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8. Which of the following is a factor of the polynomial x2 + 3x - 18?
- a)x - 6
- b)x - 12
- c)x - 18
- d)x + 3
- e)x + 6
Correct answer is option 'E'. Can you explain this answer?
Most Upvoted Answer
8. Which of the following is a factor of the polynomial x2 + 3x - 18?a...
Factor of the polynomial x^2 + 3x - 18
To determine which of the given options is a factor of the polynomial x^2 + 3x - 18, we can use the factor theorem. According to the factor theorem, if a polynomial P(x) has a factor (x - a), then P(a) = 0.
We can substitute the given options into the polynomial and check if the result is equal to zero.
Let's check each option one by one:
Option A: x - 6
Substituting x - 6 into the polynomial: (x - 6)^2 + 3(x - 6) - 18
Expanding and simplifying: x^2 - 12x + 36 + 3x - 18 - 18
Combining like terms: x^2 - 9x
The result is not equal to zero, so x - 6 is not a factor of the polynomial.
Option B: x - 12
Substituting x - 12 into the polynomial: (x - 12)^2 + 3(x - 12) - 18
Expanding and simplifying: x^2 - 24x + 144 + 3x - 36 - 18
Combining like terms: x^2 - 21x + 90
The result is not equal to zero, so x - 12 is not a factor of the polynomial.
Option C: x - 18
Substituting x - 18 into the polynomial: (x - 18)^2 + 3(x - 18) - 18
Expanding and simplifying: x^2 - 36x + 324 + 3x - 54 - 18
Combining like terms: x^2 - 33x + 252
The result is not equal to zero, so x - 18 is not a factor of the polynomial.
Option D: x + 3
Substituting x + 3 into the polynomial: (x + 3)^2 + 3(x + 3) - 18
Expanding and simplifying: x^2 + 6x + 9 + 3x + 9 - 18
Combining like terms: x^2 + 9x
The result is not equal to zero, so x + 3 is not a factor of the polynomial.
Option E: x + 6
Substituting x + 6 into the polynomial: (x + 6)^2 + 3(x + 6) - 18
Expanding and simplifying: x^2 + 12x + 36 + 3x + 18 - 18
Combining like terms: x^2 + 15x + 36
The result is equal to zero, so x + 6 is a factor of the polynomial.
Therefore, the correct answer is option E, x + 6, which is a factor of the polynomial x^2 + 3x - 18.
Community Answer
8. Which of the following is a factor of the polynomial x2 + 3x - 18?a...
To solve this problem, factor the polynomial x2 + 3x - 18. To do so, think of x2 + 3x -18 as (x + ?)(x - ?). To fill in the question marks, find two numbers that multiply to equal -18 and add up to 3. One such pair of numbers is 6 and -3. To check, make sure that (x + 6)(x - 3) = x2 + 3x - 18, which it does. Of the answer choices, only (x + 6) is a factor.
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8. Which of the following is a factor of the polynomial x2 + 3x - 18?a)x - 6b)x - 12c)x - 18d)x + 3e)x + 6Correct answer is option 'E'. Can you explain this answer?
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