AS Core Maths - Polynomials?
f(x) = x^3+ax+b, where a and b are constants.
It is given that (x+1) is a factor of f(x) and that the remainder when f(x) is divided by (x-3) is 16
1)Find the values of a and b
2)hence, verify that f(2)=0 and factorise f(x) completely
step by step answer guide please
Thanks!!
More Questions From This User See All
Answers & Comments
Verified answer
since x+`1 is a factor
f(-1)=0 there fore
-1 -a +b = 0
and f(3)=16
27 +3a + b = 16
use tgose equation to findthe a and b
a =-3 b = -2
f(x) = x3 -3x -2
f2 =
fx =x3 -3x -2= (x-2)(x=1))(AX- B) = (x2 -x -2)(x+1)
Adam has spoke back the biggest factors for the two components. For the 2d area, if 2x - a million is a ingredient then whilst we positioned 2x - a million = 0 ; x = ½ and replace this cost interior the polynomial then, ax³ + bx² - 13x + 6 = 0 a/8 + b/4 - 6½ + 6 = a/8 + b/4 - ½ = 0 and multiplying in the process by using 8 provides, a + 2b - 4 = 0 yet, Adam has shown that a = b + a million, and subsequently, b + a million + 2b - 4 = 0 : 3b - 3 = 0 : b = a million....and so a = 2 The polynomial can then be written : 2x³ + x² - 13x + 6.