Final answer:
The best method to factor the expression 4x²-26x+30 would likely be using the quadratic formula to find the roots and then convert these roots into the factored form. Factoring by grouping or trial and error might not be efficient due to the lack of obvious common factors or pairs of factors that add up to -26. Checking the answer is essential to ensure accuracy.
Step-by-step explanation:
To factor the expression 4x²-26x+30, we can apply several methods depending on what we notice about the coefficients and terms of the quadratic. The methods that could be relevant here are the following:
- Factoring by grouping: Although this method works well when we can split the middle term into two terms whose coefficients have a common factor with either the first or the last term, for this particular expression, this may not be straightforward due to the lack of obvious common factors.
- Using the quadratic formula: When factoring seems tough, we can find the roots using the quadratic formula, x = (-b ± √(b² - 4ac))/(2a), where a, b, and c are the coefficients of the terms in the quadratic equation ax² + bx + c = 0. Once we find the roots (let's call them r1 and r2), the expression can be factored as (x - r1)(x - r2).
- Factoring by trial and error: This is often the method of last resort and involves guessing pairs of factors of the constant term (in this case, 30) that add up to the coefficient of the linear term (in this case, -26). However, this can be time-consuming and may not always yield results quickly.
Considering these methods, the quadratic formula may be the most reliable method to factor the given expression, especially when the coefficients do not suggest an easy grouping or the terms do not have apparent common factors. After applying the quadratic formula, we would then convert the roots into the factored form of the expression.
To eliminate terms and simplify algebra, we could also consider combining like terms or identifying common factors, although for this expression, such simplification is not initially evident.
Finally, it is crucial to check the answer to ensure it is reasonable. This involves verifying that the factors, when multiplied out, give back the original expression.