Partial fractions and binomial expansion: check 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
Decompose \(\displaystyle \frac{14 x^{2} + 142 x + 288}{x^{3} + 10 x^{2} + 27 x + 18}\) 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 and binomial expansion: review variant 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
Decompose \(\displaystyle \frac{20 x^{2} + 153 x + 294}{x^{3} + 10 x^{2} + 32 x + 32}\) in the stated form \(\displaystyle \frac{A}{x + 2} + \frac{B}{x + 4} + \frac{C}{\left(x + 4\right)^{2}}\).
Find 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 and binomial expansion: check 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
Decompose \(\displaystyle \frac{20 x^{2} + 153 x + 294}{x^{3} + 10 x^{2} + 32 x + 32}\) 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 and binomial expansion: review variant 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
Decompose \(\displaystyle \frac{22 x^{2} + 10 x + 156}{x^{3} + 3 x^{2} + 9 x + 27}\) in the stated form \(\displaystyle \frac{A}{x + 3} + \frac{B x + C}{x^{2} + 9}\).
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 and binomial expansion: check 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
Consider \(\displaystyle \frac{1}{4 x + 1}\) expanded in ascending powers of x.
Write \(\displaystyle a=4\) and \(\displaystyle r=\)\(-1\).
Find the coefficient of \(\displaystyle x^{3}\).
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 and binomial expansion: review variant 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
Consider \(\displaystyle \frac{1}{\left(5 x + 1\right)^{2}}\) expanded in ascending powers of x.
Write \(\displaystyle a=5\) and \(\displaystyle r=\)\(-2\).
Find the coefficient of \(\displaystyle x^{3}\).
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 and binomial expansion: check 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
Consider \(\displaystyle \frac{1}{\left(5 x + 1\right)^{2}}\) expanded in ascending powers of x.
Write \(\displaystyle a=5\) and \(\displaystyle r=\)\(-2\).
Find the positive radius of the validity interval.
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 and binomial expansion: review variant 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
Consider \(\displaystyle \left(6 x + 1\right)^{\frac{3}{2}}\) expanded in ascending powers of x.
Write \(\displaystyle a=6\) and \(\displaystyle r=\)\(\displaystyle \frac{3}{2}\).
Find the positive radius of the validity interval.
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.