Question

If x³ - 3x² + 3x - 7 = (x + 1)(ax² + bx +c)+d,then find (a + b + c+d)

Answer 1

Answer:

Required sum is - 10.

Step-by-step explanation:

= > x^3 - 3x^2 + 3x - 7 = ( x + 1 )( ax^2 + bx + c ) + d

= > x^3 - 3x^2 + 3x - 7 = ax^3 + ax^2 + bx^2 + bx + cx + c + d

= > x^3 - 3x^2 + 3x - 7 = ax^3 + ( a + b )x^2 + ( b + c )x + ( c + d )

Comparing both sides :

= > Coefficient of x^2 on LHS = Coefficient of x^2 on RHS

= > - 3 = a + b Or a + b = - 3 ...( 1 )

= > Constant term on LHS = constant term on RHS

= > - 7 = ( c + d ) Or c + d = - 7 ...( 2 )

Adding ( 1 ) and ( 2 ) :

= > a + b + c + d = - 3 - 7

= > a + b + c + d = - 10

Hence the required sum is - 10.

Answer 2

Question :--- If x³ - 3x² + 3x - 7 = (x + 1)(ax² + bx +c)+d,then find (a + b + c+d) ?

Answer :---

→ x³ - 3x² + 3x - 7 = (x + 1)(ax² + bx +c)+d

Multiplying RHS we get,

→ x³ - 3x² + 3x - 7 = ax³ + bx² + cx + ax² + bx + c + d .

→ x³ - 3x² + 3x - 7 = ax³ + bx² + ax² + cx + bx + c + d.

→ x³ - 3x² + 3x - 7 = ax³ + (b+a)x² + (c + b)x + c + d .

Comparing with Each Cofficient now , we get,

→ a = 1

→ (b+a) = (-3)

→ (c+b) = 3

→ (c+d) = (-7)

Adding (1) and (2) values we get, now,

→ (b+a) + (c+d) = (-3) + (-7)

→ (a+b+c+d) = (-10)

So, value of (a+b+c+d) is (-10)..