Question

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

Answer 1

Step-by-step explanation:

ANSWER:-

If x+2 is a factor,

then

x+2=0

x = -2

Now we will place the value of -2 in the equation

(-2)³+a (-2)²-(-2)+30=0

-8 + 4a +2 +30 = 0

24 + 4a = 0

4a = -24

a = -24/4 = -6

So a = -6 is the answer.

Things to Note :-

• Always take care that minus and minus make Plus
• Cubes of any number does not change the sign
• Even powers Inverse the sign if in negative
• When positive number goes towards either side of equal to sign it gets changed to negative number
• When factor is given note that it will be equal to zero.
• Place the values of x to find the value.

Answer 2

ANSWER:

• Value of a is (-6)

GIVEN:

• (x+2) is a factor of x³+ax²-x+30 .

TO FIND:

• Value of 'a'.

SOLUTION:

P(x) = x³+ax²-x+30

Here (x+2) is the factor of P(x). If we divide P(x) by (x+2) we get remainder = 0.

METHOD USED:

• Remainder theorem.

=> P(x) = x³+ax²-x+30

Let (x+2) = 0

=> x = (-2)

Substituting x = -2 in P(x) we get remainder = 0

=> P(-2) = (-2)³+a(-2)²-(-2)+30

=> 0 = -8+4a+2+30

=> 4a+24 = 0

=> 4a = (-24)

=> a = -24/4

=> a = (-6)

Value of a is (-6)

NOTE:

Some important formulas:

(a+b)² = a²+b²+2ab

(a-b)² = a²+b²-2ab

(a+b)(a-b) = a²-b²

(a+b)³ = a³+b³+3ab(a+b)

(a-b)³ = a³-b³-3ab(a-b)

a³+b³ = (a+b)(a²+b²-ab)