Consider the polynomials
Find c such that the polynomial f(x)+cg(x) has degree 3.
f(x) = 1 - 12x + 3x2 - 4x3 + 5x4 g(x) = 3 - 2x - 6x3 + 9x4
Find c such that the polynomial f(x) + c·g(x) has degree 3.
To have degree 3 means that the result must have a term or degree 3 and no term with a deree larger than 3.
So, we need a value for c such that when multiplied by the fourth-degree term of g(x) and added to the
fourth-degree term of f(x) those fourth-degree terms will cancel.
Try - 5/9 --->
( 1 - 12x + 3x2 - 4x3 + 5x4 ) + (-5/9) · ( 3 - 2x - 6x3 + 9x4 )
= 1 - 12x + 3x2 - 4x3 + 5x4 - (5/9)(3) - (5/9)(-2x) - (5/9)(-6x3) - (5/9)(9x4)
(I'll let you finish.)