Question

1. X2 - 10 X + 21
2. X2 - X - 90
3. -X2 - 8 X + 20
4. 4X2 + 44 X + 120
5. -3X2 + 24 X - 63
6. 2Х2+Х-3
7. Х2-26Х+120
8. 10Х2-11Х+3
9. Х2-24Х-56
10. 4Х2-3Х+1
11. 9Х2-12Х+4
12. Х2-18Х ЗА РАНЕЕ

Answer 1

$x^2-10x+21=\left(x^2-3x\right)+\left(-7x+21\right) = x\left(x-3\right)-7\left(x-3\right) =\left(x-3\right)\left(x-7\right)\\\\x^2-x-90=\left(x^2+9x\right)+\left(-10x-90\right)=x\left(x+9\right)-10\left(x+9\right)=\left(x+9\right)\left(x-10\right)\\\\-x^2-8x+20=-\left(x^2+8x-20\right)=-(\left(x^2-2x\right)+\left(10x-20\right))=-(x\left(x-2\right)+10\left(x-2\right))=-\left(x-2\right)\left(x+10\right)\\\\$

$4x^2+44x+120=4\left(x^2+11x+30\right)=4(\left(x^2+5x\right)+\left(6x+30\right))=4(x\left(x+5\right)+6\left(x+5\right))=4\left(x+5\right)\left(x+6\right)\\\\-3x^2+24x-63=-3\left(x^2-8x+21\right)\\\\2x^2+x-3 = \left(2x^2-2x\right)+\left(3x-3\right) = 2x\left(x-1\right)+3\left(x-1\right)=\left(x-1\right)\left(2x+3\right)$$x^2-26x+120 = \left(x^2-6x\right)+\left(-20x+120\right) =x\left(x-6\right)-20\left(x-6\right)=\left(x-6\right)\left(x-20\right)\\\\10x^2-11x+3=\left(10x^2-5x\right)+\left(-6x+3\right)=5x\left(2x-1\right)-3\left(2x-1\right)=\left(2x-1\right)\left(5x-3\right)\\\\9x^2-12x+4 =\left(3x\right)^2-2\cdot \:3x\cdot \:2+2^2=\left(3x-2\right)^2\\$

$x^2-18x+77=\left(x^2-7x\right)+\left(-11x+77\right)=x\left(x-7\right)-11\left(x-7\right)=\left(x-7\right)\left(x-11\right)$