Answer:
Step-by-step explanation:
We are given that the polynomial:
Has the remainder (<em>a</em> + 2) when divided by (<em>x</em> - <em>a</em>), and we want to determine the value of <em>a</em>.
Recall that from the Polynomial Remainder Theorem, when dividing a polynomial P(x) by a binomial (<em>x</em> - <em>a</em>), the remainder will be given by P(a).
Since the remainder is (<em>a</em> + 2) when divided by (<em>x</em> - <em>a</em>), P(a) must equal (<em>a</em> + 2):
Substitute:
Simplify and solve for <em>a: </em>
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In conclusion, the value of <em>a</em> is 4.