Algebra - Factoring Polynomials (Practice Problems)

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Section 1.5 : Factoring Polynomials

For problems 1 – 4 factor out the greatest common factor from each polynomial.

$6{x^7} + 3{x^4} - 9{x^3}$ Solution
${a^3}{b^8} - 7{a^{10}}{b^4} + 2{a^5}{b^2}$ Solution
$2x{\left( {{x^2} + 1} \right)^3} - 16{\left( {{x^2} + 1} \right)^5}$ Solution
${x^2}\left( {2 - 6x} \right) + 4x\left( {4 - 12x} \right)$ Solution

For problems 5 & 6 factor each of the following by grouping.

$7x + 7{x^3} + {x^4} + {x^6}$ Solution
$18x + 33 - 6{x^4} - 11{x^3}$ Solution

For problems 7 – 15 factor each of the following.

${x^2} - 2x - 8$ Solution
${z^2} - 10z + 21$ Solution
${y^2} + 16y + 60$ Solution
$5{x^2} + 14x - 3$ Solution
$6{t^2} - 19t - 7$ Solution
$4{z^2} + 19z + 12$ Solution
${x^2} + 14x + 49$ Solution
$4{w^2} - 25$ Solution
$81{x^2} - 36x + 4$ Solution

For problems 16 – 18 factor each of the following.

${x^6} + 3{x^3} - 4$ Solution
$3{z^5} - 17{z^4} - 28{z^3}$ Solution
$2{x^{14}} - 512{x^6}$ Solution