Jamal wants to know if x−3 is a factor of the polynomial P(x)=x3−7x+6. Jamal calculates P(3) and applies the Factor Theorem to conclude that x−3 is a factor of P(x).
Is he correct? Why or why not?
No, because P(3) is equal to 0.
No, because P(3) is not equal to 0.
Yes, because P(3) is equal to 0.
Yes, because P(3) is not equal to 0.
Well, I got P(3) = 12
So what does that mean?
To determine whether x−3 is a factor of the polynomial P(x)=x^3−7x+6, we need to calculate P(3) and check if it equals zero.
To calculate P(3), we substitute x=3 into the polynomial:
P(3) = (3)^3 − 7(3) + 6
= 27 - 21 + 6
= 12
Since P(3) is not equal to zero (P(3) ≠ 0), we can conclude that x−3 is not a factor of P(x).
Therefore, the correct answer is: No, because P(3) is not equal to 0.