Polynomials help please =) (1 Viewer)

[lpodnano]

If (x-5)(x-3)=(x-4)(x-2)-A(x-4)-B(x-5) is an identity in x, find the values A and B.


Find the values A,B and C if x(squared) ≡ A(x+1)(x+2)+B(x+2)(x+3)+C(x+3)(x+1).

Show working out please =) And thanks in advance.

 

[ninetypercent]

Let x = 4

RHS = (4-5)(4-3)
= -1
LHS = (4-4)(4-2) - A(4-4) - B(4-5)
= B

therefore, B = -1

Let x = 2

LHS = (2-5)(2-3)
= 3

RHS = (2-4)(2-2) - A(2-4) + 1(2-5)
= 2A - 3

2A - 3 = 3
2A = 6
A = 3

 

[ninetypercent]

Find the values A,B and C if x(squared) ≡ A(x+1)(x+2)+B(x+2)(x+3)+C(x+3)(x+1).

Let x = - 1

LHS = 1

RHS = B(-1+2)(-1+3)
= 2B

Equating coefficients

2B = 1
B = 1/2

Let x = -3

LHS = 9

RHS = A (-3+1)(-3+2)
= A(-2)(-1)
= 2A

2A = 9
A = 4.5

Let x = -2

LHS = 4

RHS = C(-2+3)(-2+1)
= C(1)(-1)
= - C

-C = 4
C = -4