SOLUTION: The function f is given by f(x)=x^3+2x^2+ax-8 where a is constant.when f(x) is divided by (x-2)the remainder is -6.
Show that a=-7
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-> SOLUTION: The function f is given by f(x)=x^3+2x^2+ax-8 where a is constant.when f(x) is divided by (x-2)the remainder is -6.
Show that a=-7
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Question 1159544: The function f is given by f(x)=x^3+2x^2+ax-8 where a is constant.when f(x) is divided by (x-2)the remainder is -6.
Show that a=-7 Answer by ikleyn(52780) (Show Source):
According to the Remainder theorem, the fact that the remainder is -6, when f(x) is divided by (x-2), means that f(2) = -6.
In other words,
2^3 + 2*2^2 + a*2 - 8 = -6.
It implies
2a = -6 - 2^3 - 2*2^2 + 8 = -14.
Hence, a = -14/2 = -7. ANSWER
Solved.
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Theorem (the remainder theorem)
1. The remainder of division the polynomial by the binomial is equal to the value of the polynomial.
2. The binomial divides the polynomial if and only if the value of is the root of the polynomial , i.e. .
3. The binomial factors the polynomial if and only if the value of is the root of the polynomial , i.e. .
