Question

So im working with factoring by grouping and factoring trinomials by grouping in my algebra 2 class i need some help with a 6 questions.
1. factor completely : $15 x^{2}$-x-2
2. factor completely: 10xy-5y+18x-9
3.factor completely: $30 c^{2} - 20c^{2} -15c+10$
4. what is the factored form of $2 x^{2} +20x+50$
5.what is the factored form of $5 x^{2} +28x+15$
6.what is the factored form of $4x^{2} -4x+1$

Answer 1

$15^2-x-2 \\ \\ 225 - x - 2 \\ \\ 223 - x \\ \\ Answer: \fbox {223 - x}$

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$10xy-5y+18x-9 \\ \\ 5y(2x-1)+9(2x - 1) \\ \\ (2x - 1)(5y + 9) \\ \\ Answer: \fbox {(2x-1)(5y+9)}$

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$30c^2-20c^2-15c+10 \\ \\ 10c^2 - 15c + 10 \\ \\ Answer: 10c^2 - 15c + 10$

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$2x^2 + 20x + 50 \\ \\ GCF = 2 \\ \\ 2 (\frac{2x^2}{2} + \frac{20x}{2} + \frac{50}{2} ) \\ \\ 2(x^2 + 10 + 25) \\ \\ 2(x^2 + 2(x)(5)+5^2) \\ \\ 2(x + 5)^2 \\ \\ Answer: 2(x + 5)^2$

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$5x^2+28x+15 \\ \\ 5x^2 + 25x + 3x + 15 \\ \\ 5x(x + 5) + 3(x + 5) \\ \\ (x + 5)(5x + 3) \\ \\ Answer: \fbox {(x + 5)(5x + 3)}$

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$4x^2-4x + 1 \\ \\ (2x)^2-2(2x)(1)+1^2 \\ \\ (2x - 1)^2 \\ \\ Answer: (2x - 1)^2$

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Hope this is what you need - considering I'm not the greatest at trinomials, but I have some characteristics of it.