Suku banyak f(x) , jika dibagi (x-1) sisanya 4 dan dibagi (x-2) sisanya 5. jika f(x) dibagi (x^(2)-3x+2) sisanya adalah A 3x-1 . B x-3 . C x+3 . D 3x+1 . E -x+3 .

Question

Pertanyaan

Suku banyak f(x) , jika dibagi (x-1) sisanya 4 dan dibagi (x-2) sisanya 5. jika f(x) dibagi (x^(2)-3x+2) sisanya adalah A 3x-1 . B x-3 . C x+3 . D 3x+1 . E -x+3 .

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Answer 1

The problem statement indicates that a polynomial, f(x), leaves a remainder of 4 when divided by (x-1) and a remainder of 5 when divided by (x-2). Thus, we can use the Remainder Theorem, which states that the remainder resulted from the division of a polynomial f(x) by a binomial (x-a) is f(a).

When divided by (x-1), the remainder is 4, which implies that:
f(1) = 4
When divided by (x-2), the remainder is 5, which implies that:
f(2) = 5

Therefore when the polynomial is divided by the quadratic equation \(x^2 - 3x + 2\) (which is factored into (x-1)(x-2)), the remainder can be found by employing polynomial long division.

Therefore we can put 1 in x which will give f(1) =4 and we can use the equation mx+c=y which gives m+c=4. Now suddenly we can put 2 in x which will give f(2)=5 giving 2m+c=4. therefore we can solve the two equations together. So our remainder f(x) or the function will turn into 3x+1. Hence option D.

Pertanyaan

Suku banyak f(x) , jika dibagi (x-1) sisanya 4 dan dibagi (x-2) sisanya 5. jika f(x) dibagi (x^(2)-3x+2) sisanya adalah A 3x-1 . B x-3 . C x+3 . D 3x+1 . E -x+3 .

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