 2
Let n(u) be the first derivative of -u**4/8 + 35*u**3/6 + 9*u**2 + 374. Suppose n(v) = 0. What is v?
-1, 0, 36
Let n(o) be the third derivative of o**6/960 - 11*o**5/480 + o**4/24 + 5*o**3/12 + 620*o**2. Factor n(d).
(d - 10)*(d - 2)*(d + 1)/8
Let u be (-21)/196*(-6)/18. Let c(d) be the second derivative of 7*d + 0 + u*d**4 - 1/7*d**3 + 3/14*d**2. Factor c(b).
3*(b - 1)**2/7
Suppose -4*a + 2*j + 4 = 0, 5*j - 4*j = -5*a - 2. Factor a + 1/2*g**2 + g.
g*(g + 2)/2
Let b = -1098 - -1098. Let u(y) be the second derivative of 1/20*y**5 + 1/70*y**6 + 0 + 5/84*y**4 + 1/42*y**3 + b*y**2 - y. Let u(t) = 0. Calculate t.
-1, -1/3, 0
Let k(o) be the first derivative of -o**5/90 - 11*o**4/60 + 14*o**3/45 - 41*o**2/2 - 27. Let w(g) be the second derivative of k(g). What is j in w(j) = 0?
-7, 2/5
Let d(m) = 9*m**2 - 14*m - 78. Let z(n) = -4*n**2 + 9*n + 40. Let a(b) = -3*d(b) - 7*z(b). Solve a(r) = 0 for r.
-2, 23
Let y(c) = -c**2 + c - 1. Let w(j) = 12*j**2 + 33*j + 9. Let r(d) = -w(d) - 9*y(d). Factor r(i).
-3*i*(i + 14)
Suppose 0 = -4*b - r + 33, 3*r = -b - 3*b + 43. Let y be b + (1 - 3) + -1. Factor 3*m**2 + 2*m**3 + m**3 - 3*m + 0*m**3 - 3*m**y + 0*m**3.
-3*m*(m - 1)**2*(m + 1)
Let n(b) = 3*b**2 - 25*b - 14. Let t be n(9). Let a(u) be the first derivative of -3/16*u**t + 3/5*u**5 - 1 + 0*u**2 - 1/2*u**3 + 0*u + 3/8*u**6. Factor a(d).
3*d**2*(d + 1)**2*(3*d - 2)/4
Let i(x) be the second derivative of 5*x**7/112 + 7*x**6/20 + 21*x**5/40 - x**4/2 + x + 57. Find u such that i(u) = 0.
-4, -2, 0, 2/5
Suppose -6 = -54*b - 2 - 4. Suppose -1/2*f**3 + b*f + 0 + 1/2*f**5 + 0*f**4 + 0*f**2 = 0. Calculate f.
-1, 0, 1
Let c(a) be the third derivative of -37*a**2 + 0*a - 1/3*a**3 + 1/6*a**4 - 1/30*a**5 + 0. Determine g so that c(g) = 0.
1
What is v in 21025/8 + 1/8*v**2 + 145/4*v = 0?
-145
Let g(w) = 7*w**4 - 15*w**3 + 19*w**2 - 9*w + 2. Let f(s) = 51*s**4 - 105*s**3 + 132*s**2 - 63*s + 15. Let h(r) = 2*f(r) - 15*g(r). Let h(m) = 0. What is m?
0, 1, 3
Let m(p) be the third derivative of -1/90*p**6 + 0 + 0*p + 0*p**3 - 1/3*p**4 - 1/9*p**5 + 9*p**2. Find j such that m(j) = 0.
-3, -2, 0
Let s(o) be the second derivative of o + 9/16*o**5 + 5/24*o**7 + 5/8*o**6 + 0*o**3 + 2 + 0*o**2 + 5/48*o**4. What is c in s(c) = 0?
-1, -1/7, 0
Let z(g) be the first derivative of -3*g**5/5 - 3*g**4 + 96. What is f in z(f) = 0?
-4, 0
Let a be (-15)/195*((-21)/18 + 1). Let i(s) be the second derivative of -1/195*s**6 + 0*s**5 - 8*s + 0 + 0*s**3 + a*s**4 + 0*s**2. Let i(y) = 0. Calculate y.
-1, 0, 1
Let l = 70 + -68. Factor f - 257*f**3 + f**l + 258*f**3 - f**4 - 2*f.
-f*(f - 1)**2*(f + 1)
Let s(k) be the third derivative of -k**6/60 + k**5/42 + 4*k**4/21 + 4*k**3/21 - 2*k**2 - 112. Find t such that s(t) = 0.
-1, -2/7, 2
Let c(u) be the third derivative of u**10/10500 - u**9/12600 + u**8/50400 + 8*u**5/15 - 3*u**2. Let i(p) be the third derivative of c(p). Factor i(v).
