Remainder Theorem (Grade 12 NSC Matric Mathematics): Quizzes

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Remainder Theorem
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When p(x)p(x) is divided by (cx−d)(cx - d), what does the remainder equal?

p(d/c)p(d/c)

In p(x)=(cx−d)×Q(x)+Rp(x) = (cx - d) \times Q(x) + R, what does RR represent?

The remainder (a constant)

In p(x)=(cx−d)×Q(x)+Rp(x) = (cx - d) \times Q(x) + R, what is Q(x)Q(x)?

The quotient (result of division)

What is Step 1 when applying the remainder theorem?

Identify divisor in form (cx−d)(cx - d)

If dividing by 3x−23x - 2, what value should be substituted into p(x)p(x)?

x=23x = \frac{2}{3}

The remainder when dividing a polynomial is always what type of value?

A constant

What does it mean if the remainder is zero?

The divisor is a factor of p(x)p(x)

For p(x)=3x3+5x2−x+1p(x) = 3x^3 + 5x^2 - x + 1 divided by x+2x + 2, what is RR?

−1-1

For p(x)=3x3+5x2−x+1p(x) = 3x^3 + 5x^2 - x + 1 divided by 2x−12x - 1, what is RR?

178\frac{17}{8}

What is essential to be careful with when substituting values?

Negative signs

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