A polynomial expression is shown below: 5w(-7w + 3) + pw(-pw^2 + 19w + p) The expression is simplified to -4w^3 + 3w^2 + 19w. Find the value of p.

A polynomial expression is shown below:

5w(-7w + 3) + pw(-pw^2 + 19w + p)

The expression is simplified to -4w^3 + 3w^2 + 19w.  Find the value of p.

p=___

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1 Answer

p=2 as shown below:

Expand: -35w^2+15w-p^2w^3+19w^2p+p^2w=-4w^3+3w^2+19w.

Equating coefficient: w^3: -p^2=-4, so p=2 or -2.

w^2: 3=19p-35. 19p=38 so p=2.

w: 15+p^2=19, p^2=4, so p=2 is a solution. Overall p=2.
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