-2 is a zero of f left parenthesis x right parenthesis space equals space x cubed plus 7 x squared plus 4 x minus 12 , solve the equation x cubed plus 7 x squared plus 4 x minus 12 equals 0 .
The equation is: f(x) = x^3 + 7x^2 + 4x - 12
Since x = -2 is a zero of the expression, then (x + 2) is a factor of the expression.
Dividing (x + 2) into the expression, as shown below.
x^2 + 5x – 6
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x + 2) x^3 + 7x^2 + 4x – 12
x^3 + 2x^2
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5x^2 + 4x
5x^2 + 10x
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-6x – 12
-6x – 12
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0
Our expression now becomes (x + 2)(x^2 + 5x – 6)
Which further factorises to (x + 2)(x – 1)(x + 6)
Solutions are: x = -2, x = 1, x = -6