$a^3+b^3=(a+b)(a^2-ab+b^2)$ $a^3-b^3=(a-b)(a^2+ab+b^2)$ Solving a cubic Write \(\mathrm{f}(x)=0\

Question

$a^3+b^3=(a+b)(a^2-ab+b^2)$ $a^3-b^3=(a-b)(a^2+ab+b^2)$ Solving a cubic Write $\mathrm{f}(x)=0$. Use a given root, or test candidates with the factor theorem. If the constant term is zero, factor out $x$. For integer coefficients, a rational root $\frac{p}{q}$ in lowest terms has $p$ dividing the constant and $q$ dividing the leading coefficient. A cubic need not have a rational root. If $\mathrm{f}(k)=0$, divide by $x-k$, then solve the quadratic factor. Quadratic factorWorkingRoots of the cubic Factorises Does not factorise using integers, $b^2-4ac>0$ $b^2-4ac<0$ Over the reals, leave a quadratic factor with $D<0$ unfactorised.

Accepted Answer

$(2x+3)(x+1)(3x+1)$

Quadratic factor	Working	Roots of the cubic
Factorises
Does not factorise using integers, \(b^2-4ac>0\)
\(b^2-4ac<0\)

Factorization of Cubic Equations

Factorization of Cubic Equations

Video Solution:

Solution:

Solution locked