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1.Find the greatest common factor: 20y^9 +5y^6

A5y^6
B5y^9
C10y^9
D20y^3

and

  1. Find the greatest common factor: 12xy^5+ 60x^4y^2 _ 24x^3y#3.

A3x^4y^5
B6xy^5
C6xy^2
D12xy^2

Verified Answer :

JcAlmighty

The greatest common factor is the biggest number taken from the values.

Q1. The answer is A. 5y^6

\(20 y^{9} +5 y^{6}= 4*5 y^{9}+5 y^{6}\)
Since \(x^{a}* x^{b} =x^{a+b}\), then \(x^{9}= x^{3}* x^{6}\)

Back to our expression:
\(4*5 y^{9}+5 y^{6}=4*5 y^{3}*y^{6}+5 y^{6}=4 y^{3}*5y ^{6}+ 5y ^{6}*1=5 y^{6} (4y ^{3} +1)\)
The greatest common factor is thus \(5 y^{6}\)


Q2. The answer is D. 12xy^2

\(12x y^{5}+60 x^{4} y^{2} -24 x^{3} y^{3}=12x y^{5}+5*12 x^{4} y^{2} -2*12 x^{3} y^{3}\)
We will use the rule  \(x^{a}* x^{b} =x^{a+b}\) to factorise the exponents:
\(12x y^{5}+5*12 x^{4} y^{2} -2*12 x^{3} y^{3}= \\ =12x*y^{2}*y^{3}+5*12*x* x^{3} *y^{2}-2*12x* x^{2} *y*y^{2}= \\ =12xy^{2}*y^{3}+12xy^{2}*5 x^{3} -12xy^{2}*2 x^{2} y= \\ =12xy^{2}(y^{3}+5 x^{3}-2 x^{2} y)\)
The greatest common factor is thus \(12xy^{2}\)

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