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Back to Exercise: Apply the Remainder Theorem

Exercises: Apply the Remainder Theorem

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Grade 9·22 problems·~35 min·Common Core Math - HS Algebra·standard·hsa-apr-b-2
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A

Recall / Warm-Up

1

The polynomial division algorithm states that for polynomials p(x)p(x) and d(x)d(x), there exist unique polynomials q(x)q(x) and r(x)r(x) such that which equation holds?

2

According to the Factor Theorem, which statement is true about a polynomial p(x)p(x) and a number aa?

3

When p(x)p(x) is divided by (x−a)(x - a), the Remainder Theorem says the remainder equals which of the following?

B

Fluency Practice

1

Use the Remainder Theorem to find the remainder when p(x)=x3−2x+4p(x) = x^3 - 2x + 4 is divided by (x−3)(x - 3).

2

Use the Remainder Theorem to find the remainder when p(x)=x4+x2−10p(x) = x^4 + x^2 - 10 is divided by (x+2)(x + 2).

Note: (x+2)=(x−(−2))(x + 2) = (x - (-2)), so a=−2a = -2.

Synthetic division setup table for 2x³ − 3x² + x − 5 divided by (x − 2), showing the coefficients and divisor with the working rows left blank for the student to complete.
3

Use synthetic division to divide p(x)=2x3−3x2+x−5p(x) = 2x^3 - 3x^2 + x - 5 by (x−2)(x - 2).

What is the remainder?

4

After performing synthetic division of p(x)p(x) by (x−a)(x - a), which number in the bottom row of the synthetic division table is the remainder?

5

p(x)=x3+2x2−5x−6p(x) = x^3 + 2x^2 - 5x - 6. Is (x−2)(x - 2) a factor of p(x)p(x)?

6

p(x)=x3−2x2−5x+6p(x) = x^3 - 2x^2 - 5x + 6. Test whether (x−1)(x - 1) is a factor by computing p(1)p(1).

Enter the value of p(1)p(1).

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