Question

Find the factors of 6x^3+x^2-11x-6

Answer 1

Step-by-step explanation:

Dividing : 6x3+x2-11x-6

("Dividend")

By : 2x-3 ("Divisor")

dividend 6x3 + x2 - 11x - 6

- divisor * 3x2 6x3 - 9x2

remainder 10x2 - 11x - 6

- divisor * 5x1 10x2 - 15x

remainder 4x - 6

- divisor * 2x0 4x - 6

remainder 0

Quotient : 3x2+5x+2 Remainder: 0

Answer 2

Answer:

The factors are 1, 2, and 3

Step-by-step explanation:

According to Factor theorem, if (x - a) is a polynomial factor f(x), then f(a) = 0

Let f(x) = x^{3}-6 x^{2}+11 x-6f(x)=x3−6x2+11x−6

Let us check if (x - 1) is the factor of f(x),

Then,

f(1) = 1^{3}-6\left(1^{2}\right)+11(1)-6=1-6+11-6=0f(1)=13−6(12)+11(1)−6=1−6+11−6=0

Therefore (x-1) is a factor of f(x)

Let us check for the other factors

Hence,

f(x)=(x-1)\left(x^{2}-5 x+6\right)f(x)=(x−1)(x2−5x+6)

x^{2}-5 x+6=x^{2}-2 x-3 x+6x2−5x+6=x2−2x−3x+6

=x(x-2)-3(x-2)=x(x−2)−3(x−2)

= (x - 2)(x - 3)=(x−2)(x−3)

f(x) = (x - 1)(x - 2)(x - 3)f(x)=(x−1)(x−2)(x−3)

Therefore, 1, 2, 3 are the factors of f(x)

Step-by-step explanation:

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