Question

factorise by splitting the middle term :2x^2-7x-15

Answer 1

10hay!!

Dear friend -

Here is ur answer

2x²-7x-15

=> 2x²-10x+3x-15

=> 2x(x-5) +3(x-5)

=> (2x+3) (x-5)

I hope it's help you

Answer 2

The factors of 2x²-7x-15 are (2x+3)(x-5).

Given:

• A quadratic polynomial.
• $2 {x}^{2} - 7x - 15$

To find:

• Factors of given polynomial by splitting the middle term.

Solution:

Concept to be used:

A standard quadratic polynomial is given by $\bf a {x}^{2} + bx + c, \: a \ne \: 0$ to factorise it, split the coefficient of middle term b like that multiplication of those will be ac.

Step 1:

Write the coefficients of polynomial.

Here,

$a = 2$

$b = - 7$

and

$c = - 15$

Now, split b so as multiplication is equal to ac.

So,

-10+3= -7

(-10)(3)=-30=(2)(-15)

Thus,

Split terms are -10 and 3.

Step 2:

Factorise the polynomial.

$2 {x}^{2} - 7x - 15 = 2 {x}^{2} + 3x - 10x - 15$

or

$2 {x}^{2} - 7x - 15 = x(2 {x} + 3) -5( 2x + 3)$

or

$\bf \: 2 {x}^{2} - 7x - 15 = (2 {x} + 3)(x - 5)$

Thus,

The factors of 2x²-7x-15 are (2x+3)(x-5).

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