37. Determine t so that -2*t**c - 4*t**4 - 2*t**2 + k*t**2 + 6*t**4 = 0.
-1, 0, 1
Let j be 76/(-57)*3/(18/(-29)). Determine i, given that 2*i**2 + 4/3 + j*i = 0.
-3, -2/9
Let -1/6*x**4 + 0*x + 3*x**2 + 1/2*x**3 + 0 = 0. Calculate x.
-3, 0, 6
Let -6/17*v - 2/17*v**2 - 4/17 = 0. Calculate v.
-2, -1
Factor 7569/5*b + 73167/5 + 261/5*b**2 + 3/5*b**3.
3*(b + 29)**3/5
Let h(f) be the first derivative of -f**6/24 + f**5/3 - 5*f**4/8 - 9*f**2 + 7. Let x(k) be the second derivative of h(k). Let x(c) = 0. What is c?
0, 1, 3
Let a(g) = 11*g**3 - 19*g**2 + 52*g - 26. Let n(l) = 45*l**3 - 75*l**2 + 210*l - 105. Let w(t) = -25*a(t) + 6*n(t). Factor w(k).
-5*(k - 2)**2*(k - 1)
Let a(z) be the third derivative of -z**7/70 - 3*z**6/20 - 9*z**5/20 - 3*z**2 + 15. Factor a(y).
-3*y**2*(y + 3)**2
Let h = 75 + 9. Let p = h + -82. Determine m so that 1 + 1/4*m**p - 5/4*m = 0.
1, 4
Suppose 5*k + 388 = 2*k - 4*n, 3*n + 12 = 0. Let u = k - -124. Solve -184/3*c**4 + 92/3*c**3 + u + 4/3*c**2 + 32*c**5 - 8/3*c = 0.
-1/4, 0, 1/2, 2/3, 1
Factor 2/9*y**3 + 82/9 + 86/9*y**2 + 166/9*y.
2*(y + 1)**2*(y + 41)/9
Let y(z) = -4*z + 21. Let m be y(5). Determine i so that -1 + m + 61*i**2 + 4 - 65*i**2 = 0.
-1, 1
Let p be (294/(-5))/((372/(-310))/(12/9)). Determine q, given that -112/3*q**4 - 16/3*q + 0 - 60*q**3 + p*q**5 + 112/3*q**2 = 0.
-1, 0, 2/7, 1
Suppose -5*t + 30 = -2*t. Let z = -8 + t. Factor 0*b**z + 0*b - 9*b**2 + 6*b + 3*b**4.
3*b*(b - 1)**2*(b + 2)
Let f be ((-2630)/132)/5 + 2/12. Let o = f - -4. Factor -2/11*u - o*u**2 + 2/11 + 2/11*u**3.
2*(u - 1)**2*(u + 1)/11
Suppose -5*n - 112 = h + 75, 2*n + h = -76. Let l = 42 + n. Factor -2/5*o - 2/5*o**l + 0 + 0*o**2 + 0*o**4 + 4/5*o**3.
-2*o*(o - 1)**2*(o + 1)**2/5
Let n(l) = 2*l**2 - 2*l + 1. Let m be n(2). Suppose 3*g = m*x - 18, 0*g + 3 = -3*g. What is i in 0 + x*i - 12*i**2 - 99/4*i**3 = 0?
-2/3, 0, 2/11
Suppose -368*q - 142 = -439*q. Let -7/6 - 1/6*r**q - 4/3*r = 0. Calculate r.
-7, -1
Solve 12/5*h + 4/5*h**2 + 0 = 0.
-3, 0
Let h(b) be the second derivative of 0*b**5 + 1/168*b**7 + 0*b**4 + 0*b**3 + 1/120*b**6 + 0*b**2 - 2*b - 9. Determine z, given that h(z) = 0.
-1, 0
Factor 1/2*x**3 - 2 + 3/2*x**2 + 0*x.
(x - 1)*(x + 2)**2/2
Let l(v) be the first derivative of -v**3/18 + 49*v**2/12 - 387. Let l(y) = 0. Calculate y.
0, 49
Let k(a) be the third derivative of a**6/120 + a**5/12 - a**4/12 - 7*a**3/6 - 4*a**2. Let s be k(-5). Factor 0*u - 2*u**s - 3 + 21*u - 33*u**2 + 17*u**3.
3*(u - 1)**2*(5*u - 1)
Let r(t) = -7*t**2 - 9*t + 41. Let u(p) = -3*p**2 - 3*p + 20. Let c(a) = 2*r(a) - 5*u(a). Let c(l) = 0. What is l?
-3, 6
Suppose 0 = -m + 3*k + 1 + 5, -k = -m. Let l = 7 + m. Let d**3 - 3*d - d**l + 4*d**2 + 4*d - 2*d**3 - 3*d**2 = 0. What is d?
