How to deal with Polynomial multiple choice question on factors? Please help!

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Can someone please explain to me how to do question 7? I haven't got a clue!

1 Answer
Apr 25, 2017

-9+10

=1

Explanation:

Don't be tempted to try and find the other factor - there is not enough information.

The clue is in the fact that (x-3) is a factor .... this leads us to think about the factor and remainder theorem.

If an expression is a factor, then the remainder is 0.

Form an equation to say this...

f(x) = x^2 +ax +b

If (x-3) is a factor, then f(3)=0

f(3) = (3)^2 +a(3) +b =0

rarr" "9+3a +b =0

rarr" "3a +b =-9" "larr Now THIS helps!

What is the value of 3a+b+10?

color(blue)(3a +b = -9)

So,
color(blue)((3a+b))+10
" "darr
= color(blue)(-9)+10

=1

Really nice question - had me puzzled for a while at first.
Hope this helps. :)