Question

Check whether y - 3 is a factor of y3 – 2y2 + 3y - 18?​

Answer 1

Answer:

Given, (y−3) is the factor of y

3

+2y

2

−9y−18

Then y−3=0 or y=3

Replace y by 3, we get

y

3

+2y

2

−9y−18

=(3)

3

+2(3)

2

−9(3)−18

=27+18−27−18

=0

As value is zero, then (y−3) is the factor of y

3

+2y

2

−9y−18.

y

3

+2y

2

−9y−18

=y

3

−3y

2

+5y

2

−15y+6y−18

=y

2

(y−3)+5y(y−3)+6(y−3)

=(y−3)(y

2

+5y+6)

=(y−3)(y

2

+2y+3y+6)

=(y−3)[y(y+2)+3(y+2)]

=(y−3)(y+2)(y+3)

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