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    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

    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:

    The same process should work for your problem
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