what is the square binomial of x2 + 8x + 16 ?
you mean, you are asked to factor this?
did you mean x^2 + 8 x + 16?
yes ^^
(x+4)(x+4)
yes i ask the factor of a binomial
to solve for x..obviously x=-4.
you can use ac factoring.
note, its in the form ax^2 + bx+c.
then, identify a and c, and multiply a and c.
then, identify two numbers where when you multiply you will get ac, and when you add you will get "b" (coefficient of the middle term).
then, rewrite the middle term using those numbers that you find. :))then, split into two groups, where each group has a gcf, then, factor out the gcf. then factor out the common factor. ta that's it. :))
let me give you a similar example: x^2+4x+4.so, a = 1, b = 4, and c=4.
so, ac = 1*4=4, we need two numbers which when we multiply we get 4(ac result), and when we add, we get 4(b , coefficient of "x"). note that, 2*2 = 4, and 2 +2 = 4.
so, we will rewrite the middle terms using 2 and 2.so, x^2 +4x+4 = x^2+2x+2x+4.
grouping it, (x^2+2x)+(2x+4), factoring gcf: x(x+2)+2(x+2)
factoring out the common factor, thus: (x+2)(x+2), or (x+2)^2. that's it! :))
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