The polynomial p(x) = 5x^3 – 44x^2 + 61x + 14 has a known factor of (x – 7).
Rewrite p(x) as a product of linear factors.
p(x) =

The rewrite p(x) as a product of linear factors p(x) =(x-7)(5x+1)(x-2).

Given that,

Based on the above information, the calculation is as follows:

Here we have to divide the (x - 7) from the given equation

Now if we divide it we get .

Now we have to factor the above equation.

So,

= 5x(x-2) + 1(x-2)

= (5x+1)(x-2)

Therefore we can conclude that the rewrite p(x) as a product of linear factors p(x) =(x-7)(5x+1)(x-2).

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p(x)=(x-7)(5x+1)(x-2)

Step-by-step explanation:

divide p(x) by (x-7) we got, 5x^2-9x-2

now it can further factoriesd as

5x^2-10x+x-2

=5x(x-2)+1(x-2)

=(5x+1)(x-2)

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step-by-step explanation: