Factoring by Grouping- Math?

Question

If anyone could help me with these i think that they are confusing and if yuo could show me the steps of how to get to the answer that would help me so much. thanks in advanced.

Factor Completely

1. m^2 - 10m + 9
2. x^2 + 8x -20
3. 3x^2 + 10x + 3
4. 2xy - 12xz + 3y - 18z

Thanks Again!! :-)
fyi that ^ 2means squared

Answer 1

1. m^2 - 10m + 9

You expect the factors to look like (m + a)(m + b) which, when multiplied, yield m^2 + am + bm + ab

The product ab is the constant term and a + b is the coefficient of the x term

Choices for a & b are 1 & 9 or 3 & 3

1 & 9 look right and they must both be negative to get the - 10 and the + 9

(m - 1)(m - 9)


2. x^2 + 8x -20

Here the choices for a & b are 1 & 20, 2 & 10, 4 & 5

- 2 and + 10 will give you the + 8 coefficient for the x term

(x - 2)(x + 10)


3. 3x^2 + 10x + 3

Here the factors will look like (ax + b)(cx + d) = acx^2 + adx + bcx + bd

Choice for a & c is 1 & 3, same for b & d

(3x + 1)(x + 3)

See also the lesson at the link below


4. 2xy - 12xz + 3y - 18z

This expression can be factored by grouping - you can factor 2x from the left two terms and a 3 from the right two terms

2x(y - 6z) + 3(y - 6z)

Which can be written

(y - 6z)(2x + 3)

Applying the distributive rule: a(b + c) = ab + ac from right to left

Answer 2

1. m^2 - 10m + 9 = (m^2 - m) - (9m - 9) = (m -9)(m-1)
2. x^2 + 8x -20 = ( x^2 + 10x ) - (2x + 20) = (x-2)(x+10)
3. 3x^2 + 10x + 3 = (3x^2 + x) + (9x + 3) = (x+3)(3x+1)
4. 2xy - 12xz + 3y - 18z = (2xy+3y) - (12xz + 18z) = (y - 6z)(2x -3)