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

Question

Eli Assouline · Accepted Answer

#c^2 + 3 c + 9#

we use a long division to solve it.

# c^3 -27 # #--->c^2 * (c -3)# #-(c^3 - 3 c^2)# ................................. #3 c^2 - 27# #---> 3 c * (c -3)# #-(3 c^2 - 9 c)# ................................. #9 c - 27# #---> 9 * (c -3)# #-(9 c - 27)# ............................... #0#

the answer is #c^2 + 3 c + 9#

Eva Adamson · Answer

#c^2+3c+9# The numerator is a #color(blue)"difference of cubes"# and in general is factorised as shown. #color(red)(bar(ul(|color(white)(2/2)color(black)(a^3-b^3=(a-b)(a^2+ab+b^2))color(white)(2/2)|)))# #c^3-27=(c)^3-(3)^3rArra=c" and " b=3# #rArrc^3-27=(c-3)(c^2+3c+9)# #rArr(c^3-27)/(c-3)=(cancel((c-3)^1)(c^2+3c+9))/(cancel((c-3)^1)# #=c^2+3c+9larrcolor(red)" quotient"#

Isaiah Anthony · Answer

undefined 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.

Jameson Allen · Answer

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