+193 Question 1 Fill in the numbered blanks to complete the long division process.
Divide x2 + 2x – 30 by x – 5
Step 1
x
X – 5 x2 + 2x - 30
x2 - (1) Multiply x (x – 5)
(2) - (3)
Subtract (x2 + 2x) – (x2 – 5x) and bring down -30
What values should go in these numbered blanks?
________________
_________________
_________________
Step 2 (from Step 1 above)
X + 7
X – 5 x2 + 2x - 30
x2 - 5x
7x - 30
‘(4) - (5) Multiply 7 (x – 5)
(6) Subtract (7x – 30) – (7x – 35)
What values should go in these numbered blanks?
(4) ________________
(5)_________________
(6)_________________
What is the remainder after step 2? __________________________________
Problem 2…. Find all the zeros of the function:
X3 – 4x2 + x + 6 = 0
Use whatever methods you like, and explain how you found the zeros.
+129852 (1) 5x
(2) 7x
(3) 30
(4) 7x
(5) 35
(6) 5
Remainder = 5
Second one
x^3 - 4x^2 + x + 6 = 0
Note that.....using the Rational Zeros Theorem that 2 is a root (a zero)
So using synthetic division to find the remaing polynomial we have that
2 [ 1 - 4 1 6 ]
2 -4 -6
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1 -2 -3 0
The remaining polynomial is x^2 - 2x - 3
Set to 0 and we have that
x^2 - 2x - 3 = 0 factor
(x - 3) ( x + 1) = 0
Set each factor to 0 and solve for x and the other two zeros are 3 and -1
So....the zeros are
-1 , 2 and 3
