Question 1018197
1.   Determine the GCF of 35w²z³ and 42w³z.
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The biggest number that will divide into both 35 
and 42 is 7.

The largest exponent of w that does not exceed any 
of the exponents of w is w². (Can't use w³ because 
that exceeds w²)

The largest exponent of z that does not exceed any 
of the exponents of z is z. (Can't use z³ because 
that exceeds z which is z<sup>1</sup>.)

Answer:  7w²z
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 2.   Factor each of the following polynomials using 
the greatest common factor.

/2 a.   5x³ + 25x² + 10x
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5 is the largest number that goes into 5, 25 and 10.  
x<sup>1</sup> or just x is the largest exponent of x 
that does not exceed any of the exponents of x.

Answer:  5x(x²+5x+2)
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/2 b.   10000m²n² + 1000mn² + 20000m²
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1000 is the largest number that goes into 10000, 1000 
and 2000.  m<sup>1</sup> or just m is the largest 
exponent of m that does not exceed any of the 
exponents of m.

There is no exponent of n that does not exceed any of 
the exponents of n, because there is no n in the third 
term.  So n cannot be taken out.

Answer: 1000m(10mn² + n² + 20m)
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/2 3.  Verify that 3x(5x² – 7x + 12) is equivalent to 
15x³ – 21x² + 36x3x.
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Distribute to remove parentheses:

Answer:
3x(5x² – 7x + 12)

3x(5x²) – 3x(7x) + 3x(12)

15x³ - 21x² + 36x
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 4.   Consider the expression 5(4x – 3) + x(4x – 3).
/1  a.   What is the GCF of 5(4x – 3) + x(4x  – 3)? 
Explain.
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We can factor out (4x  – 3) leaving the 5 and 
the x added in parentheses

Answer: (4x - 3)
  
/1  b.   Factor 5(4x – 3) + x(4x  – 3) using the GCF.

Answer: (4x - 3)(5 + x)

Edwin</pre>