Question

what number should be subtracted from 2x^3-5x^2+5x so that the resulting polynomial has 2x-3 ​

Answer 1

Step-by-step explanation:

Let

p(x)=2x

3

−5x

2

+5x

g(x)=2x−3

and the number to be subtracted from p(x) be a, then

p

′

(x)=p(x)−a=2x

3

−5x

2

+5x−a

Consider, g(x)=0⇒2x−3=0⇒x=

2

3

∴ By factor theorem,

For g(x) to be a factor of p

′

(x)

p(

2

3

)=0

⇒2(

2

3

)

3

−5(

2

3

)

2

+5(

2

3

)−a=0

⇒

4

27

−

4

45

−

2

15

−a=0

⇒

4

27−45−30

=a

⇒a=

4

−48

=−12

Hence, −12 should be subtracted from p(x) for g(x) to be its factor.