Factor each trinomial below. Please show your work and check your answer. (1 point each)

x2 – 8x + 15
a2 – a – 20
a2 – 5a – 20
a2 + 12ab + 27b2
2a2 + 30a + 100

Question

Factor each trinomial below. Please show your work and check your answer. (1 point each)

    x2 – 8x + 15
    a2 – a – 20
    a2 – 5a – 20
    a2 + 12ab + 27b2
    2a2 + 30a + 100

anonymous · Answer

@amistre64

amistre64 · Answer

with any luck they play nice

anonymous · Answer

What do you mean?

amistre64 · Answer

i was never good at grouping ....  so i developed my own method

anonymous · Answer

Oh, Sorry, I need to use "By the book" method. Thx anyway!

amistre64 · Answer

if we take a general setup:$$(ax+b)(mx+n)=(am)x^2+(an+bm)x+(bn)$$

by multiplying the first and last coeffs we get:$$ambn$$which we would need to determine its factors $an,~bm$ such that$$an+bm = an+bm$$
as such, we can then factor it as$$(x+\frac{an}{ambn})(x+\frac{bn}{ambn})$$
and reduce as needed

amistre64 · Answer

ugh ... got that last line a little convoluted :)$$(x+\frac{an}{am})(x+\frac{bm}{am})$$which reduces to$$(mx+n)(ax+b)~:~\text{ which was what we started with}$$