Partial Fractions – Algebraic Decomposition

STRUCTUREDMedium

Question

It is given that there exist constants $A$ and $B$ such that

x^3 + 8x^2 + 12x + 20 = A(x + 1)(x^2 + 4) + B(x^2 + 4) + 4(x + 1)^2

for all $x \in \mathbb{R}$ . Find the values of $A$ and $B$ . Hence, write down

\frac{x^3 + 8x^2 + 12x + 20}{(x + 1)^2(x^2 + 4)}

in partial fractions.

AlgebraPartial FractionsPolynomial Expansion

Related mathematics Questions(sorted by relevance)

Convert 16-bit Binary Number 1001 1010 1000 0010 to Decimal

Hard

Convert the 16-bit binary number:

1001\ 1010\ 1000\ 0010_2

into its decimal (base-10) equivalent.

binarydecimal

View

Finding the Centroid and Area of Triangle ABC Given Coordinates

Medium

If $A(6, 7)$ , $B(12, 9)$ , and $C(15, 8)$ , find the coordinates of the centroid and the area of triangle ABC

Coordinate GeometryTriangle

View

Forming a Cubic Polynomial with Known Remainders and Roots

Medium

A quadratic polynomial $G(x)$ has remainders $\frac{1}{3}$ , $\frac{1}{5}$ , and $\frac{1}{8}$ when divided by $(x - 1)$ , $(x - 3)$ , and $(x - 6)$ respectively. Show that $(x - 1)$ , $(x - 3)$ , and $(x - 6)$ are factors of the polynomial

f(x) = (x + 2)G(x) - 1

Hence, find $f(x)$

Partial FractionsPolynomialsRemainder Theorem

View

Finding Coefficients in a Cubic Polynomial Using Remainders

Medium

Let $f(x) = x^3 + 2x^2 + mx + n$ . When $f(x)$ is divided by $(x - 2)$ and $(x - 3)$ , the remainders are 33 and 70 respectively. Find the values of $m$ and $n$

PolynomialsSimultaneous Equations

View

View More Similar Questions

Partial Fractions – Algebraic Decomposition

Question

Related mathematics Questions(sorted by relevance)

Convert 16-bit Binary Number 1001 1010 1000 0010 to Decimal

Finding the Centroid and Area of Triangle ABC Given Coordinates

Forming a Cubic Polynomial with Known Remainders and Roots

Finding Coefficients in a Cubic Polynomial Using Remainders

Convert 16-bit Binary Number 1001 1010 1000 0010 to Decimal