Solve 10k^3+25k-35k^2

$$10 k ^ { 3 } + 25 k - 35 k ^ { 2 }$$

Factor

$$5k\left(k-1\right)\left(2k-5\right)$$

Solution Steps

Factor out 5.

$$5\left(2k^{3}+5k-7k^{2}\right)$$

Consider 2k^{3}+5k-7k^{2}. Factor out k.

$$k\left(2k^{2}+5-7k\right)$$

Consider 2k^{2}+5-7k. Rearrange the polynomial to put it in standard form. Place the terms in order from highest to lowest power.

$$2k^{2}-7k+5$$

Factor the expression by grouping. First, the expression needs to be rewritten as 2k^{2}+ak+bk+5. To find a and b, set up a system to be solved.

$$a+b=-7 ab=2\times 5=10$$

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 10.

$$-1,-10 -2,-5$$

Calculate the sum for each pair.

$$-1-10=-11 -2-5=-7$$

The solution is the pair that gives sum -7.

$$a=-5 b=-2$$

Rewrite 2k^{2}-7k+5 as \left(2k^{2}-5k\right)+\left(-2k+5\right).

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

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

$$k\left(2k-5\right)-\left(2k-5\right)$$

Factor out common term 2k-5 by using distributive property.

$$\left(2k-5\right)\left(k-1\right)$$

Rewrite the complete factored expression.

$$5k\left(2k-5\right)\left(k-1\right)$$

Evaluate

$$5k\left(k-1\right)\left(2k-5\right)$$