Topic 6.3 (Polynomial Operations II)
FOIL
Multiply first two terms, Add the product of the outer terms and the inner terms,
and multiply the last two terms.
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Example: (3x + 5)(x - 4)
Product of the first two terms: 3x2
Product of the outer terms: -12x
Product of the inner terms: 5x 3x2 + [(-12x) + (5x)] - 20
Product of the last terms: -20 3x2 - 7x - 20 Ans.
(Remember the answer must be put in decreasing order of the terms.)
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Special patterns to multiply two binomials.
(a + b)(a - b) = a2 - b2
(a + b)2 = a2 + 2ab + b2
(a - b)2 = a2 - 2ab + b2
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Example: (3x - 5)2 Square the first term: 9x2
Multiply the two terms together and double the product: 2(3x)(-5) = -30x
Square the second term: 25
Answer: (decreasing order) 9x2 - 30x + 25
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Example: (2x + 7)(2x - 7) Square the first term: 4x2
The sum of the cross products become zero. (14x) + (-14x)
Square the second term: 49
Answer: (decreasing order) 4x2 - 49
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Find: (5x3 + 3y2)2
(5x3)2 + 2(5x3)(3y2) + (3y2)2
25x6 + 30x3y2 + 9y4 Answer
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Find: (x + 2)(3x2 + 4x + 1) Multiply each term of the binomial by each term
of the trinomial.
(x)(3x2) + (x)(4x) + (x)(1) + (2)(3x2) + (2)(4x) + (2)(1) Multiply and combine like terms.
3x3 + 4x2 + x + 6x2 + 8x + 2
3x3 + 10x2 + 9x + 2 Answer
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Divide a polynomial by a binomial. (Read the PAN concerning this)
5x2 + 5x + 7
Example: 3x - 3 15x3 + 0x2 + 6x - 5
-(15x3 - 15x2)
15x2 + 6x - 5
-(15x2 - 15x)
21x - 5
-(21x - 21)
16 remainder
5x2 + 5x + 7 + 16 / (3x - 3) Answer