-1, 0, 1
Let p = -29/21 - -115/63. What is z in -p + 4/9*z - 1/9*z**2 = 0?
2
Determine d, given that 2*d**4 + 681472*d + 5115530 - 53*d**3 + 109*d**3 + 147*d**3 + 2380662 + 23232*d**2 + 149*d**3 = 0.
-44
Let u(h) be the second derivative of h**5/100 + h**4/10 - h**3/30 - 3*h**2/5 + 46*h. Factor u(d).
(d - 1)*(d + 1)*(d + 6)/5
Let x(c) be the third derivative of -c**6/780 + 2*c**5/65 - 11*c**4/39 + 16*c**3/13 + 38*c**2. Factor x(y).
-2*(y - 6)*(y - 4)*(y - 2)/13
Factor 8/5*i**3 + 1/5*i**4 - 32/5*i + 12/5*i**2 - 64/5.
(i - 2)*(i + 2)*(i + 4)**2/5
Let q(n) be the second derivative of -50/3*n**3 + 24*n + 0 - 250*n**2 - 5/12*n**4. Let q(u) = 0. What is u?
-10
Let f(z) be the second derivative of z**5/130 + 25*z**4/39 + 44*z**3/3 - 104*z**2 - 2*z - 148. Factor f(y).
2*(y - 2)*(y + 26)**2/13
Let -65*t - 4*t**3 - 352 - 29*t - 80*t - 34*t - 38*t**2 + 2*t**3 = 0. What is t?
-11, -4
Suppose 2017*r = 2019*r - 32. Let u(k) be the first derivative of -r*k**2 - 16*k - k**4 - 20/3*k**3 - 11. Let u(z) = 0. Calculate z.
-2, -1
Let y(r) = -r**2 + 162*r - 80. Let w(h) = 163*h - 78. Let s(q) = 6*w(q) - 5*y(q). Solve s(m) = 0.
-34, 2/5
Factor 5 + 62*u - 60*u + 2 - 2*u**3 - 20*u**2 + 13.
-2*(u - 1)*(u + 1)*(u + 10)
Let g(z) be the first derivative of z**6/4 + 3*z**5/10 - 54. Suppose g(s) = 0. What is s?
-1, 0
Let v(c) be the second derivative of c**6/90 + c**5/30 - c**4/9 - c**3/9 + c**2/2 + c - 5. Factor v(r).
(r - 1)**2*(r + 1)*(r + 3)/3
Suppose -7*g = -15*g - 368. Let s = g + 95/2. Factor -3*q + 0 + 3/2*q**3 + s*q**2.
3*q*(q - 1)*(q + 2)/2
Let x(a) = 22*a + 24. Let r be x(-1). Let g(t) be the first derivative of 0*t - 1/7*t**4 - 8/21*t**3 - 6 - 2/7*t**r. Factor g(p).
-4*p*(p + 1)**2/7
Let u(a) be the first derivative of 0*a + 0*a**2 + 2/15*a**3 - 2/25*a**5 + 0*a**4 + 4. Suppose u(v) = 0. What is v?
-1, 0, 1
Let l(b) = -4*b**2 + 312*b - 6089. Let k(f) = -2*f**2 + 156*f - 3044. Let n(z) = 5*k(z) - 2*l(z). Let n(p) = 0. Calculate p.
39
Let v be 5/(-3)*((-4)/(-56) + (-442)/455). Determine x so that -12 + v*x**2 - 21/2*x = 0.
-1, 8
Let k = -18628 - -130450/7. Let k*h**3 + 0 - 12/7*h**2 + 0*h = 0. What is h?
0, 2/9
Let o(v) be the second derivative of 1/110*v**5 + 1/11*v**2 + 1/132*v**4 - 5/66*v**3 + 0 + 9*v. Suppose o(b) = 0. What is b?
-2, 1/2, 1
Let u(x) be the first derivative of 8*x**3/3 + 14*x**2 - 16*x + 13. Factor u(d).
4*(d + 4)*(2*d - 1)
Let v = 14 - -13. Let x = 29 - v. Factor -1 + 5/2*w + 3/2*w**x.
(w + 2)*(3*w - 1)/2
Let m be (-93)/45 - 1164/(-485). Suppose 0 + 4/3*y**2 - m*y = 0. What is y?
0, 1/4
Let x be (-3)/2 + (-14)/(-4). Let n = -28 - -30. Solve -2*y**2 + 2*y**n - 2 - 26*y**x + 17*y = 0.
2/13, 1/2
Let h(l) = l**2 - 16*l - 55. Let b be h(19). Factor -5*g**b + 3*g**3 - g**3 - 10*g + 3*g**3.
