Given the function:
Let's use the long division method to show that x - 4 is a factor of the function.
Let's divide the function by x - 4, if there is no remainder (i.e remainder is 0), then x - 4 is a factor of the function.
Set the division in a long-division like method:
Divide the first term in the dividend by x, write the quotient at the top, then multiply the quotient by the divisor (x - 4), place this result under the dividend.
Subtract it from the dividend.
Continue with this process until you are done with all terms in the dividend.
The value at the top is the quotient while the term at the bottom is the remainder.
Performing the division, we have:
Therefore, the remainder is = 0.
Since the remainder is 0, the divisor (x - 4) is a factor of the given polynomial.
ANSWER:
Since the remainder is 0, the divisor (x - 4) is a factor of the given polynomial.