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# Using the Factor Theorem, Show That: (X – 2) is a Factor of X3 – 2x2 – 9x + 18. Hence, Factorise the Expression X3 – 2x2 – 9x + 18 Completely. - Mathematics

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#### Question

Using the Factor Theorem, show that:

(x – 2) is a factor of x3 – 2x2 – 9x + 18. Hence, factorise the expression x3 – 2x2 – 9x + 18 completely.

#### Solution

Let f(x)=x^3-2x^2-9x+18

x-2=0 ⇒ x=2

∴ Remainder =f(2)

= (2)^3-2(2)^2-9(2)+18

=8-8-18+18

=0

Hence, (x-2) is a factor of f (x)

Now, we have:

∴ x^3-2x^2-9x+18=(x-2)(x^2-9)=(x-2)(x+3)(x-3)

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#### APPEARS IN

Selina Solution for Concise Mathematics for Class 10 ICSE (2020 (Latest))
Chapter 8: Remainder and Factor Theorems
Exercise 8(B) | Q: 1.1 | Page no. 111
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Using the Factor Theorem, Show That: (X – 2) is a Factor of X3 – 2x2 – 9x + 18. Hence, Factorise the Expression X3 – 2x2 – 9x + 18 Completely. Concept: Factor Theorem.
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