Practice Remainder Theorem (2.3.2) - Algebra

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6 sample questions

Question 1.
What is the remainder when $P(x) = x^2 + x - 6$ is divided by $x - 3$ ?
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Use the Remainder Theorem and substitute \$x = 3\$.
Question 2.
Calculate the remainder when $P(x) = x^3 + 2x + 1$ is divided by $x + 1$ .
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Evaluate at \$x = -1\$.
3Question 3.
What does the Remainder Theorem help to calculate?
- Remainder of polynomial division
- Sum of polynomial terms
- Degree of a polynomial
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Think about what the theorem states regarding division.
4Question 4.
T/F: The remainder can be found by substituting the linear divisor's root into the polynomial.
- True
- False
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Recall the theorem's statement about division.
Question 5.
Prove that if $P(x) = x^4 - 5x^3 + 6x^2$ has a remainder of $0$ when divided by $x - 3$ , that $x - 3$ is a factor.
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Don't forget to substitute \$3\$ into \$P(x)\$.
Question 6.
Given $P(x)$ is divided by $x - 1$ , find $P(x)$ for it to yield a remainder of $4$ . Write a polynomial.
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Incorporate any polynomial as \$Q(x)\$ such that this holds true.

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