Polynomial Division and the Remainder Theorem: Algebra 2 Math Test – PDF Download

Algebra 2 Polynomial Division Test: questions 1–5

Question 1: Long division (2 points)

Divide \(x^{3}+2x^{2}-6x+5\) by \(x-1\). Write the quotient and the remainder.

Question 2: Division with a missing term (2 points)

Divide \(x^{4}-5x^{2}+3x-2\) by \(x+2\). Write the quotient and the remainder.

Question 3: Remainder Theorem (2 points)

Let \(p(x)=2x^{3}-x^{2}-7x+6\).

1. Find the remainder when \(p(x)\) is divided by \(x-3\). (1 point)
2. The remainder when \(p(x)\) is divided by \(x+2\) is \(0\). What does this tell you about \(x+2\)? (1 point)

Question 4: Factor Theorem and zeros (3 points)

The graph of \(f(x)=x^{3}-x^{2}-14x+24\) is shown.

1. Show that \(x-2\) is a factor of \(f(x)\). (1 point)
2. Write \(f(x)\) as a product of three linear factors. (1 point)
3. State the x-intercepts of the graph. (1 point)

Question 5: Find k and factor (2 points)

The binomial \(x+3\) is a factor of \(p(x)=x^{3}+kx^{2}-5x+3\).

1. Find \(k\). (1 point)
2. Factor \(p(x)\) completely. (1 point)

Algebra 2 Polynomial Division Test: questions 6–9

Question 6: Function from a graph (2 points)

The graph of a cubic function \(f\) with leading coefficient \(1\) is shown.

1. Write \(f(x)\) in factored form. (1 point)
2. Find the remainder when \(f(x)\) is divided by \(x-5\). (1 point)

Question 7: Polynomial identity (2 points)

1. Show that \((x^{2}+y^{2})^{2}=(x^{2}-y^{2})^{2}+(2xy)^{2}\) by expanding. (1 point)
2. Use the identity with \(x=4\) and \(y=1\) to find the sides of a right triangle with legs \(x^{2}-y^{2}\) and \(2xy\). (1 point)

Question 8: Dimensions of a box (3 points)

The volume of a gift box is \(V(x)=x^{3}+10x^{2}+31x+30\) cubic inches. The length is \(x+5\) inches and the width is \(x+2\) inches.

1. Find an expression for the height \(h\). (2 points)
2. Find the volume when \(x=4\) from the dimensions. (1 point)

Question 9: Divide by 2x plus 1 (2 points)

Divide \(6x^{3}-x^{2}+6x+7\) by \(2x+1\). Write the quotient and the remainder.

How to use this algebra 2 polynomial division test

Take this algebra 2 polynomial division test without notes, then grade it with the test answer key out of 20 points.

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