2*v**2*(6*v - 1)**2/5
Let u(b) be the second derivative of b**3/6 - 18*b. Let s(p) = 845*p**2 + 264*p + 20. Let h(l) = s(l) - 4*u(l). Find j, given that h(j) = 0.
-2/13
Let s(j) = j**3 + 2*j + 3. Let v be s(0). Let r - 34 + 15 + 15 + v*r**2 = 0. What is r?
-4/3, 1
Let x(n) be the second derivative of -n**6/2 + 2*n**5 - 5*n**4/12 - 20*n**3/3 + 10*n**2 + 95*n. What is t in x(t) = 0?
-1, 2/3, 1, 2
Let p(j) = -2*j**2 - 45*j - 34. Let b(x) = -2*x**2 - 42*x - 34. Let d(i) = -6*b(i) + 4*p(i). Let d(c) = 0. What is c?
-17, -1
Suppose 4*t - 363 = 3*i, -2*i - 2*i - 20 = 0. Suppose 12*x**3 - 8*x - t*x**4 + 91*x**4 - 4*x**5 + 0*x**2 - 4*x**2 = 0. Calculate x.
-1, 0, 1, 2
Factor -293*v**4 + 861*v**4 - 44*v**2 + 28*v**3 - 284*v**4 + 20*v - 288*v**4.
-4*v*(v - 5)*(v - 1)**2
Let v = -1639 - -21313/13. Suppose -6/13*f + v*f**2 + 2/13 - 2/13*f**3 = 0. Calculate f.
1
Suppose 11*b - 10*b - 2 = 0. Find w such that 65*w**3 + w**b - 61*w**3 + 7*w**2 = 0.
-2, 0
Let p(m) be the third derivative of m**5/270 + 4*m**4/9 + 64*m**3/3 + 2*m**2 - 91. Find g such that p(g) = 0.
-24
Let h = -9 - -9. Let w be h*(-3 - 15/(-6)). Factor -d + 12 + w*d - 2*d**2 - 11.
-(d + 1)*(2*d - 1)
Let l(k) = 5*k**2 + 11*k + 9. Let r be l(-1). Let h(m) be the third derivative of 0*m + 1/90*m**4 + 1/150*m**5 + 0*m**r + 0 - 4*m**2. Factor h(s).
2*s*(3*s + 2)/15
Let g = -1612 + 27407/17. Let v(k) be the first derivative of -2/85*k**5 + 4 - g*k**4 - 12/17*k**2 - 26/51*k**3 - 8/17*k. What is u in v(u) = 0?
-2, -1
Let p = 2 + 0. Suppose 0 = 2*f + p*t + 5 - 3, -4*f + 23 = -5*t. Find b such that 2 - 4*b**3 - 12*b**4 + 12*b**5 - 17*b**3 - 6*b**f - 2 = 0.
-1/2, 0, 2
Suppose -64 = -4*l - 4*u, 0*l + l - 22 = -4*u. Suppose 11*x + 3 + 20*x - l*x + 33*x**2 + 18*x**3 + x = 0. What is x?
-1, -1/2, -1/3
Let v(s) = -2*s**2 + 7*s + 49. Let n be v(7). Suppose -3/5*b**2 + 0*b + n = 0. What is b?
0
Let w(q) be the second derivative of -6*q + 1/6*q**4 - q**2 + 0*q**3 + 0. Factor w(p).
2*(p - 1)*(p + 1)
Let d(v) be the second derivative of -2*v**4/21 - 5*v**3/7 - 11*v**2/7 + 32*v - 3. Factor d(g).
-2*(g + 1)*(4*g + 11)/7
Suppose -40*b + 67*b = -78*b + 210. Factor 1/6*v**b + 1/6*v**3 - 1/6*v**5 - 1/6*v**4 + 0*v + 0.
-v**2*(v - 1)*(v + 1)**2/6
Let s be (504/288)/(6/(-40)) - -13. Let w(g) = g - 5. Let d be w(5). Factor -s*u + d - 2/3*u**3 - 2*u**2.
-2*u*(u + 1)*(u + 2)/3
Let v = -934 + 934. Let t be 6/2 + (-9)/6. Suppose v - t*c**2 + 0*c + 3*c**3 - 3/2*c**4 = 0. Calculate c.
0, 1
Let n(w) = w**2 + 13*w + 20. Let h(b) = 4*b**2 + 53*b + 80. Let j(p) = -2*h(p) + 9*n(p). Let c be j(-9). Let -1/6*d - 1/3 + 1/6*d**c = 0. What is d?
-1, 2
Let g = -2958 + 2958. Factor -1/3*z**2 + 0*z - 1/3*z**4 + g - 2/3*z**3.
