Question

Answer 1

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

2) \(2x^2+5x+2=2x\left(x+2\right)+1\left(x+2\right)=\left(x+2\right)\left(2x+1\right)\)

3) \(x^2-3x+2=x\left(x-2\right)-\left(x-2\right)=\left(x-2\right)\left(x-1\right)\)

4) \(3x^2+9x-30=3\left(x^2+3x-10\right)=3\left(x-2\right)\left(x+5\right)\)

5) \(3x^2-5x-2=3x\left(x-2\right)+\left(x-2\right)=\left(x-2\right)\left(3x+1\right)\)

6) \(x^3-7x^2-6x=x\left(x^2-7x-6\right)\) 

Answer 2

1.

$x^2-5x+6=(x^2-2x)-(3x-6)=x(x-2)-3(x-2)=(x-3)(x-2)$

2.

$2x^2+5x+2=(2x^2+4x)+(x+2)=2x(x+2)+(x+2)=(x+2)(2x+1)$

3.

$x^2-3x+2=(x^2-2x)-(x-2)=x(x-2)-(x-2)=(x-1)(x-2)$

4.
$3x^2+9x-30=3(x^2+3x-10)=3[(x^2-2x)+(5x-10)]$

$=3[x(x-2)+5(x-2)]=3(x-2)(x+5)$

Answer 3

5.

$3x^2-5x-2=(3x^2-6x)+(x-2)=3x(x-2)+(x-2)=(x-2)(3x+1)$

6.

$x^3-7x^2-6x=x(x^2-7x-6)$

7.

$x^2-7xy+10y^2=(x^2-2xy)-(5xy-10y^2)=x(x-2y)-5y(x-2y)=(x-2y)(x-5y)$

8.

$x^2-3xy+2y^2=(x^2-xy)-(2xy-y^2)$

$=x(x-y)-2y(x-y)=(x-y)(x-2y)$

Answer 4

9.

$x^4-2x^3+x^2-9=(x^4-2x^3+x^2)-9$

$=(x^2-x)^2-3^2=(x^2-x-3)(x^2-x+3)$

10.

$x^3+2x-x^2-2=(x^3-x^2)+(2x-2)$

$=x^2(x-1)+2(x-1)=(x-1)(x^2+2)$

11.

$x^4+2x^3+6x-9=(x^4+2x^3+x^2)-(x^2-6x+9)$

$=(x^2+x)^2-(x+3)^2=(x^2+x-x-3)(x^2+x+x+3)$

$=(x^2-3)(x^2+2x+3)$

12.

$2x^3+x-2x^2-1$

$=(2x^3-2x^2)+(x-1)$

$=2x^2(x-1)+(x-1)=(x-1)(2x^2+1)$