For example, we may solve for x in the following equation as follows: Hence, x = ?3 or ?2 are solutions or roots of the quadratic equation A more general
AMSG.11.Remainder%20and%20Factor%20Theorem.pdf
Example 3 2 2 Let p(x)=2x3 - 5x + 3 1 Find p(-2) using The Remainder Theorem Check your answer by substitution 2 Use the fact that x = 1 is a zero of
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linear factors corresponding to the zeros x=1,2 and 4 That is, Is this the answer? [This is the polynomial of Example 1 with last term 18 instead
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Example 3: Check your answer for the division problems in Example 2 The Division Algorithm: If f(x) and d(x) are polynomials where d(x)? 0 and degree d
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and factor theorems to find factors of polynomials Examples 1 Using previous example (Answers: yes, yes, no, yes, no) Example Factorise
A26remainder.pdf
Exercises: 1 Use the remainder theorem to find the remainder of the following divisions and then check your answers by long division
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writing the answer in ascending powers of x 2 3 5 1 x x x + + + Question 8 (**+) a) Use the factor theorem to show that ( )5 x ? is a factor of
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(x - a) is a factor of the polynomial f (x) if and only if f (a) = 0 Answer: 4 2 - Algebra - Solving Equations 4 2 8 - The Factor Theorem
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polynomial division Example 1 Divide 14 5 4 2 3
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Example 1 Determining Factors by Division Divide to determine whether x ? 1 is a factor of x 2 ? 3x + 2 Solution Here x
synthetic_division.pdf