Question

factorise using factor theorem 35y^2+13y-12 I repeat using"factor theorem" not by splitting method​

Answer 1

Step-by-step explanation:

Given:-

35y^2+13y-12

To find:-

Factorise using factor theorem 35y^2+13y-12 .

Solution:-

Given quadratic polynomial is 35y^2+13y-12

P(y)=35y^2+13y-12

We know that

Factor Theorem:-

P(x) be a polynomial of the degree is greater than or equal to 1 and (x-a) is a factor if P(a)=0 vice- versa.

Put y = 3/7 then

P(3/7) = 35(3/7)^2+13(3/7)-12

=>P(3/7)=35(9/49)+(13×3)/7-12

=>P(3/7)=(45/7)+(39/7)-12

=>P(3/7)=[(45+39)/7]-12

=>P(3/7)=(84/7)-12

=>P(3/7)=12-12

=>P(3/7)=0

So, (Y-3/7) bor (7y-3) is a factor of P(y).

and Put y = -4/5 then

=>P(y)=35(-4/5)^2+13(-4/5)-12

=>P(y)=35×(16/25)+(13×-4)/5 -12

=>P(y)=[(7×16)/5] +(-52/5)-12

=>P(y)=(112/5)-(52/5)-12

=>P(y)=[(112-52)/5]-12

=>P(y)=(60/5)-12

=>P(y)=12-12

=>P(y)=0

So, (y+4/5) or (5y+4) is a factor of P(y)

P(y)=(y- 3/7)(y +4/5) or (7y-3)(5y+4)

Answer:-

The factorization of 35y^2+13y-12 is

(y- 3/7)(y +4/5) or (7y-3)(5y+4)

Used method:-

• Factor Theorem

P(x) be a polynomial of the degree is greater than or equal to 1 and (x-a) is a factor if P(a)=0 vice- versa.