1.3 Division of Polynomials; Remainder and Factor …
remainder is 0, then the divisor is a factor of the dividend. Example 1 Determining Factors by Division Divide to determine whether x−1 is a factor of x2 −3x+2. Solution Here x2 −3x+2is the dividend and x−1 is the divisor. Step 1 Set up the division as follows: divisor → …
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Factor Theorem: c is a zero of P if and only if x – c is a factor of P(x). Example 6: Use the Factor Theorem to show that . 1 2 x + is a factor of . P (x) = 2. x. 3 + 5. x. 2 + 4. x + 1. Solution: In order to show that . 1 2 x + is a factor of P(x) = 2x3 + 5x2 + 4x + 1, we must show that 1 2 −. is a zero of P, or that . 1 2 P ⎛⎞ ⎜− ...
remainder and factor theorems to factorise and to solve polynomials that are of degree higher than 2. Before doing so, let us review the meaning of basic terms in division. Terms in division We are familiar with division in arithmetic. The number that is to be divided is called the dividend ...
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