# How do you find the quotient of #(c^3-27)div(c-3)#?

we use a long division to solve it.

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To find the quotient of (c^3-27) divided by (c-3), we can use the polynomial long division method.

First, divide the first term of the numerator (c^3) by the first term of the denominator (c). This gives us c^2 as the first term of the quotient.

Next, multiply the entire denominator (c-3) by the first term of the quotient (c^2). This gives us c^3-3c^2.

Subtract this result from the numerator (c^3-27). This gives us -3c^2-27.

Now, bring down the next term from the numerator (-3c^2) and repeat the process. Divide (-3c^2) by (c), which gives us -3c as the next term of the quotient.

Multiply the entire denominator (c-3) by the new term of the quotient (-3c). This gives us -3c^2+9c.

Subtract this result from the previous result (-3c^2-27). This gives us -18c-27.

Bring down the next term from the numerator (-18c) and repeat the process. Divide (-18c) by (c), which gives us -18 as the next term of the quotient.

Multiply the entire denominator (c-3) by the new term of the quotient (-18). This gives us -18c+54.

Subtract this result from the previous result (-18c-27). This gives us -81.

Since there are no more terms left in the numerator, the quotient is -81.

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The quotient of (c^3 - 27) divided by (c - 3) is c^2 + 3c + 9.

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