Properties of polynomials (1 Viewer)

[xibu34]

Really struggling to solve this problem as the textbook only has a example solution which doesn't really explain anything.
I understand the concept that like powers share the same coefficients but don't know how to go about applying it. I could only really get a=1, b=2
(Equal sign should be congruent sign)

Find the values of a,b and c if:

 

[kirbei.17]

since c is a constant (coefficient of the x^0 term), you can compare the constant terms when expanded.
Looking at it, the right hand side for constants only would be a +b +c and since you found what a and b were, comparing the left hand side with right hand side we will have -3 = 1 + 2 + c
Therefore, c is -6

Hopefully you understand! good luck with the rest of the course

 

[Eagle Mum]

LHS = x^2 +4x - 3
By expansion, RHS = a^2x^2 + 2ax + a + bx + b + c
Rearranging RHS to group coefficients of the same powers of x: a^2x^2 + (2a + b)x + (a + b + c)

Matching coefficients of LHS with RHS, you essentially have three simultaneous equations to solve for a, b & c:
x^2 = a^2x^2 a^2 = 1 a=1
4x = (2a+b)x 2a+b = 4 Since a =1, b=2
a+b+c = -3 Since a=1, b=2, 1+2+c = -3, c=-6 as per kerbei.17

 

[xibu34]

since c is a constant (coefficient of the x^0 term), you can compare the constant terms when expanded.
Looking at it, the right hand side for constants only would be a +b +c and since you found what a and b were, comparing the left hand side with right hand side we will have -3 = 1 + 2 + c
Therefore, c is -6

Hopefully you understand! good luck with the rest of the course

Yeah I get it now, I hope i do well i guess i'll just have to study harder.