Question

Polynomials
Ex-2.4
4) Factorise:
iii) 6x² + 5x - 6​

Answer 1

Step-by-step explanation:

6x ki square + 5x-6

6x ki square - 4x + 9x - 6

2×(3x-2)+3(3x-1)

(3x-2) (2x+3)

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Answer 2

Given:

• A polynomial is given to us.
• The polynomial is 6x²+5x-6.

To Find:

• To find the factorised form of the polynomial.

Answer:

We would factorise the polynomial by "Middle term splitting " .

Now how to do Middle term splitting?

Let us consider another polynomial x²-x-6.

We will first multiply the constant term with the coefficient of the x².

• Here constant term is 6 and coefficient of x² is 1 .So (6×1)=6.

Next we will split the middle term into two terms such that the product of two terms is equal to the product of constant term and the coefficient of x².

• For this we will look for the factors of 6 , which can be

1. 1×6
2. 2×3.

• Here now we can observe that 3-2 = 1 and which is equal to the coefficient of x .

Now after splitting we have ,

→ x² - x - 6

= x²-3x+2x-6

= x(x - 3) +2(x - 3)

= (x + 2) (x - 3).

Hence we easily factorised the above quadratic polynomial.

Now let us factorise the given one .

= 6x² + 5x -6.

= 6x² + 9x - 4x - 6.

= 3x( 2x +3) - 2(2x + 3).

= ( 3x -2)(2x+3).