factor 10y^2+17y+3 — step-by-step solution

⚠Ⓘ 10y is read as the product 10*y: for a power, write 10^y‖17y is read as the product 17*y: for a power, write 17^y

Let's factorize in

ℝ

10 y^{2} + 17 y + 3

Given the quadratic form

a x^{2} + b x + c

, you can calculate the discriminant:

Δ = b^{2} - 4 a c

Δ = 17^{2} - 4 \cdot 10 \cdot 3

ℹ

17^{2}

289

‖

4 \cdot 10

40

Δ = 289 - 40 \cdot 3

Δ = 289 - 120

Δ = 169

Δ > 0

, the equation has two solutions:

For the first solution, we obtain:

\frac{- b - \sqrt{Δ}}{2 a}

y1 = \frac{- 17 - \sqrt{169}}{2 \cdot 10}

ℹ

- \sqrt{169}

-13

‖

2 \cdot 10

20

y1 = \frac{- 17 - 13}{20}

y1 = - \frac{30}{20}

y1 = - \frac{3}{2}

The second solution is:

\frac{- b + \sqrt{Δ}}{2 a}

y2 = \frac{- 17 + \sqrt{169}}{2 \cdot 10}

ℹ

\sqrt{169}

13

‖

2 \cdot 10

20

y2 = \frac{- 17 + 13}{20}

y2 = - \frac{4}{20}

y2 = - \frac{1}{5}

▶Factors found:

10 \cdot (y + \frac{1}{5}) \cdot (y + \frac{3}{2})