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I don’t get 4 and 5 so can someone please help me

I don’t get 4 and 5 so can someone please help me-example-1
User Dmudro
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1 Answer

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a) We are given that f(x) = x^3 - 10x^2 + 19x + 30 and x - 6 is a factor of f(x). Using long division or synthetic division, we can divide f(x) by x - 6 to get the other factor(s):

6 │ x^3 - 10x^2 + 19x + 30

x^3 - 6x^2

-------------

-4x^2 + 19x

-(-4x^2 + 24x)

---------------

5x + 30

5x - 30

-------

0

Therefore, we can write:

f(x) = (x - 6)(x^2 - 4x + 5)

The quadratic factor x^2 - 4x + 5 cannot be factored further using real numbers.

b) We are given that f(x) = x^3 + 6x^2 + 5x - 12 and x + 4 is a factor of f(x). Using long division or synthetic division, we can divide f(x) by x + 4 to get the other factor(s):

-4 │ x^3 + 6x^2 + 5x - 12

-x^3 - 4x^2

--------------

2x^2 + 5x

2x^2 + 8x

------------

-3x - 12

-3x - 12

--------

0

Therefore, we can write:

f(x) = (x + 4)(x^2 + 2x - 3)

The quadratic factor x^2 + 2x - 3 can be factored further using the product-sum method:

x^2 + 2x - 3 = (x + 3)(x - 1)

Therefore, we have:

f(x) = (x + 4)(x + 3)(x - 1)

User Paul Van Jaarsveld
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