r2-2rr2+8r+12÷r3-5r2+6rr2+10r+24÷r+4r+2

Factor r out of r2.

r⋅r-2rr2+8r+12r3-5r2+6rr2+10r+24r+4r+2

Factor r out of -2r.

r⋅r+r⋅-2r2+8r+12r3-5r2+6rr2+10r+24r+4r+2

Factor r out of r⋅r+r⋅-2.

r(r-2)r2+8r+12r3-5r2+6rr2+10r+24r+4r+2

r(r-2)r2+8r+12r3-5r2+6rr2+10r+24r+4r+2

Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is 12 and whose sum is 8.

2,6

Write the factored form using these integers.

r(r-2)(r+2)(r+6)r3-5r2+6rr2+10r+24r+4r+2

r(r-2)(r+2)(r+6)r3-5r2+6rr2+10r+24r+4r+2

Factor r out of r3.

r(r-2)(r+2)(r+6)r⋅r2-5r2+6rr2+10r+24r+4r+2

Factor r out of -5r2.

r(r-2)(r+2)(r+6)r⋅r2+r(-5r)+6rr2+10r+24r+4r+2

Factor r out of 6r.

r(r-2)(r+2)(r+6)r⋅r2+r(-5r)+r⋅6r2+10r+24r+4r+2

Factor r out of r⋅r2+r(-5r).

r(r-2)(r+2)(r+6)r(r2-5r)+r⋅6r2+10r+24r+4r+2

Factor r out of r(r2-5r)+r⋅6.

r(r-2)(r+2)(r+6)r(r2-5r+6)r2+10r+24r+4r+2

r(r-2)(r+2)(r+6)r(r2-5r+6)r2+10r+24r+4r+2

Factor r2-5r+6 using the AC method.

Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is 6 and whose sum is -5.

-3,-2

Write the factored form using these integers.

r(r-2)(r+2)(r+6)r((r-3)(r-2))r2+10r+24r+4r+2

r(r-2)(r+2)(r+6)r((r-3)(r-2))r2+10r+24r+4r+2

Remove unnecessary parentheses.

r(r-2)(r+2)(r+6)r(r-3)(r-2)r2+10r+24r+4r+2

r(r-2)(r+2)(r+6)r(r-3)(r-2)r2+10r+24r+4r+2

Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is 24 and whose sum is 10.

4,6

Write the factored form using these integers.

r(r-2)(r+2)(r+6)r(r-3)(r-2)(r+4)(r+6)r+4r+2

r(r-2)(r+2)(r+6)r(r-3)(r-2)(r+4)(r+6)r+4r+2

Factor (((r^2-2r)/(r^2+8r+12))÷((r^3-5r^2+6r)/(r^2+10r+24)))÷((r+4)/(r+2))