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Algebra

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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.

Feb 6, 2020

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(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

___________________

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

Feb 6, 2020