x^4−6x^3+2x^2−15x+18 by x−6 What is the quotient?
x^3+2x+3
x^2+2x-3
x^3+2x^2-3x
x^3+2x-3
Is it the third one?
no, do the actual division to find the correct answer.
The last one?
It will start with x^3 and end with - 3 :)
note -3 * -6 = +18 has to be there
go here:
https://www.wolframalpha.com/topdoit
put in this:
(x^4-6x^3+2x^2-15x+18)/(x-6)
get this:
x^3 + 2 x - 3
Thanks you
To find the quotient of the polynomial (x^4−6x^3+2x^2−15x+18) divided by (x−6), you can use long division.
1. Begin by writing the dividend (x^4−6x^3+2x^2−15x+18) and divisor (x−6) in long division format:
________________
x - 6 | x^4 - 6x^3 + 2x^2 - 15x + 18
2. Divide the first term of the dividend (x^4) by the divisor (x), which gives x^3. Write this as the first term of the quotient above the line:
x^3
________________
x - 6 | x^4 - 6x^3 + 2x^2 - 15x + 18
3. Multiply the divisor (x−6) by the quotient term (x^3), which gives (x^3 - 6x^2). Write this below the dividend and subtract it from the dividend:
x^3
________________
x - 6 | x^4 - 6x^3 + 2x^2 - 15x + 18
- (x^3 - 6x^2)
________________
4. Bring down the next term of the dividend (-6x^2) and repeat the process:
x^3 + 6x^2
________________
x - 6 | x^4 - 6x^3 + 2x^2 - 15x + 18
- (x^3 - 6x^2)
________________
0 - 12x^2
5. Continue this process for the remaining terms of the dividend:
x^3 + 6x^2 - 12x
6. Finally, bring down the last term of the dividend (+18) and complete the division:
x^3 + 6x^2 - 12x + 18
Therefore, the correct quotient is x^3 + 6x^2 - 12x + 18. Looking at the multiple-choice options, none of them match the correct quotient.