Question

Which of the following is a factor of 2x4 + 22x3 + 60x2?

Answer 1

What common factor do the numbers 2, 22, and 60 have?

Answer 2

Here are the prime factors of each of the three numbers above:

\(2 = \color{red}{2}\)

\(22 = \color{red}{2} \times 11\)

\(60 = \color{red}{2} \times 2 \times 3 \times 5\)

Which factor do they all share in common?

Answer 3

Then look at the variable parts, \(x^4\), \(x^3\), and \(x^2\).

\(x^4 = \color{red}{x \times x} \times x \times x\)

\(x^3 = \color{red}{x \times x} \times x \)

\(x^2 = \color{red}{x \times x}\)

Which variable part do all three monomials have in common?

Answer 4

2 is what they all have in common

Answer 5

Yes, as far as the numbers are concerned, the only common factor is 2.
What about the variables? How many x's do they have in common?

Answer 6

3

Answer 7

so would it be 2x^#? @mathstudent55

Answer 8

2x^3 i mean

Answer 9

???
In each line I only see 2 x's in red.
Since the last monomial only has 2 x's there are only 2 x's in common.
Where do you see 3 x's in all three lines above?

Answer 10

I meant 3 because there were 3 lines that held at least 2 xs

Answer 11

Don't confuse the multiplication sign with the variable x.

Answer 12

Ok, then what is in common?

\(2 \times x \times x = 2x^2\)

The common factor is \(2x^2\)

Answer 13

2 and x are what is in common

Answer 14

so 2x^2 is what the answer would be?

Answer 15

Yes.

Answer 16

but that isnt one of the answer choices