Question

Answer 1

a) x(6-x)+(x-2)(x-4)

= 6x-x²+x²-4x-2x+8

=6x-4x-x²+x²+8

=2x+8

Answer 2

a)\(x\left(6-x\right)+\left(x-2\right)\left(x-4\right)=6x-x^2+x^2-6x+8=8\)

b)

\(\left(12x^3-7x^2-14x+5\right):\left(4x-5\right)\\ =\left[\left(12x^3-15x^2\right)+\left(8x^2-10x\right)-\left(4x-5\right)\right]:\left(4x-5\right)\\ =\left[3x^2\left(4x-5\right)+2x\left(4x-5\right)-\left(4x-5\right)\right]:\left(4x-5\right)\\ =\left(3x^2+2x-1\right)\left(4x-5\right):\left(4x-5\right)\\ =3x^2+2x-1\\ =\left(x-1\right)\left(x+3\right)\)