Select the polynomial that is a perfect square trinomial.
9x2 + 9x + 1
36b2 − 24b + 8
16x2 + 24x + 9
4a2 − 10a + 25
the first and last numbers must be perfect squares. So, B is out.
The middle number must be twice the product of the roots of the 1st and last, since
(a+b)^2 = a^2+2ab+b^2
If we check 9x^2+9x+1, a=3 and b=1, but that would need 2*3*1 = 6x in the middle. So, (A) is out.
Check the other two.
the third one
correct.
I don't get how you get to that conclusion, Help?
To determine if a polynomial is a perfect square trinomial, we need to follow two steps:
1. Take the square root of the first term
2. Square the square root result
3. Check if the squared result matches the third term. If it does, then it is a perfect square trinomial.
Let's apply these steps to each of the given polynomials:
1. For the polynomial 9x^2 + 9x + 1:
- The square root of the first term (9x^2) is 3x.
- Squaring 3x gives us (3x)^2 = 9x^2.
- The squared result matches the third term (1).
- Therefore, this polynomial is a perfect square trinomial.
2. For the polynomial 36b^2 - 24b + 8:
- The square root of the first term (36b^2) is 6b.
- Squaring 6b gives us (6b)^2 = 36b^2.
- The squared result does not match the third term (8).
- Therefore, this polynomial is not a perfect square trinomial.
3. For the polynomial 16x^2 + 24x + 9:
- The square root of the first term (16x^2) is 4x.
- Squaring 4x gives us (4x)^2 = 16x^2.
- The squared result matches the third term (9).
- Therefore, this polynomial is a perfect square trinomial.
4. For the polynomial 4a^2 - 10a + 25:
- The square root of the first term (4a^2) is 2a.
- Squaring 2a gives us (2a)^2 = 4a^2.
- The squared result does not match the third term (25).
- Therefore, this polynomial is not a perfect square trinomial.
So, out of the given polynomials, the one that is a perfect square trinomial is 9x^2 + 9x + 1.