Question

1. Using factor theorem, show that :
(i) (x - 3) is a factor of (x3 + x2 - 17x + 15).​

Answer 1

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Answer 2

SOLUTION :

Let's understand the concept :

• Here , concept of factor theorem is used .

We need to take the whole polynomial as f (x) and if f (x)= 0 then (x-3) is a factor .

Answer:

• x-3=0

• x = 0+3

• x=3

$\sf f (x)=x^3+x^2-17x+15$

$\sf f (x)=0$

• Substitute the values :

$\implies\sf (3)^3+(3)^2-17 (3)+15=0$

$\implies\sf 27+9-51+15=0$

$\implies\sf 27+9+15-51=0$

$\implies\sf 51-51=0$

$\implies\sf 0=0$

$\implies \bf f (3)=0$

• Hence , X-3 is a factor of the given polynomial.