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core 4 quotient and remainder watch

1. i. Find the quotient and the remainder when 3x^3 -2x^2 + x +7 is divided by x^2-2x+5.
= quotient =3x+4
remainder = -6x - 13.
ii. Hence, or otherwise, determine the values of the constants a and b such that, when 3x^3 -2x^2 +ax + b is divided by x^2 -2x+5, there is no remainder. ( 2 marks)

The mark scheme states that a should be a =7 and b=20.

I don't
understand why 6 is added onto 1x instead of being taken away since it's -6x-13?
2. (Original post by Chelsea12345)
i. Find the quotient and the remainder when 3x^3 -2x^2 + x +7 is divided by x^2-2x+5.
= quotient =3x+4
remainder = -6x - 13.
ii. Hence, or otherwise, determine the values of the constants a and b such that, when 3x^3 -2x^2 +ax + b is divided by x^2 -2x+5, there is no remainder. ( 2 marks)

The mark scheme states that a should be a =7 and b=20.

I don't
understand why 6 is added onto 1x instead of being taken away since it's -6x-13?
You ended up with:

We want the remainder to be 0, which means that if we add onto both sides we get . From here you can clearly read off the values of by looking at the cubic on the left.
3. i. Find the quotient and the remainder when 3x^3 -2x^2 + x +7 is divided by x^2-2x+5.
= quotient =3x+4
remainder = -6x - 13.
ii. Hence, or otherwise, determine the values of the constants a and b such that, when 3x^3 -2x^2 +ax + b is divided by x^2 -2x+5, there is no remainder. ( 2 marks)

The mark scheme states that a should be a =7 and b=20.

I don't
understand why 6 is added onto 1x instead of being taken away since it's -6x-13?

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