The correct linear factors are:
A: (x+1)
E: (x+4)
G: (x+8)
To find the other linear factors of the polynomial function A(x) = x² -
when (x+5) is a factor, we can use polynomial long division or synthetic division. I'll use synthetic division here.
Write the coefficients of the polynomial:
1,-2,-21, 22, 40
Since (x+5) is a factor, perform synthetic division with -5:
-5 1 -2 -21 22 40
-5 35 -5 -85
The result indicates that the quotient is x³-7x² + 4x +8.
Now, we want to find the remaining linear factors of this quotient.
The given options are:
A: (x + 1)
B: (x−1)
C: (x+2)
D: (x−2)
E: (x+4)
F: (x-4)
G: (x+8)
We can test each option by synthetic division or polynomial long division to see which one is a factor.
Let's start with option A, (x+1):
-1 1 -7 4 8
-1 8 -12
The result indicates that (x+1) is a factor of the quotient, so it is also a factor of the original polynomial A(x).
Therefore, the correct linear factors are:
A: (x+1)
E: (x+4)
G: (x+8)
Question
or the polynomial function a(x)=x^4-2x^3-21x^2+22x+40 we know(x+5)is a factor.Select all the other linear factors of A(x).
A: (x + 1)
B: (x - 1)
C: (x + 2)
D: (x - 2)
E: (x + 4)
F: (x - 4)
G: (x + 8)