If f, left bracket, x, right bracket, equals, x, cubed, plus, 10, x, squared, plus, 23, x, plus, 14

Question

f(x)=x^3+10x^2+23x+14, which of the following is not a factor of f, left bracket, x, right bracketf(x)?
Answer
Multiple Choice Answers
left bracket, x, plus, 7, right bracket(x+7)
left bracket, x, plus, 1, right bracket(x+1)
left bracket, x, minus, 2, right bracket(x−2)
left bracket, x, plus, 2, right bracket(x+2)

Answer 1

To find which of the given options is not a factor of f(x), we can try plugging in each option into f(x) and see if it equals to 0.

Let's substitute x+7 into f(x):
f(x) = (x+7)^3 + 10(x+7)^2 + 23(x+7) + 14

Expanding this expression and simplifying, we get:
f(x) = x^3 + 21x^2 + 133x + 280

Since this is not equal to 0, x+7 is not a factor of f(x).

Now, let's substitute x+1 into f(x):
f(x) = (x+1)^3 + 10(x+1)^2 + 23(x+1) + 14

Expanding this expression and simplifying, we get:
f(x) = x^3 + 13x^2 + 44x + 48

Since this is not equal to 0, x+1 is not a factor of f(x).

Now, let's substitute x-2 into f(x):
f(x) = (x-2)^3 + 10(x-2)^2 + 23(x-2) + 14

Expanding this expression and simplifying, we get:
f(x) = x^3 + 4x^2 - 13x - 12

Since this is not equal to 0, x-2 is not a factor of f(x).

Finally, let's substitute x+2 into f(x):
f(x) = (x+2)^3 + 10(x+2)^2 + 23(x+2) + 14

Expanding this expression and simplifying, we get:
f(x) = x^3 + 6x^2 + 5x + 8

Since this is not equal to 0, x+2 is not a factor of f(x).

Therefore, the option that is not a factor of f(x) is:
[x+7] (x+7)