Question

Would you kindly help me with this trinomial problem:factoring by regrouping trinomials into 4 term polynomial
3x^2+11x+10

Answer 1

You have to find 2 terms that would add up to 11x

Multiply the leading coefficient by the last term, \(\ 3 \times 10 = 30 \)

You can make a table to better visualize it: -- Unfortunately I don't know how to make a latex table yet :<

Find 2 terms that when multiplied gives you 30 and when added gives you 11:

\(\ 1 \times 30 = 30 | 1 + 30 = 31 <-- \) this doesn't work

\(\ -1 \times -30 = 30 | -1 + (-30) = -31 \) Also doesn't work.

\(\ 2 \times 15 = 30 | 2 + 15 = 17 \) <-- doesn't work

Skipping a few numbers let's use 5:

\(\ 5 \times 6 = 30 | 5 + 6 = 11 \color{green}\checkmark\)


The new expression is: \(\ 3x^2 + 5x + 6x + 10\)

Now just facotr this by grouping :P


x(3x + 5) + 2(3x + 5)

(3x + 5)(x+2)

Answer 2

I the first part, I meant to say find 2 terms that when multiplied gives you 30 and adds up to 11.