1. Determine the GCF of 35w²z³ and 42w³z.
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 z1.)
Answer: 7w²z
2. Factor each of the following polynomials using
the greatest common factor.
/2 a. 5x³ + 25x² + 10x
5 is the largest number that goes into 5, 25 and 10.
x1 or just x is the largest exponent of x
that does not exceed any of the exponents of x.
Answer: 5x(x²+5x+2)
/2 b. 10000m²n² + 1000mn² + 20000m²
1000 is the largest number that goes into 10000, 1000
and 2000. m1 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)
/2 3. Verify that 3x(5x² – 7x + 12) is equivalent to
15x³ – 21x² + 36x3x.
Distribute to remove parentheses:
Answer:
3x(5x² – 7x + 12)
3x(5x²) – 3x(7x) + 3x(12)
15x³ - 21x² + 36x
4. Consider the expression 5(4x – 3) + x(4x – 3).
/1 a. What is the GCF of 5(4x – 3) + x(4x – 3)?
Explain.
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