Question

Ax^2+bx+c=2(x-1)(2x+3)+(x^2-4x+2)

Answer 1

The quadratic form ax² + bx + c for the given set of factors is 5x² - 2x - 4.

How do we determine the quadratic equation (ax^2+bx+c) from a given set of factors?

The quadratic equation that takes the form ax^2+bx+c can be determined from a given set of factors by applying the rule:

• a + (b + c) = a + b + c

Let us expand the eqaution: 2(x-1) (2x+3)

• Ax^2+bx+c = 2(x-1) (2x+3) + x^2-4x+2

So, we have:

2(x - 1)(2x + 3) ⇒ 4x² + 2x - 6.

= 4x² + 2x - 6 + x² - 4x + 2

Now, let us group like terms, we have:

= 4x² + x² + 2x - 4x - 6 + 2

= 5x² - 2x - 4

Therefore, we can conclude that the quadratic form ax² + bx + c for the given set of factors is 5x² - 2x - 4.

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