Question

To factor the expression 3x2 – 9x, Caleb found the GCF as shown.

List the factors:
3x2 = 3 • x • x
9x = 3 • 3 • x
GCF = 3 • 3 • x • x = 9x2
What is Caleb’s error?

Answer 1

Caleb’s error was :

instead of selecting the least exponent ,Caleb took the highest exponent.

Explanation:

3x² = 3 • x • x

(in this factorization the exponent of 3 is 1 and the exponent of x is 2)

9x = 3 • 3 • x

(in this factorization the exponent of 3 is 2 and the exponent of x is 1)

• The common factors of 3x² and 9x are 3 and x

In order to determine the GCF ,we have to Compare the exponents of the common factors then take the numbers which have the least exponent value.

• in the factorization of 3x² the exponent of 3 is 1

and in the factorization of 9x the exponent of 3 is 2

The least exponent is 1 Then we take it.

• in the factorization of 3x² the exponent of x is 2

and in the factorization of 9x the exponent of x is 1

The least exponent is 1 Then we take it.

Conclusion:

GCF(3x² , 9x) = 3¹ × x¹ = 3x