To determine whether (x + 3) is a factor of the polynomial x^3 + 2x^2 - 4x + 3, we can use the remainder theorem. According to the remainder theorem, if (x + 3) is a factor of the polynomial, then when we substitute -3 for x in the polynomial, the result should be zero.
Let's substitute -3 for x in the polynomial and check if the result is zero:
(-3)^3 + 2(-3)^2 - 4(-3) + 3
= -27 + 18 + 12 + 3
= -27 + 18 + 15
= 6
Since the result is not zero, (x + 3) is not a factor of x^3 + 2x^2 - 4x + 3.
Therefore, the statement "x + 3) is a factor of x^3 + 2x^2 - 4x + 3" is false.
Answers & Comments
Verified answer
Let x + 3 be the factor
then,
x + 3 = 0
x = -3
x³+2x²-4x+3
(-3)³+2(-3)²-4(-3)+3
-27+18+12+3
6
Since, Remainder is not 0
Hence, x+3 is not its factor
Answer:
False
Step-by-step explanation:
To determine whether (x + 3) is a factor of the polynomial x^3 + 2x^2 - 4x + 3, we can use the remainder theorem. According to the remainder theorem, if (x + 3) is a factor of the polynomial, then when we substitute -3 for x in the polynomial, the result should be zero.
Let's substitute -3 for x in the polynomial and check if the result is zero:
(-3)^3 + 2(-3)^2 - 4(-3) + 3
= -27 + 18 + 12 + 3
= -27 + 18 + 15
= 6
Since the result is not zero, (x + 3) is not a factor of x^3 + 2x^2 - 4x + 3.
Therefore, the statement "x + 3) is a factor of x^3 + 2x^2 - 4x + 3" is false.
tnx