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Carter divided the polynomial 6x2 + 4x + 3 by the monomial 2x using long division, and got an answer of 3x + 2 + . His work is shown below.



Demi thought each term of the polynomial needed to be divided by the monomial. Which statement is correct?

Carter is incorrect because long division cannot be used to divide monomials.
Demi is incorrect because the polynomial cannot be broken up into individual terms.
Both Carter and Demi are correct and would get the same answer.
Both Carter and Demi are wrong because a polynomial cannot be divided by a term containing a variable.

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Answer:

C. Both Carter and Demi are correct and would get the same answer.

Step-by-step explanation:

Here, the given polynomial is : [tex]P(x) =6x^2 + 4x + 3 [/tex]

The given monomial : [tex]Q(x)  = 2 x[/tex]

Now, according to the given question:

Dividend = P(x), Divisor  = Q(x)

Now, Carter divide P(x) by Q (x) with LONG DIVISION METHOD.

If we divide P(x) by Q(x) by Long division, we get:

[tex]\frac{P(x)}{Q(x)}  = \frac{(6x^2 + 4x + 3)}{(2x)}  = 3x +  2 + \frac{3}{2} x = R(x)[/tex]

Also, if Demi divides each term of P(x) by The given monomial (2x) , we get:

[tex]\frac{P(x)}{Q(x)}  = \frac{(6x^2 + 4x + 3)}{(2x)}  = \frac{6x^2}{2x}  + \frac{4x}{2x} +\frac{3}{2x} \\= 3x +  2 + \frac{3}{2}  = R(x)[/tex]

⇒In both the case, R(X)Quotient is SAME.

Hence, Both Carter and Demi are correct and would get the same answer.

Answer:

Both Carter and Demi are correct and would get the same answer.

Step-by-step explanation:

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