16xx+24x+9
Steps (long):
1. Multiply first and third terms:
16*9=144
2. Factor 144 and find a pair of factors that adds up to the second term (24):
144=2*2*2*2*3*3
2*72, -2*-72
3*48, -3*-48
4*36, -4*-36
6*24, -6*-24
9*16, -9*-16
8*18, -8*-18
12*12, -12*-12
3. Rewrite polynomial:
16xx+24x+9
16xx+12x+12x+9
4. Factor pairs of terms (ie first and second, third and fourth):
4x(4x+3)+3(4x+3)
5. Combine common terms:
(4x+3)(4x+3) --> (4x+3)**2
Steps (short):
-since twice the product of the square roots of the first and third terms we can place it in the form (ax+c)**2 where a and c are the square roots of the first and third terms respectively
16xx+24x+9
(ax)**2+b+(c)**2
2*(sqrt(a**2)*sqrt(c**2))=b
2*(sqrt(16)*sqrt(9))=24
(sqrt(16)x+sqrt(9))**2
(4x+3)**2
If that's 16x2 + 72x + 81, that factors to (4x + 9)(4x + 9) or (4x + 9)2
Yes, and this is how. 16 x 2 - 9 16x2=32, 32 - 9 =23, so 23 is your answer! Good Question!
6x(3x2 - x + 4)
16x2 - 49 = 42x2 - 72 = (4x)2 - 72 = (4x - 7)(4x + 7)
You can try the cubic equation: t(x) = (-x3 + 16x2 - 63x - 36)/18
factor the trinomial 16x^2+24x+9
yes
(4x + 3)(4x + 3) (4x + 3)2
34-132
If you can't factor it easily, use the quadratic formula.
x2+24x+144 = 9 x2+24x+144-9 = 0 x2+24x+135 = 0 (x+9)(x+15) = 0 x = -9 or x = -15
(x^2) + 24x + 144 = -9 x = -12
16x² - 24x + 9 factors to (4x - 3)(4x - 3) or (4x - 3)2
16x2-9
3(2) + 24x + 48 = 0 6 + 24x + 48 = 0 24x + 54 = 0 24x + 54 - 54 = 0 - 54 24x = -54 24x/24 = -54/24 x = -9/4 x = -2 1/4
4x3 + 16x2 - 180x = 4x(x2 + 4x - 45) = 4x(x + 9)(x - 5)
24x^5 + 24x^3 = 24x^3(x^2 + 1)