Factor the trinomial 5x^2+16x+12
To factor the trinomial 5x^2 + 16x + 12, we need to find two binomials that, when multiplied together, equal the given trinomial.
To do this, we will look for two numbers that multiply to give 5 * 12 = 60 (the product of the coefficients of the x^2 and constant terms) and add up to give the coefficient of the x term, which is 16.
The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
We need to find a pair of factors that add up to 16. The pair that works in this case is 4 and 15.
So, we can express the middle term 16x as the sum of 4x and 15x.
Now we can factor by grouping:
5x^2 + 4x + 15x + 12
Taking out the common factors from the first two terms and the last two terms, we get:
x(5x + 4) + 3(5x + 4)
Now the expression contains a common factor of (5x + 4):
(5x + 4)(x + 3)
Therefore, the factored form of the trinomial 5x^2 + 16x + 12 is (5x + 4)(x + 3).