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Chapter 6

Chapter 6. Section 3 Dividing Polynomials. Long Division Vocabulary Reminders. Remember Long Division. Does 8 go into 6? No Does 8 go into 64? Yes, write the integer on top. Multiply 8 ∙ 8 Write under the dividend Subtract and Carry Down How many times does 8 go into 7 evenly?

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Chapter 6

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  1. Chapter 6 Section 3 Dividing Polynomials

  2. Long Division Vocabulary Reminders

  3. Remember Long Division • Does 8 go into 6? • No • Does 8 go into 64? • Yes, write the integer on top. • Multiply 8∙8 • Write under the dividend • Subtract and Carry Down • How many times does 8 go into 7 evenly? • 0 write over the 7 • Multiply 0∙8 • Subtract and write remainder as a fraction.

  4. The divisor and quotient are only FACTORS if the remainder is Zero.

  5. Examples with variables

  6. Examples • If the divisor has more than one term, always use the term with the highest degree. • A remainder occurs when the degree of the dividend is less than the degree of the divisor

  7. Example:

  8. Try These ExamplesDivide using long division.

  9. Long division of polynomials is tedious! • Lets learn a simplified process!This process is called Synthetic Division • p. 316It may look complicated, but watch a few examples and you will get the hang of it.

  10. Use synthetic division to divide 3x3-4x2+2x-1 by x+1 • Reverse the sign of the constant term in the divisor.Write the coefficients of the polynomial in standard form (Remember to include zeros) • Translation: Instead of write • Bring down the first coefficient • Multiply the first coefficient by the new divisor. Add. • Repeat step 3 until the end. The last number is the remainder. • NOW write the polynomial. • To write the answer use one less degree than the original polynomial. -1 3 -4 2 -1

  11. Example: Use synthetic division to divide • x3+4x2+x-6 by x+1 • x3-2x2-5x+6 by x+2

  12. Remainder Theorem • If a polynomial is being divided by (x-a) then the remainder is P(a). • Example: Use the remainder theorem to find P(-4) for P(x)=x3-5x2+4x+12 • DO NOT change the number P(a) to -a

  13. Try This Problem • Use synthetic division to find P(-1) for P(x)=4x4+6x3-5x2-60

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