Question

Using factor theorem, show that (x-3) is a factor of x3 – 7x2 + 15x - 9. Hence,

factorize the complete expression completely​

Answer 1

Answer:

x - 3 = 0

x = 3

(3)³ -7(3)² +15(3) -9

= 27 - 63 +45 -9

=0

hence it is a factor

Step-by-step explanation:

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Answer 2

Answer:

let f(x) = x^3 - 7x^2 - 15x - 9

for checking that (x - 3) is a factor of f(x), we find : f(3)

f(3) = (3)^3 - 7(3)^2 + 15(3) - 9

= 27 - 63 - 45 - 9

= 72 - 72

= 0

hence, (x-3) is a factor of f(x)

by division of f(x) by x-3, we get the quotient = x^2 - 4x + 3

therefore x^3 -7x^2 + 15x - 9

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

=(x-3)(x-3)(x-1)

=(x-3)^2 (x-1)

Step-by-step explanation:

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