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Level 334

Factoring Patterns of Polynomials


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What is the GCM?
short for Greatest Common Monomial, you multiply this (the GCM) by the sum/difference of the remaining monomials.
GCM: 2x
Example of a GCM question (pg. 197). 6x² + 10x
What is the DOTS method?
also known as "Difference Of Two Squares", this is when you subtract a square from another (ex. a² - b²).
1 + 3a - 3a - 9a² OR 1 - 9a²
Example of a DOTS question (pg. 206). (1 + 3a)(1 - 3a)
What is the PST?
short for Perfect Square Trinomial, the sum or difference of two numbers squared will create a new trinomial that includes a², 2ab, and b².
(4u + 7v)² = 16u² + + 49v²
Example of a PST question (pg. 210). (4u + 7v)²
(Don't forget to move your terms!)
DETERMINE IF THIS IS A PST. IF IT IS, FACTOR. IF NOT, WRITE PRIME. 4x² + 9 + 12x
Which pattern does this formula represent? (x² + bx + c)
The pattern is the one which you multiply the two integers, but they must add up to the middle term (bx). The constant term's factors will both be positive.
(a - 13)(a - 2)
Example of this pattern (x² + bx + c) (pg. 214). a² - 15a + 26
Which pattern does this formula represent? (x² + bx - c)
The pattern is the one which you multiply the two integers, but they must add up to the middle term (bx). The constant term's factors (bc) will one positive and one negative.
(y - 24)(y + 3)
Example of this pattern (x² + bx - c) (pg. 218). y² - 21y - 72
(3x + 1)(x + 2)
Example of this pattern (ax² + bx + c) (pg. 222). 3x² + 7x + 2
How do you find the Master Product for this formula? (ax² + bx +c)
You find the MP by multiplying the coefficient attached to the squared variable (ax²), which is in this case a, by quadratic term and the constant integer.
MP= 6
Only find the MP for this problem (pg. 222). 2x² + 5x + 3
MP= -15
Factor this problem using the MP (pg. 222). 3r² - 2r - 5
conjugates
the sum or difference of the same two terms