Divide f(x) by d(x), and write a summary statement in the form indicated.. f(x) = x4 + 4x3 + 6x2 + 4x + 5; d(x) = x2 + 1. a. f(x) = (x2 + 1)( x2 + 4x + 5) + 12x - 15. b. f(x) = (x2 + 1)( x2 + 4x + 5). c. f(x) = (x2 + 1)( x2 - 4x + 5). d. f(x) = (x2 + 1)( x2 - 4x + 5) + 12x - 16

Option B is correct.

Step-by-step explanation:

We given with two polynomials.

We have to check which given statement is correct.

For this divide f(x) by d(x)

Division is shown in pic.

After division we get,

Quotient = x² + 4x + 5

Remainder = 0

If, a is dividend , b is divisor , q is quotient and r is remainder ,

then by division algorthium it can be written as ,

a = bq + r

⇒ f(x) = ( x² + 1 )( x² + 4x + 5 ) + 0

f(x) = ( x² + 1 )( x² + 4x + 5 )

Therefore, Option B is correct.

the answer is:

the answer is:

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

have a nice day!