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C1 factor theorem question, urgent help needed!

I have the question "solve P(x+10) = 0."

P(x)= x³+kx²-5x+6

The factors are (x-1)(x-3)(x+2) if worked correctly and roots 1, 3 and -2. K is equal to -2.

how do i solve P(x+10) = 0 from this information i have? what is it asking?
Reply 1
Avatar for Mr. Pink
Mr. Pink
1
first of all i'm assuming there was other info given in the question that lead you to find k.

if so, then i guess you could just write:

P(x) = (x -1)(x - 3)(x + 2) and then subsitude x for (x +10) and thus set p(x) = 0
you'll then get out another set of x values

this is no different than finding the roots (x intercepts) of P(x), now its just transformed to P(x + 10). You'll find different roots.

could you please write out the question as is, with all included information?
Reply 2
Avatar for r0manticide17
r0manticide17
OP
3
ok. well it was a 4 part question. those are my factors and my K value, and my roots. part d) solve p(x+10) = 0. ive sort of done it though, i substituted x+10 in the X values and got (x+9)(x+7)(x+12)
C1 doesnt require the factor theorem btw.
Reply 4
Avatar for massimo
massimo
c2 is factor or maybe c3 but def not c1 i think

and you will need to redo that question bro !!
r0manticide17
ok. well it was a 4 part question. those are my factors and my K value, and my roots. part d) solve p(x+10) = 0. ive sort of done it though, i substituted x+10 in the X values and got (x+9)(x+7)(x+12)


Just put (x+10) in the place of all the x's in P(x) and you'll get an equation. Solve it to get the answer.
Reply 6
Avatar for r0manticide17
r0manticide17
OP
3
yeah they ask for factor theorem in the AQA exam
Reply 7
Avatar for -G-a-v-
-G-a-v-
16
Yup, it depends on the exam board - some boards put it in C1, others put it in C2.

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