Find the value of p & q if p(x)= x⁴+px³+2x²-3x+q is divisible by the polynomial of x²-1.
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f(x)=x^4+px³+2x²-3x+q
x²-1=0
x²=1
x=+-1
When x=1
(1)^4+p(1)³+2(1)²-3(1)+q
1+p+2-3+q
p+q=0
p=-q→→→→→→→→→→→→→→→→→→
↓
When x=-1 ↓
(-1)^4+p(-1)³+2(-1)²-3(-1)+q ↓
1-p+2+3+q ↓
Now, putting value of p in above statement ↓
6-(-q)+q ↓
2q=-6 ↓
q=-3⇔ ↓
p=-q ←←←←←←←←←←←←←←←←←
p=-(-3)
p=3⇔
x²-1=0
x²=1
x=+-1
When x=1
(1)^4+p(1)³+2(1)²-3(1)+q
1+p+2-3+q
p+q=0
p=-q→→→→→→→→→→→→→→→→→→
↓
When x=-1 ↓
(-1)^4+p(-1)³+2(-1)²-3(-1)+q ↓
1-p+2+3+q ↓
Now, putting value of p in above statement ↓
6-(-q)+q ↓
2q=-6 ↓
q=-3⇔ ↓
p=-q ←←←←←←←←←←←←←←←←←
p=-(-3)
p=3⇔
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