Notes
Problems
Factor
\(\textbf{1)}\) \( x^3-1000 \)
\(\textbf{2)}\) \( x^3-1 \)
\(\textbf{3)}\) \( y^6+1 \)
\(\textbf{4)}\) \( 16x^4-54x \)
\(\textbf{5)}\) \( w^3-27y^9 \)
\(\textbf{6)}\) \( x^3+64 \)
\(\textbf{7)}\) \( w^{12}+64y^3 \)
\(\textbf{8)}\) \( x^3-8 \)
Challenge Problems
\(\textbf{9)}\) Factor \( x^6-64 \) completely
\(\textbf{10)}\) Factor \( x^6-1 \) completely
See Related Pages\(\)
\(\bullet\text{ Factoring Calculator }\)
\(\,\,\,\,\,\,\,\,\text{(Symbolab.com)}\)
\(\bullet\text{ Factoring out a GCF}\)
\(\,\,\,\,\,\,\,\,3xyz^2+x^2y^2z+9x^3y=xy(3z^2+xyz+9x^2)…\)
\(\bullet\text{ Perfect Square Trinomials}\)
\(\,\,\,\,\,\,\,\,x^2-6x+9=(x-3)^2…\)
\(\bullet\text{ Factoring Trinomials with a}=1\)
\(\,\,\,\,\,\,\,\,x^2+7x+12=(x+3)(x+4)…\)
\(\bullet\text{ Factoring Trinomials with a} \ne 1\)
\(\,\,\,\,\,\,\,\,3x^2+11x+6=(3x+2)(x+3)…\)
\(\bullet\text{ Factoring with u-substitution}\)
\(\,\,\,\,\,\,\,\,x^4+5x^2+6=u^2+5u+6…\)
\(\bullet\text{ Difference of Two Squares}\)
\(\,\,\,\,\,\,\,\,x^2-16=(x+4)(x-4)…\)
\(\bullet\text{ Factor by Grouping}\)
\(\,\,\,\,\,\,\,\,8x^3-4x^2-6x+3=(4x^2-3)(2x-1)…\)
\(\bullet\text{ Solving Quadratic Equations by Factoring}\)
\(\,\,\,\,\,\,\,\,x^2+10x−24=0…\)
In Summary
Factoring is the process of expressing a number or algebraic expression as the product of other simpler numbers or expressions. The general formula for factoring the sum or difference of two cubes is as follows:
\(a^3 + b^3 = (a + b)(a^2 – ab + b^2)\)
\(a^3 – b^3 = (a – b)(a^2 + ab + b^2)\)