How do you find the quotient of #(a^2+a-12)div(a-3)#?

Question

Nathan Axel · Accepted Answer

The quotient is #a+4# Factorise first: #(a^2 +a -12)/(a-3) = ((a+4)(a-3))/(a-3)# Cancel the like factors: # ((a+4)cancel((a-3)))/cancel((a-3))# The quotient is #a+4#

Nathan Axel · Answer

undefined To find the quotient of (a^2+a-12) divided by (a-3), you can use long division or synthetic division.

Using long division:
- Divide the first term of the numerator (a^2) by the first term of the denominator (a). This gives a as the first term of the quotient.
- Multiply the entire denominator (a-3) by the first term of the quotient (a), and subtract the result from the numerator (a^2+a-12).
- Bring down the next term (-12) from the numerator.
- Repeat the process by dividing the first term of the new numerator (a^2-2a) by the first term of the denominator (a), and continue until there are no more terms left in the numerator.
- The resulting quotient is a+4.

Using synthetic division:
- Write the coefficients of the numerator (1, 1, -12) and the divisor (1, -3) in descending order.
- Bring down the first coefficient (1) from the numerator.
- Multiply the divisor (1, -3) by the value brought down (1), and write the result below the next coefficient (-3).
- Add the corresponding coefficients (-3 and 1) and write the sum (-2) below the line.
- Repeat the process by multiplying the divisor (1, -3) by the new value (-2), and continue until there are no more coefficients left.
- The resulting quotient is a+4.