To factor the expression x³ + 7x² + 5x + 35 by grouping, we start by grouping the terms in pairs:
- Group 1: x³ + 7x²
- Group 2: 5x + 35
Next, we factor out the common factors from each group:
- From x³ + 7x², we can factor out x², giving us: x²(x + 7)
- From 5x + 35, we can factor out 5, giving us: 5(x + 7)
Now, our expression looks like this:
x²(x + 7) + 5(x + 7)
We notice that (x + 7) is a common factor, so we can factor it out:
(x + 7)(x² + 5)
Thus, the resulting expression after factoring by grouping is:
(x + 7)(x² + 5)