Question

Factor the quadratic expression 14x²−5x+2 completely.

Answer 1

To factor the quadratic expression 14x²−5x+2 completely, use the factoring method. The factored form is (2x - 1)(7x - 2).

Step-by-step explanation:

To factor the quadratic expression 14x²−5x+2 completely, we can use the quadratic formula or the factoring method. Let's use the factoring method:

1. Multiply the first coefficient, 14, by the constant term, 2. This gives us 28.
2. Find two numbers that multiply to 28 and add up to the middle coefficient, -5. The numbers are -4 and -7 because (-4)(-7) = 28 and -4 + (-7) = -11.
3. Split the middle term using -4x and -7x, and rewrite the quadratic expression as: 14x² - 4x - 7x + 2.
4. Factor by grouping: (14x² - 4x) + (-7x + 2).
5. Factor out the greatest common factor from each binomial: 2x(7x - 2) - 1(7x - 2).
6. Combine the binomials: (2x - 1)(7x - 2).

Therefore, the quadratic expression 14x²−5x+2 can be factored completely as (2x - 1)(7x - 2).