Back to Tutor Intake Assessment: Apply the Remainder Theorem

HSA.APR.B.2 Tutor Intake — Remainder Theorem and Factor Theorem

This short check helps your tutor understand where to start with the Remainder
and Factor Theorems. Answer each question on your own without help. If you are
unsure, give your best try.

Grade 9·6 problems·~10 min·Common Core Math - HS Algebra·standard·hsa-apr-b-2

Work through problems with immediate feedback

Concepts

Which statement correctly describes the Remainder Theorem?

When $p(x)$ is divided by $(x - a)$ , the remainder equals $p(a)$ .

When $p(x)$ is divided by $(x - a)$ , the remainder equals $p(0)$ .

When $p(x)$ is divided by $(x - a)$ , the remainder is the
quotient polynomial evaluated at $x = a$ .

When $p(x)$ is divided by $(x - a)$ , the remainder equals $a$ .

Which statement about the Factor Theorem is correct?

$(x - a)$ is a factor of $p(x)$ if $p(a) = 0$ .

$(x - a)$ is a factor of $p(x)$ only if $p(0) = a$ .

$(x - a)$ is a factor of $p(x)$ if and only if $p(a) = 0$ .

$(x - a)$ is a factor of $p(x)$ if and only if $p(x) = 0$ .

Procedures

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

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

Enter the remainder.

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