Question

divide (x^3-6x^2+11x-6) by (x-3)​

Answer 1

hi mate,

que. divide (x^3-6x^2+11x-6) by (x-3)

Polynomial Long Division

Dividing : x^3 - 6x^2 + 11x - 6

("Dividend")

By : x - 3 ("Divisor")

dividend x^3 - 6x^2 + 11x - 6

- divisor * x^2 x^3 - 3x^2

remainder - 3x^2 + 11x - 6

- divisor * -3x^1 - 3x^2 + 9x

remainder 2x - 6

- divisor * 2x^0 2x - 6

remainder 0

Quotient : x^2-3x+2 Remainder: 0

Factoring x^2-3x+2

The first term is, x^2 its coefficient is 1 .

The middle term is, -3x its coefficient is -3 .

The last term, "the constant", is +2

Step-1 : Multiply the coefficient of the first term by the constant 1 • 2 = 2

Step-2 : Find two factors of 2 whose sum equals the coefficient of the middle term, which is -3 .

-2 + -1 = -3 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -2 and -1

x^2 - 2x - 1x - 2

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x-2)

Add up the last 2 terms, pulling out common factors :

1 • (x-2)

Step-5 : Add up the four terms of step 4 :

(x-1) • (x-2)

Which is the desired factorization

Final result :

(x - 1) • (x - 2)

i hope it helps you.