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Factor the difference of cubes: $a^3-b^3 = (a-b)(a^2+ab+b^2)$
Learn how to solve limits by direct substitution problems step by step online.
$\lim_{x\to1}\left(\frac{\left(x-1\right)\left(x^2+x+1\right)}{4x^3-x-3}\right)$
Learn how to solve limits by direct substitution problems step by step online. Find the limit (x)->(1)lim((x^3-1)/(4x^3-x+-3)). Factor the difference of cubes: a^3-b^3 = (a-b)(a^2+ab+b^2). We can factor the polynomial 4x^3-x-3 using the rational root theorem, which guarantees that for a polynomial of the form a_nx^n+a_{n-1}x^{n-1}+\dots+a_0 there is a rational root of the form \pm\frac{p}{q}, where p belongs to the divisors of the constant term a_0, and q belongs to the divisors of the leading coefficient a_n. List all divisors p of the constant term a_0, which equals -3. Next, list all divisors of the leading coefficient a_n, which equals 4. The possible roots \pm\frac{p}{q} of the polynomial 4x^3-x-3 will then be.