Polynomials Question (1 Viewer)

[Wonder]

From Cambridge Year 12 3 unit, Exercise 4D

The two parts are similar so how would I generally approach this type of question, as well as specifically with this one?

Thanks!

 

[QZP]

The question is aimed at the fundamentals: P(x) = D(x).Q(x) + R(x), where deg D(x) > deg R(x)

Example: Divide 9 by 4
9 = 4(2) + 1

It makes no sense to write it as
9 = 4(1) + 5, since you can still keep dividing further (5 = 4(1) +1)

So, for that question (and more generally), you can express the polynomial P(x) = (x-1)(x+2).Q(x) + (ax + b). Notice how the remainder is linear (deg 1) whereas the divisor (x-1)(x+2) is deg two.

Then sub in the values you're given and you can solve simultaneously

 

[braintic]

It makes no sense to write it as 9 = 4(1) + 5, since you can still keep dividing further (5 = 4(1) +1)

I know what you are saying there, but 'it makes no sense' is not really accurate. It is a true statement, so it makes sense. It might be better to say that it is not in a form which displays the remainder.

Also, in case you don't know the terminology, P(x) = D(x).Q(x) + R(x) is called the Division Transformation.

 

[QZP]

I know what you are saying there, but 'it makes no sense' is not really accurate. It is a true statement, so it makes sense. It might be better to say that it is not in a form which displays the remainder.

Also, in case you don't know the terminology, P(x) = D(x).Q(x) + R(x) is called the Division Transformation.

Yep, you're right. I should have been better in my expression.
And thanks for the terminology, I never knew that

 

[Wonder]

Okay, thank you!