Question

What is a factor of 9x^2– 16?

A. 3x + 4


B. 3x^2 - 4


C. 3x - 4


D. Both A and C.


E. None of the above.​

Answer 1

D. Both A and C.

Explanation:

First, notice that 9
`x^(2)`-16 is in the pattern
`a^(2)`-
`b^(2)`.

We know that
`a^(2)`-
`b^(2)` = (a-b)(a+b)**

**If you don't know this formula, it works because if you expand you will get
`a^(2)`+ab-ab-
`b^(2)` and it cancels out to
`a^(2)`-
`b^(2)`

We can rewrite 9
`x^(2)`-16 as
`(3x)^(2)` -
`(4)^(2)`, where a = 3x and b = 4. We can plug this into (a-b)(a+b) to get that 9
`x^(2)`-16 = (3x-4)(3x+4).

Therefore, two of the factors of 9
`x^(2)`-16 are 3x-4 and 3x+4. This is answer choices A and C.

Answer 2

D. Both A and C.

Explanation:

To determine a factor of the quadratic expression 9x^2 - 16, we can factorize it using the difference of squares formula. The difference of squares formula states that for any two numbers a and b, the expression a^2 - b^2 can be factored as (a + b)(a - b).

In the given expression, 9x^2 - 16, we can rewrite 9x^2 as (3x)^2 and 16 as 4^2. Applying the difference of squares formula, we have:

9x^2 - 16 = (3x)^2 - 4^2

Now, we can factorize using the difference of squares formula:

9x^2 - 16 = (3x + 4)(3x - 4)

Therefore, the factors of the expression 9x^2 - 16 are (3x + 4) and (3x - 4).