to rewrite x3−64
. (1 point)
Responses
x3−64=(x+4)(x2+4x+16)
x cubed minus 64 equals left parenthesis x plus 4 right parenthesis left parenthesis x squared plus 4 x plus 16 right parenthesis
x3−64=(x−4)(x2+4x+16)
x cubed minus 64 equals left parenthesis x minus 4 right parenthesis left parenthesis x squared plus 4 x plus 16 right parenthesis
x3−64=(x+4)(x2−4x+16)
x cubed minus 64 equals left parenthesis x plus 4 right parenthesis left parenthesis x squared minus 4 x plus 16 right parenthesis
x3−64=(x−4)(x2−4x+16)
x cubed minus 64 equals left parenthesis x minus 4 right parenthesis left parenthesis x squared minus 4 x plus 16 right parenthesis
1 answer
To rewrite \( x^3 - 64 \) using the polynomial identity \( x^3 - a^3 = (x - a)(x^2 + ax + a^2) \), we first identify \( a \).
Here, \( a^3 = 64 \) implies \( a = 4 \) (since \( 4^3 = 64 \)).
Now we apply the polynomial identity:
\[ x^3 - 64 = x^3 - 4^3 = (x - 4)(x^2 + 4x + 16) \]
Thus, the correct response is:
\[ x^3 - 64 = (x - 4)(x^2 + 4x + 16) \]
So, the option is:
x³−64=(x−4)(x²+4x+16)
