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Investigate the concept of a polynomial and apply the factor and remainder theorems to solve problems(VCMNA357)

[/fusion_text][fusion_text]LO: To understand the factor and remainder theorems

Know:

  • What is a factor
  • How to factorise expressions
  • Divide polynomials

Understand:

  • that the factor and remainder theorems help us to determine the factors of a polynomial,

Do:

  • I can use the factor theorem to find the factors of a polynomial.
  • I can use the remainder theorem to find the remainder of a polynomial.

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What is a Polynomial?

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A polynomial is an expression that contains only one variable. Each term contains the variable raised to a non-negative integer value (the degree always has to be positive).

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What is the Remainder Theorem?

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If a polynomial, f(x) is divided by x – k, the remainder is equal to f(k).

For example, when f(x) is divided by (x – 2), the remainder is f(2).

when f(x) is divided by (x + 3), the remainder is f(-3).

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What is the Factor Theorem?

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The polynomial, x – k is a factor of the polynomial f(x) if and only if f(k) = 0.

For example, dividing f(x) = x^3 + x^2 – 10x + 8 by (x -1) gives a quotient of x^2 + 2x – 8.

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Long Division with Polynomials Videos

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Factor Theorem and Remainder Theorem Videos

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Student Generated Videos

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Textbook Questions

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My Maths 10

Ex 6A pg. 271 Q. 1-5

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