Q1: Dividend = f(x) = 2x^3-7x^2+12x-13
Q2: x+1 is not a factor of f(x) = x^99 - 2x^98 + 1
Q3: p(-3) = 93
Further explanation:
Question No. 1:
Find f(x) if the remainder is -4 when f(x) is divided by (2x-3) and the quotient is x^2 - 2x + 3
Here
[tex]Divisor = 2x-3\\Remainder = -4\\Quotient = x^2-2x+3[/tex]
We have to find the dividend which was the original function
So,
[tex]Dividend=(divisor * Quotient)+ Remainder\\= [(2x-3)*(x^2-2x+3)]+(-4)\\=[2x(x^2-2x+3)-3(x^2-2x+3)]-4\\=2x^3-4x^2+6x-3x^2+6x-9]-4\\=[2x^3-4x^2-3x^2+6x+6x-9]-4\\=2x^3-7x^2+12x-9-4\\=2x^3-7x^2+12x-13[/tex]
Question No. 2:
Is (x+1) a factor of f(x) = x^99 - 2x^98 + 1?
In order to check this we will put x+1 =0,
x=-1 in f(x)
So,
[tex]f(x) = x^{99} - 2x^{98} + 1\\f(-1) = (-1)^{99}-2(-1)^{98} +1\\= -1-2(1)+1\\= -1-2+1\\=-3+1\\=-2 \neq 0[/tex]
So, x+1 is not a factor of given function.
Question No. 3:
Find p(-3) by SYNTHETIC DIVISION for p(x) = -4x^3 + 4x - 3
The solution is attached in the form of picture.
Hence, p(-3) = 93
Keywords: Synthetic Division, Remainder theorem, polynomials
Learn more about polynomials at:
- brainly.com/question/12700460
- brainly.com/question/1414350
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