Use the factor theorem to show that (x-1) is a factor of x^3 - 3x^2 -13x + 15

If (x-1) is a factor of x3 - 3x2 -13x + 15 then one of the solutions for x must be x = 1.(This is because, if (x-1) is a factor of this equation then it is true that x-1=0, because this is a point where the curve crosses the x axis and therefore is = to 0. Solving x-1=0 gives x=1)Because we know that if (x-1) is a factor of the curve, the equation must equal 0 when x=1, we can just substitute this in as such:(1)3 - 3(1)2 -13(1) + 15= 1 - 3 - 13 + 15= 16 -16 = 0Therefore we can conclude, using the factor theorem that (x-1) is a factor of x3 - 3x2 -13x + 15

JB
Answered by James B. Further Mathematics tutor

3771 Views

See similar Further Mathematics GCSE tutors

Related Further Mathematics GCSE answers

All answers ▸

If z=4+i, what is 1/z? (in the form a+bi)


Simplify fully the expression ( 7x^2 + 14x ) / ( 2x + 4 )


Using differentiation, show that f(x) = 2x^3 - 12x^2 + 25x - 11 is an increasing function.


If y=(x^2)*(x-10), work out dy/dx


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning