Solve -126x^2j+4j-10xj

$$- 126 x ^ { 2 } j + 4 j - 10 x j$$

Factor

$$-2j\left(7x-1\right)\left(9x+2\right)$$

Solution Steps

Factor out 2.

$$2\left(-63x^{2}j+2j-5xj\right)$$

Consider -63x^{2}j+2j-5xj. Factor out j.

$$j\left(-63x^{2}+2-5x\right)$$

Consider -63x^{2}+2-5x. Rearrange the polynomial to put it in standard form. Place the terms in order from highest to lowest power.

$$-63x^{2}-5x+2$$

Factor the expression by grouping. First, the expression needs to be rewritten as -63x^{2}+ax+bx+2. To find a and b, set up a system to be solved.

$$a+b=-5 ab=-63\times 2=-126$$

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 -126.

$$1,-126 2,-63 3,-42 6,-21 7,-18 9,-14$$

Calculate the sum for each pair.

$$1-126=-125 2-63=-61 3-42=-39 6-21=-15 7-18=-11 9-14=-5$$

The solution is the pair that gives sum -5.

$$a=9 b=-14$$

Rewrite -63x^{2}-5x+2 as \left(-63x^{2}+9x\right)+\left(-14x+2\right).

$$\left(-63x^{2}+9x\right)+\left(-14x+2\right)$$

Factor out -9x in the first and -2 in the second group.

$$-9x\left(7x-1\right)-2\left(7x-1\right)$$

Factor out common term 7x-1 by using distributive property.

$$\left(7x-1\right)\left(-9x-2\right)$$

Rewrite the complete factored expression.

$$2j\left(7x-1\right)\left(-9x-2\right)$$

Evaluate

$$-2j\left(7x-1\right)\left(9x+2\right)$$