Find out the sum by suitable arrangement. 1 + 2 + 3 + 4 + 5 + 95 + 96 + 97 + 98 + 99
2 answers:
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Answer:
Step-by-step explanation:
According to the Polynomial Remainder Theorem, if we have a polynomial P(x) divided by a binomial in the form of (<em>x</em> - <em>a</em>), then the remainder will be given by P(a).
And according to the Factor Theorem, if the remainder of P(x) / (<em>x</em> - <em>a</em>) is zero: that is, if P(a) = 0, then (<em>x</em> - <em>a</em>) is a factor of P(x).
We are given the polynomial:
And we know that it is divisible by:
We can rewrite our divisor as (<em>x</em> - (-2)). Hence, <em>a</em> = -2.
According to both the PRT and Factor Theorem, P(-2) must equal 0. Hence:
Substitute:
Solve for <em>k</em>. Simplify:
Hence: