Question

Use the factor theorem to determine whether x-1 is a factor of x3+8x2-7x-2

Answer 1

Factor theorem = if (x - a) is factor of p(x), then p(a) = 0

Given polynomial,

p(x) = x^3 + 8x^2 - 7x - 2

Given,

factor = x - 1

Here a = 1

Let, x - 1 = 0

x = 1

Now, Put the value of x in given polynomial

p(1) = (1)^3 + 8(1)^2 - 7(1) - 2

p(1) = 1 + 8(1) - 7(1) - 2

p(1) = 1 + 8 - 7 - 2

p(1) = 9 - 9

p(1) = 0

i.e p(a) = 0

Hence x - 1 is a factor of x^3 + 8x^2 - 7x - 2

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Answer 2

Step-by-step explanation:

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