5*g*(g - 2)*(g + 1)
Let x = 45 - 43. Suppose i - 14 = -2*i - x*q, 2*i = q. Factor 0 - 1/4*p**3 + 0*p + 0*p**i.
-p**3/4
Factor 25*m**3 - 1106 + 10*m + 2*m**5 + 9*m**4 + 27*m**2 + 1106 - m**5.
m*(m + 1)**2*(m + 2)*(m + 5)
Suppose 23*h + 24*h - 14*h = 66. Factor -14/3*p**3 - 200/9*p + 0 - 80/3*p**h - 2/9*p**4.
-2*p*(p + 1)*(p + 10)**2/9
Let m be (-2)/((-4 + -1)*(-24)/(-120)). Let i(k) be the first derivative of m*k**2 - 5 + 4*k - k**4 - 4/3*k**3. Let i(o) = 0. What is o?
-1, 1
Let u(h) be the second derivative of -h**7/14 - 13*h**6/10 + 3*h**5/10 + 141*h**4/2 - 513*h**3/2 + 729*h**2/2 + h + 7. Find y such that u(y) = 0.
-9, 1, 3
Let i = 2102 - 2100. Find h, given that 0*h + 0 + 1/2*h**i = 0.
0
Determine s, given that 1922/3 + 1798/3*s + 2/3*s**3 - 122/3*s**2 = 0.
-1, 31
Let w = 5 - 15. Let b be (15 + w)*(-4)/(-5). Suppose c**2 + c**5 - 4*c**3 + 2*c**b - 6*c**4 + 3*c**3 + 3*c**4 = 0. What is c?
-1, 0, 1
Let c(x) be the third derivative of 0 - 3/64*x**4 + 0*x**5 + 1/320*x**6 + 0*x - 5*x**2 - 1/8*x**3. Determine v, given that c(v) = 0.
-1, 2
Let k = 6866/39 - 2280/13. Factor 0 + 1/3*a - 2/3*a**4 - 1/3*a**5 + k*a**2 + 0*a**3.
-a*(a - 1)*(a + 1)**3/3
Let f(s) = -2*s + 8 + s - 6 + 3*s. Let j be f(-1). Factor -2/9*t**2 + 0*t + j + 2/9*t**3.
2*t**2*(t - 1)/9
Determine y so that 0 - 5*y**3 + 22*y - 12 + 7*y**3 + 7*y**2 - 19*y**2 = 0.
1, 2, 3
Let p = -39 - -41. Let -k + k + 2*k**3 + p*k**3 + 2*k + 6*k**2 = 0. What is k?
-1, -1/2, 0
Let t(m) be the second derivative of m**4/4 + 49*m**3/2 + 72*m**2 + 466*m. Factor t(q).
3*(q + 1)*(q + 48)
Let c(m) be the third derivative of -m**6/600 - m**5/150 + 21*m**4/40 - 885*m**2. Factor c(s).
-s*(s - 7)*(s + 9)/5
Let f(d) be the third derivative of d**5/30 + d**4/4 + 300*d**2. What is t in f(t) = 0?
-3, 0
Let k(h) = h**4 + 27*h**3 + 7*h**2 + 5*h + 5. Let x(b) = 28*b**3 + 6*b**2 + 6*b + 6. Let s(f) = 6*k(f) - 5*x(f). Find y such that s(y) = 0.
-3, -2/3, 0
Let 9 + 16*m - 75 + 5*m**2 - 5*m**2 + m**2 + m**2 = 0. Calculate m.
-11, 3
Let w(r) be the second derivative of -r**8/33600 + r**7/3150 - r**6/1200 - 2*r**4/3 - 12*r. Let f(z) be the third derivative of w(z). Factor f(h).
-h*(h - 3)*(h - 1)/5
Let w be 4/14 + (4/2 - (-6)/(-21)). Solve 0*s**3 + 4/3*s**w + 0 + 2/3*s**5 - 2/3*s - 4/3*s**4 = 0.
-1, 0, 1
Determine v so that 304*v**2 - 88*v**4 - 110*v + 25*v**3 + 20*v**5 + 64 - 162*v - 61*v**3 + 8*v**3 = 0.
-2, 2/5, 1, 4
Let a be -19 + (-17 - -26) + 13. Factor -13/2*j**2 + 3/4*j**a + 4*j + 0.
j*(j - 8)*(3*j - 2)/4
Let z(u) be the first derivative of 4*u**3 + 109/12*u**4 + 42/5*u**5 + 37 + 2/3*u**2 + 49/18*u**6 + 0*u. Factor z(d).
d*(d + 1)**2*(7*d + 2)**2/3
Let q(z) be the first derivative of z**6/105 - z**5/70 - z**4/21 - 55*z + 22. Let j(i) be the first derivative of q(i). Factor j(f).
