Question

2x^3-6x+5¡Ô(x-2)(2x^2+ax+2)+b
I'm afraid I'm not very good at identities... what is a? I think b=9...

Answer 1

I cant read it.

Answer 2

its 2x cubed minus 6x plus 5 equals (x plus 2)(2x squared plus ax plus 2) plus b.

Answer 3

2x^3-6x+5=(x+2)(2x^2+ax+2)+b
multiply out the right.
= 2x^3+2ax^2+2x+2x^2+2ax+4+b
now compare coefficents of x^n

2x^3=2x^3 checks.
X^2: 0=2a + 2 or a=-1 check that
x: -6 = 2+2a a=-1
constants: 5=4+b
so b= ....

Answer 4

" 2x^3-6x+5≡(x-2)(2x^2+ax+2)+b "
What you would do is to expand the right hand side to be
(x-2)*(2*x^2+a*x+2)+b
=2*x^3+(a-4)*x^2+(2-2*a)*x+b-4

So the identity becomes:
2x^3-6x+5≡2*x^3+(a-4)*x^2+(2-2*a)*x+b-4

Then you compare the coefficients of each term with the left hand side,
For x³, you have 2 on the left, which equals to 2 on the right.
Proceed with x²
you will establish the equation
0 = (a-4) by comparing the coefficients on each side of the ≡ sign.
That gives us a=4.
Continue this way to find b and confirm all terms of the identity are consistent.

Note: If your computer is set to have encoding in a foreign language, be sure to revert to Western 8859-1 encoding before writing Math symbols so everyone can read. On most browsers, it would be under "view-encoding" and then choose the encoding (for the current page only).