Given that the polynomials f (x)=6-x-x^2 is a factor of the polynomials g (x)=ax^3+5x^2+bx=18 find:
The value of the constant a and b
The remainder when g (x)is divided by x+2
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Answer my question
impatient much?
You have
ax^3 + 5x^2 + bx - 18 = (-x^2-x+6)(mx+n)
Clearly,
n=3 and m = -a for the first and last terms to work out
Now, doing the multiplication, we get
g(x) = (-x^2-x+6)(-ax-3) = ax^3 + (a+3)x^2 + (3-6a)x - 18
So, a+3 = 5 ==> a=2
3-6a = -9
Thus, g(x) = 2x^3 + 5x^2 - 9x - 18 = (-x^2-x+6)(-2x-3)
You have
ax^3 + 5x^2 + bx - 18 = (-x^2-x+6)(mx+n)
Clearly,
n=3 and m = -a for the first and last terms to work out
Now, doing the multiplication, we get
g(x) = (-x^2-x+6)(-ax-3) = ax^3 + (a+3)x^2 + (3-6a)x - 18
So, a+3 = 5 ==> a=2
3-6a = -9
Thus, g(x) = 2x^3 + 5x^2 - 9x - 18 = (-x^2-x+6)(-2x-3)
The remainder when g ( x) is divided by x+2
Please could you make the answers clearer and in details
1 answer