Is the following trinomial a perfect square?
x^2+8x-16 ??
x^2-8x+16
(x-4)(x-4)
So, since x=-4 that makes a perfect square right??
2007-12-15 08:31:09 · 7 answers · asked by cuvelx 3 in Science & Mathematics ➔ Mathematics
What makes a trinomial a perfect square is that it is equal to some binomial times itself.
In this problem,
x² - 8x + 16 = (x - 4)²
so this one is a perfect square.
In general, a quick way to check that a trinomial
ax² + bx + c
is a perfect square is with the discriminant D = b² - 4ac.
The trinomial is a perfect square under the condition that
a > 0 and D = 0.
Under this condition, you will be able to find numbers p and q so that
ax² + bx + c = (px + q)²
In fact, it will be p = sqrt(a) and q = sqrt(c), but this only works
when a > 0 and D = 0.
2007-12-15 08:59:21 · answer #1 · answered by jim n 4 · 1⤊ 0⤋
No x² +8x - 16 is not a square because -16 is not a square.
x² + 8x + 16 is. That is (x+4)².
The error in your thinking is that -4² = 16, not -16.
2007-12-15 08:38:49 · answer #2 · answered by steiner1745 7 · 1⤊ 0⤋
with a view to remedy this challenge, factor out the quadratic trinomial you have particular: x² + 18x + 80 one to do this, chop up 18x into 9x + 9x: x² + 18x + 80 one = x² + 9x + 9x + 80 one next, factor x² + 9x by making use of casting off an x: x² + 9x + 9x + 80 one = x(x + 9) + 9x + 80 one Do the comparable for 9x + 80 one, yet factor out a 9 somewhat of x: x(x + 9) + 9x + 80 one = x(x + 9) + 9(x + 9) because of the fact x and 9 are the two prolonged by making use of the comparable binomial, x + 9, you ought to use the distributive assets which states that for actual numbers a, b, and c: ac + bc = (a + b)c ab + cb = (a + c)b ba + ca = (b + c)a making use of this assets interior the equation that has been won to this point: x(x + 9) + 9(x + 9) = (x + 9)(x + 9) Simplify this extra: (x + 9)(x + 9) = (x + 9)² because of the fact your equation is the sq. of a binomial, x + 9, it is a suitable sq.. for this reason, the respond is confident, x² + 18x + 80 one is a suitable sq. trinomial. wish this facilitates!
2016-11-03 09:26:11 · answer #3 · answered by hosfield 4 · 0⤊ 0⤋
Close, x = +4 for the second equation to equal zero. That would make the second equation a perfect square.
The first equation is not a perfect square
2007-12-15 08:35:45 · answer #4 · answered by Louise 3 · 0⤊ 0⤋
The second one is a perfect square.
2007-12-15 08:36:59 · answer #5 · answered by Anonymous · 0⤊ 0⤋
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2007-12-15 12:46:22 · answer #6 · answered by Anonymous · 0⤊ 0⤋
the first one is not, the second one is.
2007-12-15 08:35:43 · answer #7 · answered by carmelboy91 2 · 0⤊ 0⤋