Question

if X + 2 and x minus 2 are factors of ax to the power 4 + 2 x cube minus 3 X square + bx - 4 then find the value of a + b

Answer 1

it is by factor method .


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Answer 2

Answer:

Value of a + b is -7

Step-by-step explanation:

Given:

( x + 2 ) and ( x - 2 ) are factors of polynomial say $p(x)=ax^4+2x^3-3x^2+bx-4$

To find: Value of a + b

We use the factor theorem of polynomials.

Factor Theorem states that is x - a is factor of a polynomial p(x) then p(a) = 0.

Here, x + 2  is factor of p(x)

then p(-2) = 0

$a(-2)^4+2(-2)^3-3(-2)^2+b(-2)-4=0$

$16a+2(-8)-3(4)-2b-4=0$

$16a-16-12-2b-4=0$

$16a-2b-32=0$

8a - b = 16 ................(1)

Now, x - 2 is factor of p(x)

then p(2) = 0

$a(2)^4+2(2)^3-3(2)^2+b(2)-4=0$

$16a+2(8)-3(4)+2b-4=0$

$16a+16-12+2b-4=0$

$16a+2b=0$

8a + b = 0 ................(2)

Add (1) and (2),

8a + 8a = 16

16a = 16

a = 1

put in (2), we get

8(1) + b = 0

b = -8

So, a + b = 1  + (-8) = 1 - 8 = -7

Therefore, Value of a + b is -7