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Interactive practice · 24 questions on terms, evaluating single- and multi-variable expressions and formulas, and finding the zeros / undefined values of polynomial and rational expressions, with step-by-step solutions.
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Easy How many terms does \(5x^2-2x+10\) contain?
terms
Answer: \(3\)
Medium Evaluate \(5x^2-2x+10\) when \(x=-2\) (no calculator).
\(=\)
Answer: \(34\)
Easy How many terms does \(x^2-64\) contain?
terms
Answer: \(2\)
Medium Evaluate \(x^2-2x-8\) when \(x=4\).
\(=\)
Answer: \(0\)
Easy In Exercise 2, \(x=4\) makes \(x^2-2x-8\) equal \(0\). What is \(x=4\) called?
Answer: A zero of the expression
Medium Evaluate \(x^2-2x-8\) when \(x=-2\) (this shows \(-2\) is its other zero).
\(=\)
Answer: \(0\)
Medium What are the two zeros of \(x^2-64\)? Select all that apply.
Answer: A, C
Easy Which is the correct factored form of \(x^2-64\)?
Answer: \((x-8)(x+8)\)
Medium What are the two zeros of \(x^2-49\)? Select all that apply.
Answer: B, C
Medium What is the value of \(\dfrac{x-10}{x+2}\) when \(x=0\)? (No calculator.)
\(=\)
Answer: \(-5\)
Medium What is the value of \(\dfrac{x-10}{x+2}\) when \(x=10\)?
\(=\)
Answer: \(0\)
Hard Why is \(x=10\) the only zero of \(\dfrac{x-10}{x+2}\)?
Answer: D fraction is \(0\) only when its numerator is \(0\), and \(x-10=0\) only at \(x=10\)
Medium For \(\dfrac{x-10}{x+2}\), which value of \(x\) makes the expression undefined?
\(x=\)
Answer: \(-2\)
Easy A rational expression (fraction) equals \(0\) exactly when its ______ equals \(0\).
Answer: numerator (top)
Easy A rational expression is undefined when its ______ equals \(0\).
Answer: denominator (bottom)
Medium State the zero of \(\dfrac{x+6}{x-4}\).
\(x=\)
Answer: \(-6\)
Medium State the value where \(\dfrac{x+6}{x-4}\) is undefined.
\(x=\)
Answer: \(4\)
Medium State the zero of \(\dfrac{2y-1}{y}\).
\(y=\)
Answer: \(1/2\)
Easy State the value where \(\dfrac{2y-1}{y}\) is undefined.
\(y=\)
Answer: \(0\)
Hard State the zeros of \(\dfrac{x^2-25}{x^2-81}\). Select all that apply.
Answer: A, C
Hard State the values where \(\dfrac{x^2-25}{x^2-81}\) is undefined. Select all that apply.
Answer: B, D
Hard Evaluate \(5x^2-\tfrac{1}{2}y^3\) for \(x=3\) and \(y=-2\).
\(=\)
Answer: \(49\)
Hard Evaluate \(\dfrac{(a+3b)^2}{a-b}\) for \(a=8\) and \(b=-2\).
\(=\)
Answer: \(2/5\)
Medium The volume of a cylinder is \(\pi r^2 h\). Find the volume when \(r=4\) cm and \(h=10\) cm. Round to the nearest cubic centimeter.
cm³
Answer: \(503\)