Answer:

(2x2 - x) - 3 = 0

STEP

2

:

Trying to factor by splitting the middle term

2.1 Factoring 2x2-x-3

The first term is, 2x2 its coefficient is 2 .

The middle term is, -x its coefficient is -1 .

The last term, "the CONSTANT", is -3

Step-1 : Multiply the coefficient of the first term by the constant 2 • -3 = -6

Step-2 : Find two factors of -6 whose SUM equals the coefficient of the middle term, which is -1 .

-6 + 1 = -5

-3 + 2 = -1 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -3 and 2

2x2 - 3x + 2X - 3

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (2x-3)

Add up the last 2 terms, pulling out common factors :

1 • (2x-3)

Step-5 : Add up the four terms of step 4 :

(x+1) • (2x-3)

Which is the desired factorization

Equation at the end of step

2

:

(2x - 3) • (x + 1) = 0

STEP

3

:

Theory - Roots of a product

3.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

3.2 Solve : 2x-3 = 0

Add 3 to both sides of the equation :

2x = 3

Divide both sides of the equation by 2:

x = 3/2 = 1.500

Solving a Single Variable Equation:

3.3 Solve : x+1 = 0

Subtract 1 from both sides of the equation :

x = -1

Supplement : Solving Quadratic Equation Directly

Solving 2x2-x-3 = 0 directly

Earlier we FACTORED this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

Step-by-step explanation:

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