Explain in your own words how to reverse FOIL when factoring a polynomial of the form ax2 + bx + c when a = 1. Give an example with your explanation
First write down
(x _ _)(x _ _)
Case 1: If the sign of c is positive, then
1. Think of a pair of positive integers which have product c
and SUM |b|.
2. If there are no such, then the polynomial
cannot be factored, and is said to be "prime".
Otherwise write those two numbers in the second blanks where
the "@" are, like this
(x _ @)(x _ @)
3. Look at the sign of b. If it is +, place +'s in the remaining
two blanks. If it is -, place -'s in the remaining
two blanks.
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(x _ _)(x _ _)
Case 2: If the sign of c is negative, then
1. Think of a pair of positive integers which have product |c|
and DIFFERENCE |b|.
2. If there are no such, then the polynomial
cannot be factored, and is said to be "prime".
Otherwise write those two numbers in the second blanks where
the "@" are, like this
(x _ @)(x _ @)
3. Look at the sign of b. If it is +, place + before the LARGER
of the @'s and - before the SMALLER. If it is -, place - before
the LARGER of the @'s and + before the SMALLER.
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Example for case 1:
x2-5x+6
1. Think of a pair of positive integers which have product 6
and SUM 5.
We think of 3 and 2.
2. So we write those two numbers in the second blanks like this
(x _ 3)(x _ 2)
3. Look at the sign of -5. It is -, so we place -'s in the
remaining two blanks.
(x - 3)(x - 2)
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Example for case 1:
x2-5x-6
1. Think of a pair of positive integers which have product 6
and DIFFERENCE 5.
We think of 6 and 1.
2. So we write those two numbers in the second blanks like this
(x _ 6)(x _ 1)
3. Look at the sign of -5. It is -, so we place a - before the
larger, which is the 6, and a + before the 1
(x - 6)(x + 1).
Edwin