Given the expression: 3x10 − 48x2
part a: rewrite the expression by factoring out the greatest common factor. (4 points)
part b: factor the entire expression completely. show the steps of your work. (6 points)

see explanation

step-by-step explanation:

given

3 - 48x² ← factor out 3x² from each term

= 3x²( - 16) ← difference of squares which factors in general as

a² - b² = (a - b)(a + b)

= ( )² ⇒ a =

16 = 4² ⇒ b = 4, so

- 16 = ( - 4)( + 4)

- 4 ← is also a difference of squares and factors as

(x² - 2)(x² + 2)

x² - 2 can be factored as a difference of squares also, that is

= (x - )(x + )

hence

3 - 48x²

= 3x²(x - )(x + )(x² + 2)(x² + 4)

lockers 1, 4, 9, 16, 25, 40, and 49 are open

i ran through it by the other answer is wrong