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).