Solve 10y^2+2y-15y-3

$$10 y ^ { 2 } + 2 y - 15 y - 3$$

Factor

$$\left(2y-3\right)\left(5y+1\right)$$

Solution Steps

Multiply and combine like terms.

$$10y^{2}-13y-3$$

Factor the expression by grouping. First, the expression needs to be rewritten as 10y^{2}+ay+by-3. To find a and b, set up a system to be solved.

$$a+b=-13 ab=10\left(-3\right)=-30$$

Since ab is negative, a and b have the opposite signs. Since a+b is negative, the negative number has greater absolute value than the positive. List all such integer pairs that give product -30.

$$1,-30 2,-15 3,-10 5,-6$$

Calculate the sum for each pair.

$$1-30=-29 2-15=-13 3-10=-7 5-6=-1$$

The solution is the pair that gives sum -13.

$$a=-15 b=2$$

Rewrite 10y^{2}-13y-3 as \left(10y^{2}-15y\right)+\left(2y-3\right).

$$\left(10y^{2}-15y\right)+\left(2y-3\right)$$

Factor out 5y in 10y^{2}-15y.

$$5y\left(2y-3\right)+2y-3$$

Factor out common term 2y-3 by using distributive property.

$$\left(2y-3\right)\left(5y+1\right)$$

Evaluate

$$\left(2y-3\right)\left(5y+1\right)$$

Solution Steps

Combine 2y and -15y to get -13y.

$$10y^{2}-13y-3$$