Which of the following is a factor of the polynomial?
f(x)=x^3+6x^2+3x-10
A. (x+1)
B. (x-1)
C. (x-2)
D. (x-10)
y = (x - 1)(x + 2)(x + 5)
Explanation:
Since a + b + c + d = 0, f(1) = 0. One factor is (x - 1).
After division -->
y=(x−1)(x2+7x+10)
The trinomial in parentheses can be factored
Find 2 numbers knowing sum (7) and product (10). They are 2 and 5.
x 2+7x+10=(x+2) (x+5)
y=(x−1) (x+2) (x+5)
A would be correct!
@Lola —
"would be" <~~??
Or "is"?
And in the future, please don't plagiarize anything from other websites onto Jiskha.com. Plagiarized replies will be removed.
To check if a given expression is a factor of the polynomial, you need to see if it results in a remainder of zero when divided into the polynomial using polynomial long division or synthetic division.
Let's check option A: (x + 1)
Using synthetic division:
Step 1: -1 | 1 6 3 -10
-1 -5 2
-------------------------
1 5 -2 -12
The remainder is -12, which means (x + 1) is not a factor of the polynomial.
Now let's check option B: (x - 1)
Using synthetic division:
Step 1: 1 | 1 6 3 -10
1 7 10
-------------------------
1 7 10 0
The remainder is zero, which means (x - 1) is a factor of the polynomial.
Therefore, the correct answer is B. (x - 1)
To determine if a given polynomial has a certain factor, we need to check if the factor is a root of the polynomial. In other words, we substitute the value of the factor into the polynomial and see if the result is zero.
Let's check each option:
A. Substitute x = -1 into the polynomial:
f(-1) = (-1)^3 + 6(-1)^2 + 3(-1) - 10
= -1 + 6 + (-3) - 10
= -8
Since f(-1) is not zero, (x+1) is not a factor of the polynomial.
B. Substitute x = 1:
f(1) = (1)^3 + 6(1)^2 + 3(1) - 10
= 1 + 6 + 3 - 10
= 0
Since f(1) is zero, (x-1) is a factor of the polynomial.
C. Substitute x = 2:
f(2) = (2)^3 + 6(2)^2 + 3(2) - 10
= 8 + 24 + 6 - 10
= 28
Since f(2) is not zero, (x-2) is not a factor of the polynomial.
D. Substitute x = 10:
f(10) = (10)^3 + 6(10)^2 + 3(10) - 10
= 1000 + 600 + 30 - 10
= 1620
Since f(10) is not zero, (x-10) is not a factor of the polynomial.
Therefore, the factor of the polynomial f(x) is (x-1), which is option B.