Express the polynomial as a product of linear factors.
f(x) = 2x2 + 4x2 - 2x - 4
O A. (x-2)(x + 1)(x - 1)
O B. (x-2)(x-2)(x-1)
O c. 2(x + 2)(x + 1)(x-1)
O D. (x-4)(x + 1)(x-1)
Answers
I attached a photo with the procedure in case you need it
The polynomial f(x) = 2x³ + 4x² - 2x - 4 can be expressed as a product of linear factors as (x + 2)2(x - 1)(x + 1)
We have,
To express the polynomial f(x) = 2x³ + 4x² - 2x - 4 as a product of linear factors, we can use a technique called factorization by grouping.
First, let's group the first two terms and the last two terms together:
f(x) = (2x³ + 4x²) + (-2x - 4)
Factor out the greatest common factor from each group:
f(x) = 2x²(x + 2) - 2(x + 2)
Notice that we now have a common factor of (x + 2) in both terms.
We can factor it out:
f(x) = (x + 2)(2x² - 2)
Now we can factor the quadratic expression 2x^2 - 2 by factoring out the greatest common factor of 2:
f(x) = (x + 2)2(x² - 1)
Now we can factor the expression x² - 1 as the difference of squares:
f(x) = (x + 2)2(x - 1)(x + 1)
Therefore,
The polynomial f(x) = 2x³ + 4x² - 2x - 4 can be expressed as a product of linear factors as (x + 2)2(x - 1)(x + 1)
Learn more about polynomials here:
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Answer:
see explanation
Step-by-step explanation:
(a)
The student has distributed the second parenthesis by 1 instead of - 1
(b)
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Step-by-step explanation:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Learn with an example
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Hope this helps; have a great day!