Partial fractions: distinct, repeated and quadratic factors: check 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
Decompose \(\displaystyle \frac{23 x^{2} + 5 x + 81}{x^{3} + 3 x^{2} + 4 x + 12}\) in the stated form \(\displaystyle \frac{A}{x + 3} + \frac{B x + C}{x^{2} + 4}\).
Find A.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Partial fractions: distinct, repeated and quadratic factors: review variant 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
Decompose \(\displaystyle \frac{23 x^{2} + 211 x + 408}{x^{3} + 10 x^{2} + 27 x + 18}\) in the stated form \(\displaystyle \frac{A}{x + 1} + \frac{B}{x + 3} + \frac{C}{x + 6}\).
Find A.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Partial fractions: distinct, repeated and quadratic factors: check 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
Decompose \(\displaystyle \frac{23 x^{2} + 211 x + 408}{x^{3} + 10 x^{2} + 27 x + 18}\) in the stated form \(\displaystyle \frac{A}{x + 1} + \frac{B}{x + 3} + \frac{C}{x + 6}\).
Find B.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Partial fractions: distinct, repeated and quadratic factors: review variant 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
Decompose \(\displaystyle \frac{27 x^{2} + 205 x + 394}{x^{3} + 10 x^{2} + 32 x + 32}\) in the stated form \(\displaystyle \frac{A}{x + 2} + \frac{B}{x + 4} + \frac{C}{\left(x + 4\right)^{2}}\).
Find B.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Partial fractions: distinct, repeated and quadratic factors: check 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
Decompose \(\displaystyle \frac{27 x^{2} + 205 x + 394}{x^{3} + 10 x^{2} + 32 x + 32}\) in the stated form \(\displaystyle \frac{A}{x + 2} + \frac{B}{x + 4} + \frac{C}{\left(x + 4\right)^{2}}\).
Find C.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Partial fractions: distinct, repeated and quadratic factors: review variant 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
Decompose \(\displaystyle \frac{29 x^{2} + 11 x + 588}{x^{3} + 3 x^{2} + 25 x + 75}\) in the stated form \(\displaystyle \frac{A}{x + 3} + \frac{B x + C}{x^{2} + 25}\).
Find C.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Partial fractions: distinct, repeated and quadratic factors: check 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
Decompose \(\displaystyle \frac{29 x^{2} + 11 x + 588}{x^{3} + 3 x^{2} + 25 x + 75}\) in the stated form \(\displaystyle \frac{A}{x + 3} + \frac{B x + C}{x^{2} + 25}\).
Find the value of the rational function at \(\displaystyle x=0\).
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Partial fractions: distinct, repeated and quadratic factors: review variant 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
Decompose \(\displaystyle \frac{30 x^{2} + 263 x + 483}{x^{3} + 10 x^{2} + 27 x + 18}\) in the stated form \(\displaystyle \frac{A}{x + 1} + \frac{B}{x + 3} + \frac{C}{x + 6}\).
Find the value of the rational function at \(\displaystyle x=0\).
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.