Final answer:
To divide the polynomial (y³ + 140) by the binomial (y + 5), use long division method. The quotient is (y² - 5) and the remainder is (165 - 5y²).
Step-by-step explanation:
To divide the polynomial (y³ + 140) by the binomial (y + 5), we can use long division method. Let's start by dividing the first term of the polynomial, which is y³, by the first term of the binomial, which is y. This gives us y² as the first term of the quotient. Then multiply this term by the binomial, which gives (y² * (y + 5)) = y³ + 5y². Subtract this result from the original polynomial to get the remainder, which is (140 - 5y²).
Next, bring down the next term of the polynomial, which is 0y². Divide this term by the first term of the binomial, which is y, giving us 0 as the second term of the quotient. Multiply this term by the binomial, which gives (0 * (y + 5)) = 0. Subtract this from the remainder to get a new remainder of (140 - 5y²).
Finally, bring down the last term of the polynomial, which is 140. Divide this term by the first term of the binomial, which is y, giving us -5 as the third term of the quotient. Multiply this term by the binomial, which gives (-5 * (y + 5)) = -5y - 25. Subtract this from the remainder to get a new remainder of (140 - 5y² - (-5y - 25)) = 165 - 5y².
So, the result of dividing the polynomial (y³ + 140) by the binomial (y + 5) is the quotient (y² + 0 - 5) and a remainder of (165 - 5y²).
Learn more about Dividing polynomials