Question

Factorise by using the factor theorem
x^3-x^2-14x+24​

Answer 1

ＳＯＬＵＴＩＯＮ :

Let,

p(x) = x^3 - x² -14x +24

FACTOR THEOREM :

If the remainder F(r) = R =0 , then (x -r) is a factor of f(x) .

Therefore,

substitute x = 2 in p(x)

p(x) = 3^3 - 3²- 14(3) +24

p ( 3) = 27-9-42-24

p(3) = 0

Thus x = -3 is a factor of p(x)

Substitute x = -4 in p (x)

p(-4) = -43-(-4²) -14 (-4) + 24

p(-4) = 0

THUS x + 4IS A FACTOR OF p(x)

SO, THE FACTORED FORM IS :

p(x) = (x-2) (x-3) (x+4)

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