18
Warm-Up: January 5, 2012 Use long division (no calculators) to divide 7425 9

Warm-Up: January 5, 2012 Use long division (no calculators) to divide

Embed Size (px)

Citation preview

Page 1: Warm-Up: January 5, 2012  Use long division (no calculators) to divide

Warm-Up: January 5, 2012 Use long division (no calculators) to divide

74259

Page 2: Warm-Up: January 5, 2012  Use long division (no calculators) to divide

Homework Questions?

Page 3: Warm-Up: January 5, 2012  Use long division (no calculators) to divide

Dividing Polynomials;Remainder and Factor Theorems

Section 2.4

Page 4: Warm-Up: January 5, 2012  Use long division (no calculators) to divide

Long Division of Polynomials Very similar to numerical division

quotientdividenddivisor

divisor

dividend

Page 5: Warm-Up: January 5, 2012  Use long division (no calculators) to divide

Long Division Steps(on page 283 and handout)1. Arrange the terms of both the dividend and the divisor

in descending power. Include zeros for missing terms.2. Divide the first term of the dividend by the first term

of the divisor. The result is the first term of the quotient.

3. Multiply every term in the divisor by the first term in the quotient. Write the resulting product beneath the dividend with like terms lined up.

4. Subtract the product from the dividend.5. Bring down the next term in the original dividend.6. Repeat steps 2-5 until the remaining dividend

(remainder) can no longer be divided by the divisor.7. Write the remainder over the divisor as the last part of

the quotient.

Page 6: Warm-Up: January 5, 2012  Use long division (no calculators) to divide

Example 1

1673 xxx

Page 7: Warm-Up: January 5, 2012  Use long division (no calculators) to divide

x3+3x2-4x-12 divided by x-2

You-Try #1

124322

1243 2323

xxxx

x

xxx

Page 8: Warm-Up: January 5, 2012  Use long division (no calculators) to divide

You-Try #2

12684 2 xxx

Page 9: Warm-Up: January 5, 2012  Use long division (no calculators) to divide

x3+3x2-4x-12 divided by x-2

Example 4 – Long and Synthetic Division

Page 10: Warm-Up: January 5, 2012  Use long division (no calculators) to divide

Can only be used to divide a polynomial by a linear binomial of the form x-r.

Do not write the x’s, only the coefficients. Write r in the upper left, and the coefficients

of the polynomial on the top. r has the opposite sign of the number next to x Polynomial must be in standard form. Write a zero for any missing term.

Synthetic Division

Page 11: Warm-Up: January 5, 2012  Use long division (no calculators) to divide

Synthetic Division Steps (page 286)1. Arrange the terms of the dividend in

descending power, with a zero for any missing terms.

2. Write “r” (switch the sign) of the divisor, x-r. Put “r” in a half box. Write the coefficients of the divisor to the right (don’t forget the zeros).

3. Skip a space, draw a horizontal line, and write the leading coefficient of the dividend below the line, below where it is above.

4. Multiply “r” by the number you just wrote below the line. Write the product above the line in the next column.

Page 12: Warm-Up: January 5, 2012  Use long division (no calculators) to divide

Synthetic Division Steps, cont. (page 286)5. Add the values in this new column, and write

the sum below the line.6. Repeat steps 4 and 5 until all columns are

filled in.7. The numbers below the line are the

coefficients of the quotient, plus the remainder. The degree of the first term of the quotients is always one less than the degree of the first term of the dividend.

8. Write the quotient with the variable. The degree of the quotient is always one less than the degree of the dividend.

Page 13: Warm-Up: January 5, 2012  Use long division (no calculators) to divide

Example 5

133 xx

Page 14: Warm-Up: January 5, 2012  Use long division (no calculators) to divide

You-Try #5

2623 34 xxxx

Page 15: Warm-Up: January 5, 2012  Use long division (no calculators) to divide

Solving Polynomials If you divide f(x) by (x-r) and receive a

remainder of zero, then r is a zero of f(x), and a solution of f(x)=0.

If you know one zero of f(x), you can use synthetic division to divide by (x-r) and get a lower degree polynomial.

Solve this new polynomial. Any roots of this polynomial are also roots of f(x).

Remember: root, zero, solution, and x-intercept all mean approximately the same thing.

Page 16: Warm-Up: January 5, 2012  Use long division (no calculators) to divide

Example 6 Solve the equation 3x3+7x2-22x-8=0 given

that -1/3 is a root.

Page 17: Warm-Up: January 5, 2012  Use long division (no calculators) to divide

You-Try #6 Solve the equation 2x3-3x2-11x+6=0 given

that -2 is a root.

Page 18: Warm-Up: January 5, 2012  Use long division (no calculators) to divide

Assignment Page 290 #1-31 every other odd, 37-41 odd