Question

9. The factors of x ^ 4 - 81 are: 1)(x^ 2 -9)(x+9)^ 2 (3) (x + 3) * (x ^ 2 - 9) ^ 2 (2)(x - 3) * (x + 3) * (x ^ 2 + 9) (4 )(x-3)^ 4​

Answer 1

Answer:

(2) . (x-3)(x+3)(x²+9)

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Answer 2

Answer:

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Step-by-step explanation:

Solution

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Given

f(x)=x

3

+2x

2

−5x−6

To find a factor of f(x) we assume different values of x and substitute it in f(x)

First we consider the factors of the constant term −6 i.e., ±1,±2,±3,±6

Now we substitute the values of x in f(x)

If f(x)=0 for some value a

Then (x−a) is a factor of f(x)

[Note : This is a hit and trial method, So you have to iterate the process until you get the required x]

Substituting x=−1 in f(x) , We get,

f(−1)=(−1)

3

+2(−1)

2

−5(−1)−6

=−1+2(1)+5−6

=−1+2+5−6

=−7+7

=0

∴ By factor theorem,

(x+1) is a factor of f(x)

Now dividing f(x) by (x+1) as shown in the above figure, we get;

x

3

+2x

2

−5x−6

=(x+1)(x

2

+3x−2x−6)

=(x+1){x(x+3)−2(x+3)}

=(x+1)(x−2)(x+3)

∴(x−2),(x+1),(x+3) are the factors of the given cubic equation.