Question

Using remainder theorem, factorize the polynomial x – 5x? – 177+21 completely.​

Answer 1

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Reserved powers, residual powers, or residuary powers are the powers that are neither prohibited nor explicitly given by law to any organ of government.

Answer 2

Answer:

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.