Quotient Dividend Remainder Divisor Long Division.

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Presentation transcript:

Quotient Dividend Remainder Divisor Long Division

Long Division - A Review Divisor Remainder Dividend Quotient

Divide: (x 2 + 7x + 2) ÷ (x + 2) 1. The polynomial must be in descending order of powers. Any missing terms are to be filled with a zero placeholder. x 2 + 7x + 2 x Only the first term is used when doing the division. Divide x 2 x x 3. Multiply your answer with the entire divisor. x(x + 2) = x 2 + 2x x 2 + 2x 4. Subtract, bring down the next term and repeat the process. 5x5x + 5 5x = x + 2 multiply Division by a Binomial -( ), x  -2

4x x 2 + 8x + 10x - 2 4x24x2 4x 3 - 8x 2 - 3x 2 - 3x - 3x 2 + 6x 2x2x + 2 2x x + 10 Division by a Binomial NPV’s

x 3 + 0x x + 8x + 4 x2x2 x 3 + 4x 2 - 4x 2 - 4x - 4x x -4x x x + 8 NPV’s

Divide x 3 - 2x x + 90 by (x - 5) using synthetic division Write only the constant term of the divisor, and the coefficients of the dividend. 2. Bring down the first term of the dividend Multiply 1 by -5, record the product and subtract. -5 Multiply 3 4. Multiply 3 by -5, record the product and subtract Multiply -18 by -5, record the product and subtract. subtract 90 0 Quotient Rem Written as x 2 + 3x - 18 Using the division statement: P(x) = (x - 5)(x 2 + 3x - 18) Synthetic Division

Divide: (x 4 - 2x 3 + x x - 6) ÷ (x - 2) (x - 2)(x 3 + x + 14)+ 22 Using Synthetic Division x 4 - 2x 3 + x x – 6 =

Given P(x) = x 3 - 4x 2 + 5x + 1, determine the remainder when P(x) is divided by x The remainder is 3. Using f(x) = x 3 - 4x 2 + 5x + 1, determine P(1): P(1) = (1) 3 - 4(1) 2 + 5(1) + 1 = = 3 NOTE: P(1) gives the same answer as the remainder using synthetic division. Therefore P(1) is equal to the remainder. In other words, when the polynomial x 3 - 4x 2 + 5x + 1 is divided by x - 1, the remainder is P (1). The Remainder Theorem

Remainder Theorem: When a polynomial P(x) is divided by x - a, the remainder is P(a). [think x - a, then x = a] Determine the remainder when x 3 - 4x 2 + 5x - 1 is divided by: a) x - 2b) x + 1 Calculate P(2) P(2) = (2) 3 - 4(2) 2 + 5(2) - 1 = = 1 The remainder is 1. Calculate P(-1) P(-1) = (-1) 3 - 4(-1) 2 + 5(-1) - 1 = = -11 The remainder is -11. Point (2, 1) is on the graph of of f(x) = x 3 - 4x 2 + 5x - 1 Point (-1, -11) is on the graph of of f(x) = x 3 - 4x 2 + 5x - 1

Determine the value of k. Whenthe remainder is 30.is divided by

When the polynomial 3x 3 + ax 2 + bx -9 is divided by x - 2, the remainder is -5. When the polynomial is divided by x + 1, the remainder is -16. What are the values of a and b?

Page 124 1, 3c,f, 4a,c, 6a,7b, 8a,c, 9, 11, 14

1. (4x x 2 + 8x + 6) ÷ (x - 2) P(x) = (x - 2)(4x 2 - 3x + 2) (2x 3 - 2x 2 + 3x + 3) ÷ (x - 1) P(x) = (x - 1)(2x 2 + 3) + 6 Using Synthetic Division