ALGEBRA II HONORSGIFTED SECTION 5 4 DIVIDING POLYNOMIALS

ALGEBRA II HONORS/GIFTED @ SECTION 5 -4 : DIVIDING POLYNOMIALS

1) Divide.

dividend divisor 2) Divide. 236 31 7345 - 62 114 - 93 quotient vinculum 31 x 2 = 62, subtract remainder, bring 4 down Start over 215 - 186 29 THE remainder

3) Divide. b 3 2 b+3 - 3 b 2 Put each polynomial in descending order and divide lead term by lead term. + 13 b - 18 2 b 4 - 3 b 3 + 17 b 2 + 3 b - 15 -(2 b -2 b 44+3 b - 3 b 33) -6 b 3 + 17 b 2 - (-6 b 6 b 3 –+ 9 b 22) 26 b 2 + 3 b - -26 b (26 b 22 -+39 b 39 b) -36 b - 15 - (-36 b -+54) 54 39

4) Divide. ANSWER : x 2 – x - 1

5) Divide. ANSWER : …let’s try the same problem a slightly different way. 2 ANSWER : 1 -3 2 4 -2 -12 4 1 -1 2 -8

SYNTHETIC DIVISION : A shorthand method for polynomial division in the special case of dividing by a linear factor (x + k or x – k). Divide using synthetic division. ANSWER :

ANSWER : x 2 + 9 x + 4 a) Divide synthetically by x - 9. Note the remainder. b) Find P(9). Note the remainder and P(9) both equal 0. Therefore, 9 is a root of x 2 – 5 x – 36 and x – 9 is a factor of x 2 – 5 x – 36.

REMAINDER THEOREM : If a polynomial, f(x), is divided by (x – k), then the remainder is the value of f(k). FACTOR THEOREM : A polynomial, f(x), has a factor (x – k) if and only if f(k) = 0. Additionally, k is a root of f(k).

10) Determine whether each binomial is a factor of 2 x 3 + 5 x 2 + x – 2. a) 2 x - 1 Answer : yes b) x + 3 Answer : no

For more information, see http: //www. purplemath. com/modules/synthdiv. htm http: //www. wtamu. edu/academic/anns/mps/math/ mathlab/col_algebra/col_alg_tut 37_syndiv. htm A Truism : Mathematics is made of 40 percent formulas, 40 percent proofs and 40 percent imagination.