Question

factorise the following polynomial 3y² 2y-1​

Answer 1

Correct Question:-

Factorise the following polynomial:

• 3y²+2y-1

Step-by-step Explanation:-

We have to factorise:

3y²+2y-1

Let's do it by middle term splitting!!

⇒ 3y²+2y-1

⇒ 3y²+3y-y-1

⇒ 3y(y+1)-1(y+1)

⇒ (3y-1)(y+1)

y=1/3, -1

So 1/3 and -1 are factors of y.

Alternate method:-

Let's do it by quadratic formula:

In the given equation:

Coefficient of y², a=3

Coefficient of y, b=2

Constant term, c =-1

Let's apply quadratic formula!

$\dashrightarrow \sf x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

Now put the values of a,b and c.

$\dashrightarrow \sf x=\dfrac{-(2)\pm\sqrt{(2)^2-4(3)(-1)}}{2(3)}$

$\dashrightarrow \sf x=\dfrac{-2\pm\sqrt{4+12}}{6}$

$\dashrightarrow \sf x=\dfrac{-2\pm\sqrt{16}}{6}$

$\dashrightarrow \sf x=\dfrac{-2\pm 4}{6}$

For positive:-

$\dashrightarrow \sf x=\dfrac{-2+ 4}{6}$

$\dashrightarrow \sf x=\dfrac{ 2}{6}$

Divide by 2 from both numerator and denominator.

$\dashrightarrow \sf x=\dfrac{ 2\div2}{6\div2}$

$\boxed{\dashrightarrow \sf x=\dfrac{ 1}{3}}$

For negative:-

$\dashrightarrow \sf x=\dfrac{-2- 4}{6}$

$\dashrightarrow \sf x=\dfrac{-6}{6}$

Divide by 6 from both numerator and denominator.

$\dashrightarrow \sf x=\dfrac{-6\div6}{6\div6}$

$\dashrightarrow \sf x=\dfrac{-1}{1}$

$\boxed{\dashrightarrow \sf x=-1}$

So factors are 1/3 and -1