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Which of the following is a polynomial factor of x2 - 2x - 24?
- a)x - 4
- b)x + 4
- c)x + 6
- d)6 - x
- e)x
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Which of the following is a polynomial factor of x2 - 2x - 24?a)x - 4b...
To solve this problem it is necessary to factor the polynomial x2 − 2x − 24. In this case, since the final term is negative, you know that when this equation is factored, one sign will be positive and the other will be negative. Further, since the term is −24, the numbers in the problem will be factors of 24. The factors of 24 are 1 and 24, 2 and 12, 3 and 8, or 4 and 6. It is logical to look for the factors that have a difference of 2 because of the −2x term in the original polynomial. In this case, 4 and 6 are the only factors of 24 that have a difference of 2. Because the term -2x is negative, the logical expression is (x + 4)(x - 6). Therefore, x + 4 is the correct answer choice.
Community Answer
Which of the following is a polynomial factor of x2 - 2x - 24?a)x - 4b...
Explanation:
To find the polynomial factor of the quadratic equation x^2 - 2x - 24, we need to factorize the equation.
We can factorize the equation by using the quadratic formula or by factoring the equation directly.
Factoring the equation directly:
To factorize the equation directly, we need to find two numbers whose product is -24 and whose sum is -2.
The two numbers that satisfy these conditions are -6 and 4.
Therefore, the factored form of the equation is:
(x - 6)(x + 4)
Now, we can see that (x + 4) is one of the factors of the equation x^2 - 2x - 24.
Checking the options:
a) x - 4: This is not a factor of the equation because the equation has a positive coefficient for x^2, so the factor should have a positive value for x.
b) x + 4: This is a factor of the equation as we found in the factoring process.
c) x + 6: This is not a factor of the equation because the equation has a negative coefficient for x, so the factor should have a negative value for x.
d) 6 - x: This is not a factor of the equation because the equation has a negative coefficient for x, so the factor should have a negative value for x.
e) x: This is not a factor of the equation because the equation has a constant term -24, so the factor should have a non-zero constant term.
Therefore, the correct answer is option 'B' (x + 4).
To find the polynomial factor of the quadratic equation x^2 - 2x - 24, we need to factorize the equation.
We can factorize the equation by using the quadratic formula or by factoring the equation directly.
Factoring the equation directly:
To factorize the equation directly, we need to find two numbers whose product is -24 and whose sum is -2.
The two numbers that satisfy these conditions are -6 and 4.
Therefore, the factored form of the equation is:
(x - 6)(x + 4)
Now, we can see that (x + 4) is one of the factors of the equation x^2 - 2x - 24.
Checking the options:
a) x - 4: This is not a factor of the equation because the equation has a positive coefficient for x^2, so the factor should have a positive value for x.
b) x + 4: This is a factor of the equation as we found in the factoring process.
c) x + 6: This is not a factor of the equation because the equation has a negative coefficient for x, so the factor should have a negative value for x.
d) 6 - x: This is not a factor of the equation because the equation has a negative coefficient for x, so the factor should have a negative value for x.
e) x: This is not a factor of the equation because the equation has a constant term -24, so the factor should have a non-zero constant term.
Therefore, the correct answer is option 'B' (x + 4).
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Which of the following is a polynomial factor of x2 - 2x - 24?a)x - 4b)x + 4c)x + 6d)6 - xe)xCorrect answer is option 'B'. Can you explain this answer?
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