Question

Factoring trinomials 2x² -5x-3, 3x² +10x-9, 2y² +15y+7, 7a² -11a+4, 5n² +17n+6.

Answer 1

To factor trinomials, we can use the AC method to find two binomials that multiply to give the trinomial. By multiplying the coefficient of the quadratic term and the constant term, we can find two numbers that add up to the coefficient of the linear term.

Step-by-step explanation:

To factor the trinomials, we need to find two binomials that multiply to give the trinomial. We can use the 'AC method' to factor trinomials of the form ax² + bx + c. First, we multiply the coefficient of the quadratic term (a) and the constant term (c), then find two numbers that multiply to give ac and add up to the coefficient of the linear term (b). For example:

1. For 2x² - 5x - 3, ac = 2*(-3) = -6 and the factors of -6 that add up to -5 are -6 and +1. So, the factored form is (2x + 1)(x - 3).
2. For 3x² + 10x - 9, ac = 3*(-9) = -27 and the factors of -27 that add up to 10 are +12 and -15. So, the factored form is (3x - 1)(x + 9).
3. For 2y² + 15y + 7, ac = 2*7 = 14 and the factors of 14 that add up to 15 are +1 and +14. So, the factored form is (2y + 1)(y + 7).
4. For 7a² - 11a + 4, ac = 7*4 = 28 and the factors of 28 that add up to -11 are -7 and -4. So, the factored form is (7a - 4)(a - 1).
5. For 5n² + 17n + 6, ac = 5*6 = 30 and the factors of 30 that add up to 17 are -3 and -10. So, the factored form is (5n + 3)(n + 2).