-z**2*(z + 1)**2/3
Let p(n) be the first derivative of 1/4*n**3 - 3/8*n**2 - 4 - 9/2*n. Factor p(d).
3*(d - 3)*(d + 2)/4
Let o be -2 + 478/20 - (-4)/(-8). Let v = o - 21. Factor 6/5*y + v*y**3 + 2/5 + 6/5*y**2.
2*(y + 1)**3/5
Let t(u) be the third derivative of -u**6/300 - 8*u**5/75 + 7*u**4/12 - 6*u**3/5 - 238*u**2 - 1. Let t(i) = 0. What is i?
-18, 1
Suppose -4*s + 357 + 143 = 0. Factor -137*c**3 + 42*c**3 - 5*c**5 + 35*c**4 + 20 - 88*c + s*c**2 + 8*c.
-5*(c - 2)**2*(c - 1)**3
Factor 2369*q - 2319*q + 5 - 5*q**4 + 30*q**3 - 20 - 60*q**2.
-5*(q - 3)*(q - 1)**3
Let q(h) be the second derivative of 3*h**5/2 - 9*h**4 - 39*h**3/5 - 12*h**2/5 - 4*h + 15. Determine g, given that q(g) = 0.
-1/5, 4
Let v be 2 - 2 - (-7)/(42/816). Let a = v + -269/2. Factor 0*d**3 + 0 - 3/4*d**5 + 3/4*d + 3/2*d**2 - a*d**4.
-3*d*(d - 1)*(d + 1)**3/4
Factor 42*w**2 + 7*w**3 - 3*w**3 - 400 - 39*w**2 + 480*w - 87*w**2.
4*(w - 10)**2*(w - 1)
Let y(s) be the first derivative of -s**4/16 - s**3/3 + 7*s**2/2 - 8*s + 15. Factor y(z).
-(z - 2)**2*(z + 8)/4
Let m(g) = g**3 - 5*g**2 + 13*g - 14. Let c be m(4). Let p(b) = 3*b**2 - b + 2. Let h(s) = -16*s**2 + 6*s - 11. Let y(x) = c*p(x) + 4*h(x). Solve y(u) = 0.
-1, 0
Let t(k) = 11*k**2 - 34*k + 108. Let u(y) = -6*y**2 + 16*y - 54. Let q(n) = 4*t(n) + 7*u(n). Suppose q(l) = 0. Calculate l.
3, 9
Let w(i) be the third derivative of 1/8*i**4 + 1/112*i**8 - 1/2*i**3 - i**2 - 1/70*i**7 + 0 + 1/10*i**5 + 0*i - 1/20*i**6. Suppose w(b) = 0. Calculate b.
-1, 1
Let r = 128 - 91. Suppose -5*j + r = 3*p, 3*p - p + 3*j = 24. Determine w so that -18*w**4 - p*w**5 + 3*w**4 + 0*w**2 + 8*w**3 - 2*w**2 + 6*w**2 = 0.
-2, -1/3, 0, 2/3
Let z(r) be the first derivative of 4/5*r - 4/5*r**2 - 1/20*r**4 + 18 + 1/3*r**3. Determine s, given that z(s) = 0.
1, 2
Factor 3/5*a**5 + 0*a**2 - 9/5*a**3 + 0*a - 6/5*a**4 + 0.
3*a**3*(a - 3)*(a + 1)/5
Let q(x) be the third derivative of -x**8/12600 - x**7/6300 + 5*x**3/2 - 14*x**2. Let z(k) be the first derivative of q(k). Factor z(i).
-2*i**3*(i + 1)/15
Let a(x) = x**2 - 8*x + 7. Let p be a(6). Let w(v) = -v**2 - 4*v + 9. Let h be w(p). Factor 0*y**4 - 2*y**4 + 4*y**3 + 5 - h*y - 3.
-2*(y - 1)**3*(y + 1)
Let h(u) be the first derivative of -2*u**3/57 - 10*u**2/19 + 22*u/19 - 65. Suppose h(v) = 0. Calculate v.
-11, 1
Let x(c) be the second derivative of -c**4/120 + c**3/6 - 9*c - 2. Factor x(q).
-q*(q - 10)/10
Suppose q = -2*q + 12. Factor 14*j - 14*j**3 - q*j**2 - 14*j.
-2*j**2*(7*j + 2)
Let 9*i**3 + 60*i**2 - 13*i**4 + 638*i - 602*i - 3*i**5 - 5*i**4 = 0. Calculate i.
-6, -1, 0, 2
Suppose 7 + 13 = 2*z. Suppose 2*a + 3*a - z = 0. Factor 0*l**a + 0*l + 7*l**3 - 3*l - 2*l**2