Question

2x^2-3x-2 splitting the middle term

Answer 1

Answer:

2x²-3x-2 = (2x+1)(x-2)

Step-by-step explanation:

Given,

The quadratic polynomial is 2x²-3x-2

To find,

The factors of the given polynomial, by splitting the middle term

Solution:

Given polynomial is 2x²-3x-2.

To split the middle term, we need to find two integers such that

their sum = -3 and their product = -4

Two such integers are (-4) and (+1), such that(-4) + (1)  = (-3)

(-4)×(1) = (-4)

by splitting the middle term, we get

2x²-3x-2 = 2x²-4x + x-2

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

= (2x+1)(x-2)

2x²-3x-2 = (2x+1)(x-2)

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Answer 2

Answer:

2 and $\frac{-1}{2}$ are the required value of x.

Explanation:

Given in the question that, $2x^2 - 3x - 2$

We solve this equation by splitting the middle-term method.

• This approach splits the middle phrase into two components. In a quadratic factorization employing splitting of the middle term, where x is the product of two factors and last term is the sum of the two factors.

Step 1:

We have, $2x^2 - 3x - 2$

So, by middle term splitting method

⇒ $2x^2 - 3x - 2$

⇒ $2x^2 -4x + x - 2$

⇒ 2x(x -2) + 1(x - 2)

⇒(x - 2)(2x + 1)

⇒ x - 2 = 0   and 2x + 1 = 0

⇒ x = 2   and x = $\frac{-1}{2}$

Final answer:

Hence, 2 and $\frac{-1}{2}$ are the required value of x.

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