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

Question

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

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Answer 1 · 2017-04-25T11:46:42

# -9+10#

#=1#

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. :)