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The polynomial function p(x)=x3-3x2 - 10x +24 has a known factor of (x-4) rewrite p(x) as the product of linear factors

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Answer:

The polynomial p(x) can be rewritten as:

p(x) = (x - 4)((3 + sqrt(33))/2 - (3 - sqrt(33))/2)

= (x - 4)(sqrt(33))

The polynomial p(x) can also be rewritten as:

p(x) = (x - 4)(sqrt(11) - sqrt(3))(sqrt(11) + sqrt(3))

= (x - 4)(sqrt(11) - sqrt(3))(sqrt(11) + sqrt(3))

This shows that the polynomial p(x) can be written as the product of linear factors.

Explanation:

To rewrite the polynomial function p(x) as the product of linear factors, we need to factor out the known factor of (x - 4) from the polynomial. The polynomial p(x) can be written as:

p(x) = (x - 4)(x^2 - 3x - 6)

The polynomial x^2 - 3x - 6 can be rewritten as the product of two linear factors using the quadratic formula:

x^2 - 3x - 6 = 0

x = (3 +/- sqrt(3^2 - 4 * 1 * -6)) / (2 * 1)

x = (3 +/- sqrt(9 + 24)) / 2

x = (3 +/- sqrt(33)) / 2

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