Factor [tex]2x^2 - 24x + 72[/tex].

A. [tex]2(x + 6)(x - 6)[/tex]

B. [tex]2(x + 6)^2[/tex]

C. [tex]2(x - 6)^2[/tex]

D. Can't be factored

2 x 2 − 24 x + 72 = 2 ( x 2 − 12 x + 36 ) = 2 ( x 2 − 2 x ⋅ 6 + 6 2 ) = 2 ( x − 6 ) 2 A n s w er : C .

Answered by Anonymous | 2024-06-10

The quadratic expression 2x² - 24x + 72 is factored as 2(x - 6)², falling under option 'C'.
To factor the quadratic expression 2x² - 24x + 72, we start by looking for two numbers that multiply to give the product of the coefficient of x² (which is 2) and the constant term (which is 72), and at the same time add up to the coefficient of x (which is -24). Those two numbers are -12 and -12, since (2)(72) = 144 and -12 + -12 = -24.
Now we can express the quadratic as 2(x - 6)², which shows that the correct factorization is in the form of a perfect square.
This aligns with option 'C': 2(x - 6)².

Answered by ToddBoyce | 2024-06-24

The expression 2x^2 - 24x + 72 can be factored by first taking out the greatest common factor of 2, resulting in 2(x^2 - 12x + 36). The trinomial can then be factored to (x - 6)^2, leading to the final answer of 2(x - 6)^2. Therefore, the correct option is C.
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Answered by Anonymous | 2024-12-22