A-Level Edexcel Maths Pure Exponential & Logarithms: Given that $$rac{2x^4

Given that $$rac{2x^4 - 3x^3 + x + 1}{x^2 - 1} = (ax^2 + bx + c) + \frac{dx + e}{x^2 - 1},$$ find the values of the constants a, b, c, d and e. - Edexcel - A-Level Maths Pure - Question 3 - 2008 - Paper 6

Question 3

$Given-that--$$-rac{2x^4---3x^3-+-x-+-1}{x^2---1}-=-(ax^2-+-bx-+-c)-+-\frac{dx-+-e}{x^2---1},$$--find-the-values-of-the-constants-a,-b,-c,-d-and-e.-Edexcel-A-Level Maths Pure-Question 3-2008-Paper 6.png$

Given that $$rac{2x^4 - 3x^3 + x + 1}{x^2 - 1} = (ax^2 + bx + c) + \frac{dx + e}{x^2 - 1},$$ find the values of the constants a, b, c, d and e.

Worked Solution & Example Answer:Given that $$rac{2x^4 - 3x^3 + x + 1}{x^2 - 1} = (ax^2 + bx + c) + \frac{dx + e}{x^2 - 1},$$ find the values of the constants a, b, c, d and e. - Edexcel - A-Level Maths Pure - Question 3 - 2008 - Paper 6

Step 1

Find the value of a

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Answer

To find the value of a, we first notice that the numerator on the left must be a polynomial of degree 2 when we perform polynomial long division. Since the term with the highest degree on the left is $2x^4$ , we match the leading coefficients. Therefore, we have:

$a = 2.$

Step 2

Find the value of c

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Answer

Now we consider the constant term matching. By comparing the constant terms of both sides as we simplify the left side, we find:

$c = -1.$

Step 3

Find the values of b, d, and e

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Answer

After determining a and c, we can substitute back into the equation and compare remaining terms. This gives:

For $b$ , it is determined to be 0,
For $d$ , we find it to be 1,
For $e$ , we can conclude it is 0.

Thus, we have:

$a = 2, \, b = 0, \, c = -1, \, d = 1, \, e = 0.$

Given that $$ rac{2x^4 - 3x^3 + x + 1}{x^2 - 1} = (ax^2 + bx + c) + \frac{dx + e}{x^2 - 1},$$ find the values of the constants a, b, c, d and e. - Edexcel - A-Level Maths Pure - Question 3 - 2008 - Paper 6

Worked Solution & Example Answer:Given that $$ rac{2x^4 - 3x^3 + x + 1}{x^2 - 1} = (ax^2 + bx + c) + \frac{dx + e}{x^2 - 1},$$ find the values of the constants a, b, c, d and e. - Edexcel - A-Level Maths Pure - Question 3 - 2008 - Paper 6

Find the value of a

Find the value of c

Find the values of b, d, and e

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Given that $$rac{2x^4 - 3x^3 + x + 1}{x^2 - 1} = (ax^2 + bx + c) + \frac{dx + e}{x^2 - 1},$$ find the values of the constants a, b, c, d and e. - Edexcel - A-Level Maths Pure - Question 3 - 2008 - Paper 6

Worked Solution & Example Answer:Given that $$rac{2x^4 - 3x^3 + x + 1}{x^2 - 1} = (ax^2 + bx + c) + \frac{dx + e}{x^2 - 1},$$ find the values of the constants a, b, c, d and e. - Edexcel - A-Level Maths Pure - Question 3 - 2008 - Paper 6