To find the value of "p" from the polynomial x^2 + 3x + p, if one of the zeroes of the polynomial is 2, we can use the fact that if 2 is a zero of the polynomial, then (x - 2) is a factor of the polynomial.
So, let's divide the polynomial x^2 + 3x + p by (x - 2) using polynomial long division:
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(x - 2) | x^2 + 3x + p
- (x^2 - 2x)
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5x + p
- (5x - 10)
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p + 10
The remainder of the division is p + 10.
Now, since 2 is a zero of the polynomial, the remainder of the division should be zero. Therefore, we can equate the remainder to zero:
p + 10 = 0
Solving for "p", we subtract 10 from both sides:
p = -10
So, the value of "p" is -10.
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