Question

If you have a quadratic equation in standard form and it has values of a=4, b = -8 and c = -60, what would the equation look like if you factored it out completely ?

Answer 1

4(x - 5)(x + 3) = 0

Explanation:

To factor a quadratic equation in standard form, we need to find two binomials that multiply together to give us the quadratic equation.

The quadratic equation in standard form with a=4, b=-8, and c=-60 is:

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4x^2 - 8x - 60 = 0

To factor it completely, we need to find two binomials that multiply together to give us this quadratic equation. The first term of each binomial must be 2x since 2x times 2x gives us 4x^2. The last term of each binomial must be negative since -6 times 10 is -60.

So, we need to find two factors of -60 that add up to -4 (which is -b/a).

The two factors of -60 that add up to -4 are -10 and 6.

Therefore, we can factor the quadratic equation as:

4x^2 - 8x - 60 = 0

4(x^2 - 2x - 15) = 0

4(x - 5)(x + 3) = 0

So the factored form of the quadratic equation is 4(x - 5)(x + 3) = 0