Section 3.3 Homework

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Section 3.3 Homework

1. If we divide the polynomial P by the factor x − c and we obtain the equation P(x) = (x − c)Q(x) + R(x), then we say that x − c is the divisor, Q(x) is the _________, and R(x) is the ___________.

2. (a) If we divide the polynomial P(x) by the factor x − c and we obtain a remainder of 0, then we know that c is a ______ of P.

(b) If we divide the polynomial P(x) by the factor x − c and we obtain a remainder of k, then we know that P(c) = _____ .

3. Two polynomials P and D are given. Use either synthetic or long division to divide P(x) by D(x), and express the quotient P(x)/D(x) in the form

\frac{P (x)}{D (x)} = Q (x) + \frac{R (x)}{D (x)}

P (x) = 2 x^{2} - 5 x - 6, D (x) = x - 2

\frac{P (x)}{D (x)} =

4. Two polynomials P and D are given. Use either synthetic or long division to divide P(x) by D(x), and express the quotient P(x)/D(x) in the form

\frac{P (x)}{D (x)} = Q (x) + \frac{R (x)}{D (x)}

P(x) =

x^{4} + 2 x^{3} - 14 x, D (x) x - 4

\frac{P (x)}{D (x)} =

\frac{x^{3} + 2 x^{2} - x + 1}{x + 3}

5. Two polynomials P and D are given. Use either synthetic or long division to divide P(x) by D(x), and express the quotient P(x)/D(x) in the form

\frac{P (x)}{D (x)} = Q (x) + \frac{R (x)}{D (x)}

P (x) = 14 x^{3} + x^{2} - 30 x + 13, D (x) = 7 x - 10

\frac{P (x)}{D (x)} =

6. Two polynomials P and D are given. Use either synthetic or long division to divide P(x) by D(x), and express P in the form P(x) = D(x) · Q(x) + R(x).

P (x) = 4 x^{3} + 5 x + 8, D (x) = 2 x + 1

7. Find the quotient and remainder using long division.

\frac{x^{2} - 5 x + 10}{x - 3}

Quotient

Remainder

8. Find the quotient and remainder using long division.

\frac{x^{3} + 2 x^{2} - x + 1}{x + 3}

Quotient

Remainder

9. Find the quotient and remainder using long division.

\frac{8 x^{3} + 4 x^{2} - 4 x - 6}{4 x + 2}

Quotient

Remainder

10. Find the quotient and remainder using synthetic division.

\frac{2 x^{2} - 7 x + 2}{x - 4}

Quotient

Remainder

11. Find the quotient and remainder using synthetic division.

\frac{- x^{2} + x - 2}{x + 1}

Quotient

Remainder

12. Find the quotient and remainder using synthetic division.

\frac{8 x^{2} - 6}{x - 3}

Quotient

Remainder

13. Find the quotient and remainder using synthetic division.

\frac{x^{3} + 4 x^{2} + 6 x + 5}{x + 4}

Quotient

Remainder

14. Find the quotient and remainder using synthetic division.

\frac{3 x^{3} - 12 x^{2} - 9 x + 3}{x - 5}

Quotient

Remainder

15. Find the quotient and remainder using synthetic division.

\frac{x^{3} - 2 x + 1}{x + 2}

Quotient

Remainder

16. Find the quotient and remainder using synthetic division.

\frac{x^{3} - 9 x^{2} + 27 x - 27}{x - 3}

Quotient

Remainder

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