To factor a polynomial with four terms like 3x³ + 5x + 6x² + 10, one effective method to consider is factoring by grouping.
In factoring by grouping, we can separate the polynomial into two groups and look for common factors within those groups. Let’s rearrange the polynomial so we can visualize the grouping more clearly:
(3x³ + 6x²) + (5x + 10)
Now, we can factor out the common factors from each group:
- From the first group (3x³ + 6x²), we can factor out 3x², giving us: 3x²(x + 2).
- From the second group (5x + 10), we can factor out 5, giving us: 5(x + 2).
Now, we can express the original polynomial as:
3x²(x + 2) + 5(x + 2)
Since (x + 2) is a common factor in both terms, we can factor it out:
(x + 2)(3x² + 5)
This results in the factored form of the polynomial. Thus, when dealing with a polynomial that has four terms, factoring by grouping can be an effective strategy to simplify the expression.