Preparing for the MCA

Solve x2 + bx + c = 0 by factoringSection 4.3What is a trinomial?????It has 3 terms connected by addition or subtractionExample : 3x2 6x + 7

What are the rules for factoring?TrinomialExampleRulesx2 + bx + cx2 + 5x + 6All Positive(x + )(x + )x2 - bx + cx2 - 5x + 6

b is negative(x - )(x - )x2 - bx - cx2 - 5x - 6

c is negative(x - )(x + )x2 + bx - cx2 + 5x - 6

c is negative(x - )(x + )

Rules ReviewHow do you decide what numbers go in the parentheses?If the last term is positive: x2 + 5x + 6 or x2 - 5x + 6(x + )(x + ) or (x - )(x - )(x + 2)(x + 3) or (x 2)(x 3)

You are looking for 2 numbers that :Multiply = 6 and Add to = 52 and 3

Rules ReviewHow do you decide what numbers go in the parentheses?

If the last term is negative: x2 + 5x - 6 or x2 - 5x - 6(x - )(x + ) or (x - )(x + )(x - 1)(x + 6) or (x 6)(x + 1)You are looking for 2 numbers that :Multiply = 6 and are 5 apart6 and 1

ORDER MATTERS!!!!!!!!!!!xx

Factors of +8: 1 & 8 2 & 4-1 & -8-2 & -4 2x + 4x = 6x1x + 8x = 9xO + I = bx ?-2x - 4x = -6x-1x - 8x = -9x-2-4

Check your answer by using FOIL

FOIL

Difference of Squaresa2 b2 = (a + b)(a b)x2 9 = (x + 3)(x 3)49a2 81 = (7a + 9)(7a 9)To factor, express each term as a square of a monomial then apply the rule...

Here is another example:

One your whiteboardD: x2 + 18x + 32 E: x2 - 11x + 24 F: x2 + 10x 24G: x2 - 5x 36 H: x2 - 10x + 24

Try these on your own: