Notes

Questions & Answers

Factor the Following

\(\textbf{1)}\) \(x^2+4x+4\)

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The answer is \((x+2)^2\)

 

\(\textbf{2)}\) \(x^2-6x+9\)

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The answer is \((x-3)^2\)

 

\(\textbf{3)}\) \(x^2+8x+16\)

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The answer is \((x+4)^2\)

 

\(\textbf{4)}\) \(x^2-10x+25\)

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The answer is \((x-5)^2\)

 

\(\textbf{5)}\) \(4x^2+12x+9\)

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The answer is \((2x+3)^2\)

 

\(\textbf{6)}\) \(9x^2+6x+1\)

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The answer is \((3x+1)^2\)

 

\(\textbf{7)}\) \(x^2-2x+1\)

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The answer is \((x-1)^2\)

 

\(\textbf{8)}\) \(x^2-12x+36\)

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The answer is \((x-6)^2\)

 

\(\textbf{9)}\) \(x^2-20x+100\)

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The answer is \((x-10)^2\)

 

\(\textbf{10)}\) \(x^2-14x+49\)

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The answer is \((x-7)^2\)

 

Challenge Problem

\(\textbf{11)}\) Simplify \(\sqrt{54-14\sqrt{5}}\)

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The answer is \(7-\sqrt{5}\)

 

 

See Related Pages\(\)

\(\bullet\text{ Factoring Calculator }\)
\(\,\,\,\,\,\,\,\,\text{(Symbolab.com)}\)

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

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

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

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

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

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

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

\(\bullet\text{ Solving Quadratic Equations by Factoring}\)
\(\,\,\,\,\,\,\,\,x^2+10x−24=0…\)