Question

4x³ +7x² (7x³+ 15x)- (5 x²-8x³+ 7)​

Answer 1

Given,

f(x)=x

3

−7x

2

+15x−9

Let us assume

x−3=0⇒x=3

Now, f(3)=(3)

3

−7(3)

2

+15(3)−9

=27−63+45−9=72−72=0

∴ By remainder theorem,

(x−3) is a factor of f(x)

Now, dividing f(x) by (x−3), we get

x

3

−7x

2

+15−9=(x−3)(x

2

−4x+3)

=(x−3)(x

2

−x−3x+3)

=(x−3){x(x−1)−3(x−1)}

=(x−3)(x−3)(x−1)

=(x−3)

2

(x−1)

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