Factorise 6x^2 + 17x + 5 by using the "Factor Theorem"
Solve it in detail.
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Factorise 6x^2 + 17x + 5 by using the "Factor Theorem"
Solve it in detail.
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Question :
Factorize 6x² + 17x + 5 by using the "Factor Theorem"
Solution :
What factor theorem means?
Factor theorem states that a polynomial P(x) has a factor (x - a) if and only if P(x) = 0
P(x) = 6x² + 17x + 5
Now,
⇒ P(-1/3) = 6(-1/3)² + 17(-1/3) + 5
= 6 * (1/9) - 17/3 + 5
= 2/3 - 17/3 + 5
= (2 - 17 + 15)/3
= (-15 + 15)/3
= 0/3
= 0
Now according to factor theorem, {x - (-1/3)} or, x + 1/3 or, (3x + 1)/3 or, (3x + 1) is a factor of P(x). [Here, denominator '3' gets cancelled as the factor implies to 0 so it gets cancelled]
Now we have 1 factor of P(x) as (3x + 1)
P(x) = 6x² + 17x + 5
⇒ P(x) = 6x² + 2x + 15x + 5
⇒ P(x) = 2x(3x + 1) + 5(3x + 1)
⇒ P(x) = (2x + 5)(3x + 1)
Therefore,
Factors of the given polynomial = (2x + 5)(3x + 1)
Answer
Let p(x)=6x
2
+17x+5 the term
6
5
can be written as many terms one would be (±
2
5
,±
3
1
),(±
6
5
,±1),...……....
Let p(
3
−1
)=0 then by factor theorem
3
−1
then the other will be;
6x
2
+17x+5=(2x+5)(3x+1)