How do you find the quotient of (x^3-43x+42) divided by (x^2+6x-7)?

Question

Ethan Adkins · Accepted Answer

#x-6# #"factorise numerator/denominator"# #x^3-43x+42# #=x^2(x-1)+x(x-1)-42(x-1)# #=(x-1)(x^2+x-42)=(x-1)(x+7)(x-6)# #x^2+6x+7=(x+7)(x-1)# #rArr(x^3-43x+42)/(x^2+6x-7)# #=(cancel((x-1))cancel((x+7))(x-6))/(cancel((x+7))cancel((x-1)))=x-6#

Jace Anderson · Answer

undefined To find the quotient of (x^3-43x+42) divided by (x^2+6x-7), you can use polynomial long division or synthetic division. Here is the step-by-step process using polynomial long division:

1. Divide the first term of the dividend (x^3) by the first term of the divisor (x^2). The result is x.

2. Multiply the entire divisor (x^2+6x-7) by the result from step 1 (x). The result is x^3+6x^2-7x.

3. Subtract the result from step 2 (x^3+6x^2-7x) from the dividend (x^3-43x+42). This gives you (-49x+42).

4. Bring down the next term from the dividend (-49x). The new dividend is now (-49x+42).

5. Divide the first term of the new dividend (-49x) by the first term of the divisor (x^2). The result is -49x.

6. Multiply the entire divisor (x^2+6x-7) by the result from step 5 (-49x). The result is -49x^2-294x+49.

7. Subtract the result from step 6 (-49x^2-294x+49) from the new dividend (-49x+42). This gives you (-336x-7).

8. Bring down the next term from the dividend (-336x). The new dividend is now (-336x-7).

9. Divide the first term of the new dividend (-336x) by the first term of the divisor (x^2). The result is -336.

10. Multiply the entire divisor (x^2+6x-7) by the result from step 9 (-336). The result is -336x^2-2016x+2352.

11. Subtract the result from step 10 (-336x^2-2016x+2352) from the new dividend (-336x-7). This gives you (-2023x+2345).

The quotient is x-49 with a remainder of (-2023x+2345) divided by the divisor (x^2+6x-7).