Is P(-2) a root of P(x) =x^3 - 2x^2 - 5x + 6 ? Explain why or why not

pleasee explainn

Root means that it cuts x axis where the value of y = 0

substitute this value of x=-2 into the equation to get:

-P(-2) = -2^3 -2(-2^2) - 5*-2 + 6
= -8 -2(4) +10 + 6
= -8-8+10+6
= 0

P(-2) is equal to zero and thus is a root of P(x) =x^3 - 2x^2 - 5x + 6

Rich B had the right idea, but didn't have the right numbers.

Think of roots, being the literal roots of the equation being held down by the x axis. P(-2) is suggesting that at x = -2 , the y co ordinate of the function will be at the x axis (y = 0)

so, putting the value in gives:

P (-2) = (-2)^3 - 2 (-2)^2 - 5 (-2) + 6
= -8 - 8 + 10 + 6
= 0

Therefore, the point is is x = -2 and y = 0, therefore it is a root at that point.

Substitute -2 for x.
(-2)^3-2(-2)^2+10+6
-8-8+16
0
Since you get P(x)=0, -2 is a root.
A root just means a solution or the x coordinate of the x intercept.
So, the root is what x is when y is 0. P(x) is interchangeable with y.

P(-2) = (-2)^3 - 2(-2)^2 - 5(-2) + 6 = - 8 - 8 + 10 + 6 = 0

so, x = - 2 is a root and x + 2 is a factor of P(x).

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