Respuesta :
Answer:
A
Step-by-step explanation:
Given
5x² - 45 ← factor out 5 from each term
= 5(x² - 9)
x² - 9 is a difference of squares and factors in general as
a² - b² = (a + b)(a - b), thus
x² - 9
= x² - 3² = (x + 3)(x - 3)
and
5x² - 45
= 5(x + 3)(x - 3) → A
Answer:
A. 5(x + 3)(x - 3)
Step-by-step explanation:
Given expression: [tex]\[5x^{2}-45\][/tex]
= [tex]\[5(x^{2}-9)\][/tex]
= [tex]\[5(x^{2}-3^{2})\][/tex] -------------(1)
But [tex]\[(x^{2}-3^{2}) = (x+3)(x-3)\][/tex]
Substituting in (1):
= [tex]\[5(x+3)(x-3)\][/tex]
Among the given options, This corresponds to option A in the list.
Option B corresponds to [tex]\[5x^{2}-225\][/tex]
Option C corresponds to [tex]\[5x^{2}-405\][/tex]
Option D corresponds to [tex]\[5x^{2}-16x-45\][/tex]
