3x2 – 12x + 7x – 28 factor the polynomial by grouping

3x^2 - 12x + 7x - 28

= 3x^2 -5x - 28
= (3x + 7)(x - 4)

To factor the polynomial 3x^2 - 12x + 7x - 28 by grouping, we can group the terms in pairs:

(3x^2 - 12x) + (7x - 28)

Now, we find the greatest common factor (GCF) of each pair separately:

In the first pair, the GCF is 3x:

3x(x - 4)

In the second pair, the GCF is 7:

7(x - 4)

Notice that both pairs have a common factor of (x - 4). We can factor out this common factor from both terms:

(x - 4)(3x + 7)

Therefore, the factored form of the given polynomial is (x - 4)(3x + 7).