Question

determine whether (x+2) is a factor of x cube+xsquare -4x-5 or not ​

Answer 1

Answer:

no

Step-by-step explanation:

because zero of (x+2) is -2

therefore, when we put -2 in place of x at last we get -1 which is not equal to 0

so, (x+2) is not the factor of x³+x²-4x-5.

hope it helps you

Answer 2

Answer:

(x + 2) is not a factor of the polynomial x³ + x² - 4x - 5

Step-by-step explanation:

Given is a cubic polynomial,

x³ + x² - 4x - 5

Let p(x) = x³ + x² - 4x - 5

we have to check whether (x + 2) is a factor of the given polynomial.

(x + 2) is a factor

⇒ x + 2 = 0

   x = -2

-2 must be a zero of the polynomial if (x+2) is a factor of the polynomial.

• If (x + 2) is a factor of the given polynomial, when we substitute x = -2 the result must be zero.

Put x = -2,

p(-2) = (-2)³ + (-2)² - 4(-2) - 5

p(-2) = -8 + 4 + 8 - 5

p(-2) = 4 - 5

p(-2) = -1

=> p(-2) ≠ 0

As the remainder is not equal to zero, it's not a factor of the given polynomial.

Hence (x + 2) is not a factor of the polynomial p(x) = x³ + x² - 4x - 5

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