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# Show that (X − 2), (X + 3) and (X − 4) Are Factors of X3 − 3x2 − 10x + 24. - Mathematics

Answer in Brief

Show that (x − 2), (x + 3) and (x − 4) are factors of x3 − 3x2 − 10x + 24.

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#### Solution

Let  f(x) = 2^3 - 3x^2 - 10x + 24 be the given polynomial.

By factor theorem,

(x-2) , (x+3)and  (x-4) are the factor of f(x).

If   f(2) , f(-3)and f(4) are all equal to zero.

Now,

f(2) = (2)^3 - 3(2)^2 - 10(2) + 24

= 8 -12 - 20 +24

= 32 -32

 = 0

also

f(-3) = (-3)^3 -3(-3)^2 - 10(-3) + 24

 = -27 -27 + 30 + 24

 = -54 + 54

 = 0

And

f(4)= (4)^3 - 3(4)^2 - 10(4) + 24

 = 64 - 48 - 40 + 24

= 88 - 88

= 0

Hence, (x − 2), (x + 3) and (x-4) are the factor of polynomial f(x).

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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 6 Factorisation of Polynomials
Exercise 6.4 | Q 8 | Page 24
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