f(x)=x^3-x^2-14x+24 a) show that x+4 is a factor of f(x) b) factorise f(x) c) solve the equation f(x)=0.
pls help im stuck
a) If x-a is a factor, then f(a) = 0. Using this, you can show x+4 is a factor. b) Use polynomial division to divide by x+4. Then factorise what's left. Alternatively, use the same approach as in part (a) with trial and error for random numbers (try -1, 1, 2, -2...) c) Follows from your answer to b. If (x-a)(x-b)(x-c) = 0 then x=a, b, c.
(a) The Factor Theorem is such that if you have some factor, (ax+b), then f(-b/a) = 0. Use this to show (x+4) is a factor. (You may also come across the remainder theorem, where f(-b/a) is the remainder when f(x) is divided through by (ax+b)
(b) So now that you have shown that (x+4) is a factor. Factorising a cubic may look tricky at first ... but you'll soon see that it is fairly straightforward. To factorise a cubic, it would be in the form: (ax+b)(cx^2 + dx + e) ... since you would get an x^3 term if you expand this.
Using part (a), you should have the (ax+b) bit ... which is (x+4). If you divide f(x) by this factor by doing some algebraic long division, you'll obtain the quadratic (cx^2 + dx + e). Then see if this can be factorised further as you normally would with a quadratic
(c) Having factorised f(x), let each bracket equal 0 and solve