Practice Problems

\(\textbf{1)}\) \(x^2+5x+6=0\)

Show Answer

The answer is \(x=-3,\,\,\,x=-2\)

Show Work

\(\,\,\,\,\,\,x^2+5x+6=0\)
\(\,\,\,\,\,\,(x+3)(x+2)=0\)
\(\,\,\,\,\,\,x+3=0\,\,\,\text{ or } \,\,\, x+2=0 \)
\(\,\,\,\,\,\,x=-3\,\,\,\text{ or } \,\,\, x=-2 \)

 

\(\textbf{2)}\) \(x^2-6x+8=0\)

Show Answer

The answer is \(x=2,\,\,\,x=4\)

 

\(\textbf{3)}\) \(x^2-8x-20=0\)

Show Answer

The answer is \(x=-2,\,\,\,x=10\)

 

\(\textbf{4)}\) \(0=2x^3+6x^2-32x-96\)

Show Answer

The answer is \(x=-4,\,\,\, x=4,\,\,\, x=-3\)

 

\(\textbf{5)}\) \(x^3+x^2=4x+4\)

Show Answer

The answer is \(x=-2,\,\,\, x=-1,\,\,\, x=2\)

Show Work

\(\,\,\,\,\,x^3+x^2=4x+4\)
\(\,\,\,\,\,x^3+x^2-4x-4=0\)
\(\,\,\,\,\,x^2\left(x+1\right)-4(x+1)=0\)
\(\,\,\,\,\,\left(x^2-4\right)(x+1)=0\)
\(\,\,\,\,\,(x+2)(x-2)(x+1)=0\)
\(\,\,\,\,\,x=-2,\,\,\, x=-1,\,\,\, x=2\)

 

 

See Related Pages\(\)

\(\bullet\text{ Factoring out a GCF}\)
\(\,\,\,\,\,\,\,\,3xyz^2+x^2y^2z+9x^3y=xy(3z^2+xyz+9x^2)…\)

\(\bullet\text{ Perfect Square Trinomials}\)
\(\,\,\,\,\,\,\,\,x^2-6x+9=(x-3)^2…\)

\(\bullet\text{ Factoring Trinomials with a}=1\)
\(\,\,\,\,\,\,\,\,x^2+7x+12=(x+3)(x+4)…\)

\(\bullet\text{ Factoring Trinomials with a} \ne 1\)
\(\,\,\,\,\,\,\,\,3x^2+11x+6=(3x+2)(x+3)…\)

\(\bullet\text{ Factoring with u-substitution}\)
\(\,\,\,\,\,\,\,\,x^4+5x^2+6=u^2+5u+6…\)

\(\bullet\text{ Difference of Two Squares}\)
\(\,\,\,\,\,\,\,\,x^2-16=(x+4)(x-4)…\)

\(\bullet\text{ Sum/Difference of Two Cubes}\)
\(\,\,\,\,\,\,\,\,x^3-8=(x-2)(x^2+2x+4)…\)

\(\bullet\text{ Factor by Grouping}\)
\(\,\,\,\,\,\,\,\,8x^3-4x^2-6x+3=(4x^2-3)(2x-1)…\)