Question

Factor completely: 16x2 + 40x + 25

Answer 1

do you know how to slide and divide?

Answer 2

You've got a polynomial that has perfect squares for its x^2 and x^0 terms. What would happen if you multiplied (ax+b)(ax+b) where a = sqrt{16} and b = sqrt{25}?

Answer 3

multiply the last number by 16, then divide by 16

Answer 4

I don't know, but my teacher taught me slide and divide and it works best for me at least

Answer 5

(4x+5)(4x+5)

Answer 6

We've got a polynomial of form ax^2+bx+c where a and c are squares. we know that (ax+b)(ax+b) = a^2x^2 + 2abx + b^2 so we just need to verify that 2ab = 40 (the coefficient of x^1 in our polynomial to be factored). 4*4=16, 5*5 = 26, and 2*4*5 = 40, so essentially by inspection we were able to factor it as (4x+5)^2.

Answer 7

Thanks