Factorise x3 + 6x2 + 11x + 6 completely using factor theorem.

Factorise x³ + 6x² + 11x + 6 completely using factor theorem.

Sum

Let f(x) = x³ + 6x² + 11x + 6

For x = –1

f(–1) = (–1)³ + 6(–1)² + 11(–1) + 6

= –1 + 6 – 11 + 6

= 12 – 12

= 0

Hence, (x + 1) is a factor of f(x).

x² + 5x + 6
`x + 1")"overline(x^3 + 6x^2 + 11x + 6)`
x³ + x²
5x² + 11x
5x² + 5x
6x + 6
6x + 6
0
∴ x³ + 6x² + 11x + 6 = (x + 1)(x² + 5x + 6)

= (x + 1)(x² + 2x + 3x + 6)

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

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

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Applications of Factor Theorem

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