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, the given quadratic expression is:

$4x^2 + 28x + 49$

So we've to find two numbers such that:

Their sum = b = 28

Their product = $ac = 4\times 49 = 196$

We can see that 196 is square of 14, and that 14 added twice forms 28, thus:

14 + 14 = 28

14×14 = 196

Writing b = 28 as sum of 14 twice, we get:

$4x^2 + 28x + 49 = 4x^2 + 14x + 14x +49 \\4x^2 + 28x + 49 = 2x(2x+7) + 7(2x + 7)\\4x^2 + 28x + 49 = (2x+7)(2x+7)$

Thus, the completely factored form of 4x^2 + 28x + 49 is given by: Option C: (2x+7)(2x+7)

Learn more about factorization of quadratic expression here:

brainly.com/question/26675692

8 0

2 years ago

Find the error in the problem.

Sonbull [250]

The 2nd step, you're supposed to combine like terms (20h and 2h) but not the 5 because it doesn't have a h next to it.

5 0

3 years ago

Read 2 more answers

Explain how you write products when there are not enough digits in the product to place a decimal point

Anni [7]

If you there isn't enough digits to place, just add zeroes to product to make it a full product or don't even use a decimal point at all.

6 0

3 years ago