Question

Factorise completely x3+10x2+23x+14
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Answer 1

(x + 1(x + 2)(x + 7).

Explanation:

f(x) = x^3+10x^2+23x+14

Let x = -1, then:

f(-1) = (-1)^3+10(-1)^2+23(-1)x+14

= -1 + 10 - 23 + 13

= -14 + 14

= 0

So one zero is x = -1 and (x + 1) is one factor of f(x) ( by The Factor Theorem).

Dividing:

x + 1) x^3 + 10x^2 + 23x + 14 ( x^2 + 9x + 14 <------- Quotient

x^3 + x^2

9x^2 + 23x

9x^2 + 9x

14x + 14

14x + 14

. . . . . .

Now x^2 + 9x + 14

= (x + 2)(x + 7)

So the factors are:

(x + 1(x + 2)(x + 7)