Warm-Up Use long division to divide 5 into 3462. 692 5 3462-30 46-45 12-10 2
Warm-Up Use long division to divide 5 into 3462. Divisor 692 5 3462-30 46-45 12-10 2 Quotient Dividend Remainder
Warm-Up Use long division to divide 5 into 3462. Dividend Divisor 3462 2 692 5 5 Quotient Remainder Divisor
Remainders This means that the divisor is a factor of the dividend If you are lucky enough to get a remainder of zero when dividing, then the divisor divides evenly into the dividend For example, when dividing 3 into 192, the remainder is 0. Therefore, 3 is a factor of 192.
Objective 1a You will be able to divide polynomials using long division
Dividing Polynomials Dividing polynomials works just like long division. In fact, it is called long division! Before you start dividing: Make sure the divisor and dividend are in standard form If your polynomial is missing a term, add it in with a coefficient of 0 as a place holder
Dividing Polynomials Dividing polynomials works just like long division. In fact, it is called long division! Before you start dividing: 2x 3 + x + 3 2x 3 + 0x 2 + x + 3 If your polynomial is missing a term, add it in with a coefficient of 0 as a place holder
Exercise 1 Divide x + 1 into x 2 + 3x + 5 x 2 2 x 1 x 3x 5 2 - x - x 2x 5-2 x - 2 3 How many times does x go into x 2? Multiply x by x + 1 Multiply 2 by x + 1 Line up the first term of the quotient with the term of the dividend with the same degree.
Exercise 1 Divide x + 1 into x 2 + 3x + 5 x 2 2 x 1 x 3x 5 2 - x - x 2x 5-2 x - 2 Divisor 3 Quotient Dividend Remainder
Exercise 1 Divide x + 1 into x 2 + 3x + 5 Dividend x 2 3x 5 3 x 2 x 1 x 1 Remainder Divisor Divisor Quotient
Exercise 2 Divide 3x 4 5x 3 + 4x 6 by x 2 3x + 5
Exercise 3 In a polynomial division problem, if the degree of the dividend is m and the degree of the divisor is n, what is the degree of the quotient?
Exercise 4 Divide using long division. 1. x 3 x 2 +4x 10 x+2 2. 2x 4 +x 3 +x 1 x 2 +2x 1
Exercise 4 Divide using long division. 1. x 3 x 2 +4x 10 x+2
Exercise 4 Divide using long division. 2. 2x 4 +x 3 +x 1 x 2 +2x 1
Objective 1b You will be able to divide polynomials using synthetic division
Exercise 5 Use long division to divide x 4 10x 2 + 2x + 3 by x 3
Synthetic Division When you divisor is of the form x k, where k is a constant, then you can perform the division quicker and easier using just the coefficients of the dividend. This is called fake division. I mean, synthetic division.
Synthetic Division Synthetic Division (of a Cubic Polynomial) To divide ax 3 + bx 2 + cx + d by x k, use the following pattern. k a b c d = Add terms a ka Coefficients of Quotient (in decreasing order) = Multiply by k Remainder
Synthetic Division Synthetic Division (of a Cubic Polynomial) To divide ax 3 + bx 2 + cx + d by x k, use the following pattern. k a b c d = Add terms a ka = Multiply by k You are always adding columns using synthetic division, whereas you subtracted columns in long division.
Synthetic Division Synthetic Division (of a Cubic Polynomial) To divide ax 3 + bx 2 + cx + d by x k, use the following pattern. Add a coefficient of zero for any missing terms! k can be positive or negative. If you divide by x + 2, then k = -2 because x + 2 = x (-2). You are always adding columns using synthetic division, whereas you subtracted columns in long division.
Exercise 6 Use synthetic division to divide x 4 10x 2 + 2x + 3 by x 3
Exercise 7 Divide 2x 3 + 9x 2 + 4x + 5 by x + 3 using synthetic division
Exercise 8 Divide using long division. 1. x 3 +4x 2 x 1 x+3 2. 4x 3 +x 2 3x+7 x 1
Exercise 9 Given that x 4 is a factor of x 3 6x 2 + 5x + 12, rewrite x 3 6x 2 + 5x + 12 as a product of two polynomials.
Exercise 10 The volume of the solid is 3x 3 + 8x 2 45x 50. Find an expression for the missing dimension. x + 5?
Exercise 10 The volume of the solid is 3x 3 + 8x 2 45x 50. x + 5?
Exercise 11 Use long division to divide 6x 4 11x 3 + 14x 2 3x 1 by 2x 1. Then figure out a way to perform the division synthetically.
Exercise 11 Use long division to divide 6x 4 11x 3 + 14x 2 3x 1 by 2x 1. Then figure out a way to perform the division synthetically.
5.5ish: Divide Polynomials Objectives: 1. To divide polynomials using long division and synthetic division