Question

Using factor theorem factorise x^3+6x^2+11x+6.
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Answer 1

Hope it helps...!!!!!!

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Answer:

x^3+6x^2+11x+6=(x+1)(x+2)(x+3)

Explanation:

Given:

x^3+6x^2+11x+6

You are actually likely to encounter this pattern of coefficients 1,6,11,6 often.

For illustration purposes, let us see what happens if we start by applying a standard method used when solving a general cubic:


Tschirnhaus transformation

In order to simplify any cubic of the form ax^3+bx^2+cx+d we can apply a linear substitution t=x+b/3a to give a cubic in the form at^3+et+f with no quadratic term. This is the simplest form of Tschirnhaus transformation.

In our example, a=1 and b=6, so we want t=x+2.

Note that:

(x+2)^3=x^3+6x^2+12x+8

So we find:

x^3+6x^2+11x+6=(x+2)^3−(x+2)

=t^3−t

=t(t^2−1)

=t(t−1)(t+1)

=(x+2)(x+1)(x+3)

In more sensible order:

x^3+6x^2+11x+6=(x+1)(x+2)(x+3)


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Answer 2

Hello dear






Thanks !!