factor 2y^2+11y+15 — step-by-step solution

Let's factorize in

ℝ

2 y^{2} + 11 y + 15

Given the quadratic form

a x^{2} + b x + c

, let's compute the discriminant:

Δ = b^{2} - 4 a c

Δ = 11^{2} - 4 \cdot 2 \cdot 15

ℹ

11^{2}

121

‖

4 \cdot 2

8

Δ = 121 - 8 \cdot 15

Δ = 121 - 120

Δ = 1

Since

Δ > 0

, the equation has two solutions:

The first solution is:

\frac{- b - \sqrt{Δ}}{2 a}

y1 = \frac{- 11 - 1}{2 \cdot 2}

ℹ

- 11 - 1

-12

‖

2 \cdot 2

4

y1 = - \frac{12}{4}

y1 = -3

The second solution is:

\frac{- b + \sqrt{Δ}}{2 a}

y2 = \frac{- 11 + 1}{2 \cdot 2}

ℹ

- 11 + 1

-10

‖

2 \cdot 2

4

y2 = - \frac{10}{4}

y2 = - \frac{5}{2}

▶Factors identified:

(y + 3) \cdot (2 y + 5)