Use long division to find the quotient below. Enter your answer as a polynomial in descending order, using the caret ( ^ ) for exponents; for example, enter x2 as x^2.(x2 + 10x + 21) (x + 3)
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To find the quotient using long division, follow the steps below:
Step 1: Arrange the dividend and the divisor in descending order.
The dividend is: x^2 + 10x + 21
The divisor is: x + 3
Step 2: Divide the first term of the dividend by the first term of the divisor.
x^2 ÷ x = x
Step 3: Multiply the divisor by the result obtained in Step 2 and write the product beneath the dividend.
(x + 3) * x = x^2 + 3x
Step 4: Subtract the result obtained in Step 3 from the dividend.
(x^2 + 10x + 21) - (x^2 + 3x) = 7x + 21
Step 5: Bring down the next term (if any) from the dividend.
Since there's no next term, you have only the remainder left, which is 7x + 21.
Therefore, the quotient is x, and the remainder is 7x + 21.
In polynomial form, the quotient in descending order is x and the remainder is 7x + 21.