6.11: Proficiency Exam
The product is \(27a^3+9a^2+9a\) and a factor is \(3a\). Find the other factor.
- Answer
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\(9a^2+3a+3\)
The product is \(15x^{n+5}y^{3n−2}\). Find the other factor.
- Answer
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\(5x^ny^{2n−3}\)
For the following problems, factor, if possible, the polynomials.
\(−14x^2y^4b−28x^2y^3b−42x^2y^2\)
- Answer
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\(−14x^2y^2(y^2b+2yb+3)\)
\((y+2)a+(y+2)c\)
- Answer
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\((a+c)(y+2)\)
\( 6x^2y^2z+5x^2y^3−12xyz−10xy^2\)
- Answer
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\(xy(xy−2)(6z+5y)\)
\(4a^2−16c^2\)
- Answer
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\(4(a+2c)(a−2c)\)
\(m^4−n^4\)
- Answer
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\((m^2+n^2)(m+n)(m−n)\)
\(b^2+8b+16\)
- Answer
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\((b+4)^2\)
\(9y^2−30y+25\)
- Answer
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\((3y−5)^2\)
\(x^2+5x−15\)
- Answer
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not factorable
\(x^2−x−30\)
- Answer
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\((x−6)(x+5)\)
\(4x^6−36x^4+80x^2\)
- Answer
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\(4x^2(x^2−5)(x+2)(x−2)\)
\(9x^2+25x−6\)
- Answer
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\((9x−2)(x+3)\)