Question

With a as the variable factor the expression: ab + 2ac + 3b^2 + 6bc - 5a - 13b + 4c - 10. The answer is (b+2c-5)(a+3b+2) Please show all steps.

Answer 1

ab+2ac+3b^2+6bc-5a-13b+4c-10

Re-arrange to get pure "b" and pure "a" terms togerther, the remaining terms have the "c".

(3b^2 - 13b - 10) + (ab - 5a) +(2ac + 6bc + 4c)

Factor each group to get:

(3b + 2)(b -5) + a(b - 5) + 2c(a + 3b + 2)

Re-associate the first two groups to get:

(a + 3b + 2)(b - 5) + 2c(a + 3b + 2)

Now, re-associate again to get:

(a + 3b + 2)(b + 2c - 5) Voila! It's done!

Answer 2

ab+2ac+3b^2+6bc-5a-13b+4c-10

Re-arrange to get pure "b" and pure "a" terms togerther, the remaining terms have the "c".

(3b^2 - 13b - 10) + (ab - 5a) +(2ac + 6bc + 4c)

Factor each group to get:

(3b + 2)(b -5) + a(b - 5) + 2c(a + 3b + 2)

Re-associate the first two groups to get:

(a + 3b + 2)(b - 5) + 2c(a + 3b + 2)

Now, re-associate again to get:

(a + 3b + 2)(b + 2c - 5) Voila! It's done!

Answer 3

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