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# Remainder theorem question? C2

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1. Given that f(x) =px^3+23x^2+qx-8
And f(-1)=15 and f(-2) =48

I) find values of p and q (I got p equals 6 and q equals -6)
2) use remainder theorem to factorise the expression completely.

I wasn't sure how to use the remainder theorem to factorise this, Im not sure if using the factor theorem would be accepted. I tried using long division to somehow factorise it but I'm not sure how.
Any help or explanation would be much appreciated
2. The easiest and simplest way to factorise a cubic, is just by inspection. Your first step is to find a factor, which is basically just through trail and error.
Take the function f(x)= 2x^3 + 7x^2 + 7x +2 , for example. Trial and error will give that f(-1)=0 hence, by the factor theorem (x+1) is a factor.
Then let f(x)=(x+1)(Ax^2+Bx+C)
By inspection/equating coefficients, you can see that, from the coefficients of the constants (x^0), C=2.
From the coefficients of x^3, A=2
And from coeff. of x^2, A+B=7 => B=5
Therefore f(x)=(x+1)(2x^2+5x+2)
Then all that's left is to factorise the quadratic:
f(x)=(x+1)(x+2)(2x+1)

The same process should work for your problem

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