Question

(x4−5x3−8x2+13x−12)÷(x−6)

Answer 1

To divide a polynomial by a binomial, use polynomial long division. The result of dividing (x^4−5x^3−8x^2+13x−12) by (x−6) is x^3+x^2-2x+3 with a remainder of -6.

Step-by-step explanation:

To divide a polynomial by a binomial, you can use polynomial long division. First, write the dividend and divisor in descending order of exponents. Then, divide the first term of the dividend by the first term of the divisor to get the first term of the quotient. Multiply the divisor by the first term of the quotient and subtract the result from the dividend. Repeat this process with the new dividend until all terms have been divided.

Using polynomial long division, the result of dividing (x4−5x3−8x2+13x−12) by (x−6) is x3+x2-2x+3 with a remainder of -6.

Answer 2

`(x\cdot \:4-5x\cdot \:3-8x\cdot \:2+13x-12)/(x-6) \ \textgreater \ x\cdot \:4-5x\cdot \:3-8x\cdot \:2+13x-12`


`\mathrm{Add\:similar\:elements:}\:4x+13x=17x \ \textgreater \ 17x-3\cdot \:5x-2\cdot \:8x-12`


`\mathrm{Refine\; it} \ \textgreater \ 17x-15x-16x-12`


`\mathrm{Add\:similar\:elements:}\:17x-15x-16x= \ \textgreater \ -14x-12 \ \textgreater \ (-14x-12)/(x-6)`


`Therefore\;our\;final\;answer\;is\; (-14x-12)/(x-6)`

Hope this helps!