Question

If x+2 is a factor of x³+ax²-x+30 then find the value of a.

Answer 1

$\color {red} </p><p>\Large \underline {\underline {Question \: :}}$

If x + 2 is a factor of x³ + ax² - x + 30, then find the value of a.

$\color {red} </p><p>\Large \underline {\underline {Answer \: :}}$

Let x + 2 and x³ + ax² - x + 30 be g(x) and p(x) respectively.

• g(x) = x + 2
• p(x) = x³ + ax² - x + 30

First, find the value of g(x) :

x + 2 = 0

x = - 2

Then, put the value of g(x) in p(x) to find the value of a :

p(x) = x³ + ax² - x + 30

p(-2) = (-2)³ + a(-2)² - (-2) + 30

(-2)³ + a(-2)² - (-2) + 30 = 0

-8 + a(4) + 2 + 30 = 0

-8 + 4a + 32 = 0

4a + 24 = 0

4a = - 24

a = - 24/4

a = - 6

$\implies$ So, a = - 6.

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Answer 2

Answer:

a = -6

Step-by-step explanation:

If x + 2 is a factor of the polynomial x³+ax²-x+30 then,,

x + 2 = 0

x = -2

Place x = -2 in the polynomial x³+ax²-x+30

x³+ax²-x+30 = 0

(-2)³ + a(-2)² - (-2) + 30 = 0

-8 + 4a + 2 + 30 = 0

4a = -24

a = -6

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