Do you mean some thing like 4x2 - 28xy + 49y2 ?
notice 4x2 = (2x)2 and 49y2 = either (7y)2 or (-7y)2 (1st and last terms must be squares) and the middle term is 2(2x)(-7y) (2 times sq root of 1st times sq root of last)
Once the pattern is recognized:
(sq root 1st + sqroot 2nd)2 or (sq root 1st - sqroot 2nd)2 depending on if middle term is positive or negative.
So, back to my example:
4x2 - 28xy + 49y2 = (2x - 7y)2 because middle is negative.
Simpler example factor x2 + 6x + 9. 1st and last are both squares
sq root of 9 = 3 3 times 2 = 6 that fits the middle
so x2 + 6x + 9 = (x + 3)2
just like factoring any other trinomial.
It's not enough to copy the question off the test. If you don't tell us what the trinomial is, we can't factor it for you.
(t - 15)(t + 3)
just make the trinomial easier to factor. ex -x2 + 3x + 4 ... most books don't teach you how to factor when a leading term is negative. ... so -1(x2- 3x- 4) ... now factor again ignoring the -1 -1(x - 4)(x + 1)
That's not a trinomial, but it factors to x(x + 19)
A factor of a perfect square trinomial is eithera number that is a factor of each term of the trinomial,a binomial that is a factor of the trinomial, ora product of the above two.For example, consider 4x2 + 8x + 4It has the factors2 or 4,(x + 1) or2x+2 = 2*(x+1) or 4x+4 = 4*(x+1)
A trinomial is perfect square if it can be factored into the form
A perfect trinomial must be of the form a2x2 ± 2abxy + b2y2 and this factorises to (ax ± by)2.
the 5 kinds of factoring are common monomial factor, difference of two cubes, quadratic trinomial, perfect square trinomial,and difference of two square.
(x + 3)(x + 3)
(p - 9)(p - 9)
No.
That trinomial is unfactorable (the roots are not integers).
just like factoring any other trinomial.
A trinomial is perfect square if it can be factored into the form (a+b)2 So a2 +2ab+b2 would work.
If a trinomial is a perfect square, then the discriminant will equal 0. The discriminant is equal to B^2-4AC. The variables come from the standard form of a quadratic which is Ax^2+Bx+C In this problem, A=81, B=-72, and C=16 so the discriminant is: (-72)^2-4(81)(16)=5,184-5,184=0 so this is a perfect square trinomial. To factor, notice that 81=9^2 and 16=4^2, so 81x^2=(9x)^2. We can then factor the trinomial into (9x+4)(9x-4)
perfect trinomial square?? it has the form: a2 + 2ab + b2