Solve 5x^2y-11xy+6y

$$5 x ^ { 2 } y - 11 x y + 6 y$$

Factor

$$y\left(x-1\right)\left(5x-6\right)$$

Solution Steps

Factor out y.

$$y\left(5x^{2}-11x+6\right)$$

Consider 5x^{2}-11x+6. Factor the expression by grouping. First, the expression needs to be rewritten as 5x^{2}+ax+bx+6. To find a and b, set up a system to be solved.

$$a+b=-11 ab=5\times 6=30$$

Since ab is positive, a and b have the same sign. Since a+b is negative, a and b are both negative. List all such integer pairs that give product 30.

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

Calculate the sum for each pair.

$$-1-30=-31 -2-15=-17 -3-10=-13 -5-6=-11$$

The solution is the pair that gives sum -11.

$$a=-6 b=-5$$

Rewrite 5x^{2}-11x+6 as \left(5x^{2}-6x\right)+\left(-5x+6\right).

$$\left(5x^{2}-6x\right)+\left(-5x+6\right)$$

Factor out x in the first and -1 in the second group.

$$x\left(5x-6\right)-\left(5x-6\right)$$

Factor out common term 5x-6 by using distributive property.

$$\left(5x-6\right)\left(x-1\right)$$

Rewrite the complete factored expression.

$$y\left(5x-6\right)\left(x-1\right)$$

Evaluate

$$y\left(x-1\right)\left(5x-6\right)$$