Question

Phân tích thành nhân tử:

8). \(y^2-y-30\)

9). \(y^2-8y+15\)

10). \(y^2+y-6\)

11). \(y^2-y-12\)

12). \(x^2-5x+6\)

13). \(u^2+u-42\)

14). \(2x^2+x-6\)

15). \(7x^2+50x+7\)

16). \(12x^2+7x-12\)

17). \(15x^2+7x-2\)

18). \(2x^2-y^2+xy\)

19). \(x^2-3xy+2y^2\)

20). \(x^2+2xy-15y^2\)

21). \(3x^2+7xy-6y^2\)

22). \(6x^2+13xy+6y^2\)

23). \(-10x^2+11x+6\)

24). \(-10x^2-7x+6\)

Answer 1

8) \(y^2-y-30=y^2+5y-6y-30=y\left(y+5\right)-6\left(y+5\right)=\left(y-6\right)\left(y+5\right)\)

9) \(y^2-8y+15=y^2-3y-5y+15=y\left(y-3\right)-5\left(y-3\right)=\left(y-5\right)\left(y-3\right)\)

10) \(y^2+y-6=y^2-2y+3y-6=y\left(y-2\right)+3\left(y-2\right)=\left(y+3\right)\left(y-2\right)\)

11) \(y^2-y-12=y^2+3y-4y-12=y\left(y+3\right)-4\left(y+3\right)=\left(y-4\right)\left(y+3\right)\)

12) \(x^2-5x+6=x^2-2x-3x+6=x\left(x-2\right)-3\left(x-2\right)=\left(x-3\right)\left(x-2\right)\)

13) \(u^2+u-42=u^2+7u-6u-42=u\left(u+7\right)-6\left(u+7\right)=\left(u-6\right)\left(u+7\right)\)

Answer 2

14) \(2x^2+x-6=2x^2+4x-3x-6=2x\left(x+2\right)-3\left(x+2\right)=\left(2x-3\right)\left(x+2\right)\)

15) \(7x^2+50x+7=7x^2+49x+x+7=7x\left(x+7\right)+\left(x+7\right)=\left(7x+1\right)\left(x+7\right)\)

16) \(12x^2+7x-12=12x^2+16x-9x-12=4x\left(3x+4\right)-3\left(3x+4\right)=\left(4x-3\right)\left(3x+4\right)\)

17) \(15x^2+7x-2=15x^2-3x+10x-2=3x\left(5x-1\right)+2\left(5x-1\right)=\left(3x+2\right)\left(5x-1\right)\)

18) \(2x^2-y^2+xy=2x^2+2xy-xy-y^2=2x\left(x+y\right)-y\left(x+y\right)=\left(2x-y\right)\left(x+y\right)\)

19) \(x^2-3xy+2y^2=x^2-xy-2xy+2y^2=x\left(x-y\right)-2y\left(x-y\right)=\left(x-2y\right)\left(x-y\right)\)

Answer 3

14)\(2x^2+x-6=2x^2+4x-3x-6=2x.\left(x+2\right)-3.\left(x+2\right)=\left(x+2\right).\left(2x-3\right)\)15)\(7x^2+50x+7=7x^2+49x+x+7=7x.\left(x+7\right)+\left(x+7\right)=\left(x+7\right).\left(7x+1\right)\)16)\(12x^2+7x-12=12x^2+16x-9x-12=4x.\left(3x+4\right)-3.\left(3x+4\right)=\left(3x+4\right).\left(4x-3\right)\)17)\(15x^2+7x-2=15x^2+10x-3x-2=5x.\left(3x+2\right)-\left(3x+2\right)=\left(3x+2\right).\left(5x-1\right)\)

Answer 4

20) \(x^2+2xy-15y^2=x^2+5xy-3xy-15y^2=x\left(x+5y\right)-3y\left(x+5y\right)=\left(x-3y\right)\left(x+5y\right)\)

21) \(3x^2+7xy-6y^2=3x^2+9xy-2xy-6y^2=3x\left(x+3y\right)-2y\left(x+3y\right)=\left(3x-2y\right)\left(x+3y\right)\)

22) \(6x^2+13xy+6y^2=6x^2+9xy+4xy+6y^2=3x\left(2x+3y\right)+2y\left(2x+3y\right)=\left(3x+2y\right)\left(2x+3y\right)\)

23) \(-10x^2+11x+6=-10x^2-4x+15x+6=-2x\left(5x+2\right)+3\left(5x+2\right)=\left(3-2x\right)\left(5x+2\right)\)

24) \(-10x^2-7x+6=-10x^2+5x-12x+6=-5x\left(2x-1\right)-6\left(2x-1\right)=\left(-5x-6\right)\left(2x-1\right)\)