Question

f f(x)=5x^(3)+4x^(2)-13x-25 and f(x-3)=5x^(3)-41x^(2)+98x+k then k=

Answer 1

answer:

f(x) =5x^3-41x^2-13x-25

f(x-3)=5x^3-41x^2+98x+k

now,

f(x) =5x^3-41x^2-13x-25

f(x-3)=by Horner's process,

we get,

f(x-3)=5x^3-41x^2+98x-85

that implies,

5x^3-41x^2+98x+k=5x^3-41x^2+98x-85

k= -85

Answer 2

Concept:

By splitting the polynomial into monomials, Horner's method for polynomial division is an algorithm that makes it easier to evaluate a polynomial f(x) at a specific value of x = x0 (polynomials of the 1st degree). There can only be one addition and one multiplication operation per monomial. Synthetic division is another name for this division procedure. Find the polynomial's value for a given value of x given a polynomial of the form cnx^n + cn-1x^n-1 + cn-2x^n-2 +... + c1x + c0 and a value of x. In this case, n is a positive integer, while cn, cn-1,.. are integers (which may be negative).

Given:

This is the given question f(x)=5x^(3)+4x^(2)-13x-25 and f(x-3)=5x^(3)-41x^(2)+98x+k

Find:

We have to find the value of k.

Solution:

The given equation is,

f(x)=5x^(3)+4x^(2)-13x-25

and, f(x-3)=5(x-3)^(3)-41(x-3)^(2)+98(x-3)+k

Now, by applying Horner's method, we have:

f(x-3) = 5(x^3 -27 -9x^2 + 27x) + 4(x^2 + 9 -6x) -13x + 39 -25

f(x-3) = 5x^3 - 45x^2 + 135x - 135 + 4x^2 -24x + 36 - 13x + 39 -25

f(x-3) = 5x^3 - 41x^2 + 98x - 85

Here, we can see that in place of k it is -85,

Hence, k = -85 by applying Horner's method.

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