Question

Which expression is the factored form of x2 – 7x 10? (x 3)(x 4) (x – 3)(x – 4) (x – 2)(x – 5) (x 2)(x 5)

Answer 1

The expression x^2 -7x + 10 can be written in factored form as given by Option C: (x-2)(x-5)

How to find the factors of a quadratic expression?

If the given quadratic expression is of the form $ax^2 + bx + c$

then its factored form is obtained by two numbers alpha( α ) and beta( β) such that:

$b = \alpha + \beta \\ ac =\alpha \times \beta$

Then writing b in terms of alpha and beta would help us getting common factors out.

Sometimes, it is not possible to find factors easily, so using the quadratic equation formula can help out without any trial and error.

For this case, we're provided the expression:

$x^2 -7x + 10$

We can write 10 as multiple of -5 and -2 and

we can write -7 as sum of -5 and -2. Thus, we get:

$x^2 -7x + 10 = x^2 -5x - 2x + 10 = x(x-5+ -2(x-5) = (x-2)(x-5)$

Thus, the expression x^2 -7x + 10 can be written in factored form as given by Option C: (x-2)(x-5)

Learn more about factorization of quadratic expression here:

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