Question

Divide 2y2 + 8 by 2y + 4. Which expression represents the quotient and remainder?

Answer 1

The quotient of dividing 2y^2 + 8 by 2y + 4 is y - 2, and the remainder is 8.

Step-by-step explanation:

To divide 2y2 + 8 by 2y + 4, we should aim to match terms by factoring or long division. First, notice that both terms in the numerator, 2y2 and 8, are divisible by 2, which is also a factor in the denominator of 2y + 4. By factoring out a 2 from the numerator, we get 2(y2 + 4). Now, we can divide this resulting expression by 2y + 4.

Factorizing the term y2 + 4, we notice that it can be rewritten as (y + 2)(y - 2) + 8, but unfortunately, this does not match our denominator precisely. Therefore, we recognize that (y + 2) is not a factor of our denominator, and instead, we simply cancel out the common factor of 2 from both numerator and denominator to simplify.

The revised expression after simplifying by a factor of 2 would be y2 + 4 divided by y + 2, which does not simplify any further. Thus, the quotient is y - 2 with a remainder of 8, because y2 + 4 -(y + 2)(y - 2) = 8. The quotient and remainder of the division are y - 2 and 8, respectively.

Answer 2

When 2(y^2) + 8 is divided by 2y + 4 is equal to (y - 2) + (16 / (2y + 4)). The expression represents the quotient is the 2y + 4. While the expression represent the remainder is 16 / (2y + 4). The remainder of the given expression can also be solve using the remainder theorem.