Maths Question Help!!

naxmax9

This isn't homework. I'm studying for my upcoming Maths Halloween Test :pac:

I was practising some questions and came across this one

If 4x - 3 is a factor of 4x^3 - 23x^2 + px + 27, find the value of p.

I got to (p-15)/4 + 27 but idk if that is right and if it is idk what to do from that point on

Thank You

JoseJones

naxmax9 wrote: »

This isn't homework. I'm studying for my upcoming Maths Halloween Test :pac:

I was practising some questions and came across this one

If 4x - 3 is a factor of 4x^3 - 23x^2 + px + 27, find the value of p.

I got to (p-15)/4 + 27 but idk if that is right and if it is idk what to do from that point on

Thank You

Show me what you have done so far, then I'll show you what I have... For an answer I have got p = -21

Tropical.ing

Make the other factor equal to ( x^2 + kx - 9 ), multiply both factors together, find the value of k and sub it into the equation you get for p to find the value of p

Edit: after attempting the question with this method, I also got p = -21

MathsNerd78

A bit late now but here goes anyway. If 4x-3 is a factor then 3/4 is a root. Simply sub in 3/4 for x and put the expression equal to zero (because a root will satisfy this equation). You get 4(27/64)-23(9/16)+p(3/4)+27=0. Multiply across by 64 and solve. You'll get p=-21.