are x = 0, x = 2, and x = −2 — three distinct real zeros. The trap is choice B, factoring only to x(x² − 4) and stopping, or forgetting that x = 0 is itself a zero.

Why the other answers are wrong

A. 1

You counted only the zero from the factor x. The remaining factor x² − 4 = (x − 2)(x + 2) contributes two more zeros, x = 2 and x = −2.

B. 2

You stopped at x(x² − 4), or counted only x = 2 and x = −2 and overlooked that the factor x itself gives the zero x = 0. That's three distinct zeros.

D. 0

Setting x³ − 4x = 0 does have solutions — factor out x to get x(x − 2)(x + 2) = 0, giving x = 0, 2, and −2.

More Advanced Math questions

• Very hard
  The function f(x) = x² + 6x + 5 is rewritten in the form f(x) = (x + a)² + b. What is the value of b?
• Very hard
  What is the solution to the equation 6/(x − 2) = 3?
• Very hard
  The polynomial p is defined by p(x) = x³ + ax² + bx − 12, where a and b are constants. If x − 2 is a factor of…
• Very hard
  The function f, defined by f(x) = 3000(1.331)^(x/12), gives the value, in dollars, of an investment x months a…
• Very hard
  In the xy-plane, the parabola y = x² − 4x + 7 and the line y = mx − 2, where m is a constant, intersect at exa…
• Very hard
  The function f is defined by f(x) = ax² + bx + c, where a, b, and c are constants. If f(2) = f(8) = 0 and the …