Kindly help with this:
x^3 + 7x^2 + ax - 5 = (x^2 + x - 2) f(x) + (x -1)(bx -1), find the value of a and b. I put an underscore on the equal sign as I don't have the similar symbol. The f(x) trips me up. Answer : ( a = -3 and b= 3) . Thanks. : )
Originally posted by Jt061952:Kindly help with this:
x^3 + 7x^2 + ax - 5 = (x^2 + x - 2) f(x) + (x -1)(bx -1), find the value of a and b. I put an underscore on the equal sign as I don't have the similar symbol. The f(x) trips me up. Answer : ( a = -3 and b= 3) . Thanks. : )
Hi Jt061952,
Since both sides are equivalent, the coefficient for all the polynomials will be the same.
Since there is a x^3 on the left side, there will similarly be a x^3 on the right side. Thus, we can deduce that f(x) has a x, since (x^2)(x) = x^3
Now, we need to find out if f(x) contains any number.
There is a -5 on the left, along with a -2f(x) and a +1 on the right side, thus, -5 = -2f(x) + 1, and the number in f(x) will be 3.
To conclude, f(x) = x + 3
Simplifying for the right side, we will get x^3 + (4+b)x^2 -bx -5.
Comparing coefficients with the left side, we will know that
4+b = 7, and thus b = 3
a = -b, and thus a = -3
Cheers.
Thanks Trueheart, got it. :)