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)

walter needs to make at least 5 more cookies but no more than 40. 5 ≤ x ≤ 40

step-by-step explanation:

20 ≤ x + 15 ≤ 55

subtract 15 from all parts

20-15 ≤ x + 15-15 ≤ 55-15

5 ≤ x ≤ 40

this means how many more cookies he has to make

walter needs to make at least 5 more cookies, but no more than 40 cookies; 5 ≤ x ≤ 40