et r(h) be the first derivative of 35/3*h**3 - 5*h**2 + 0*h + 24. Suppose r(y) = 0. What is y?
0, 2/7
Let r be (1/10 - 406/(-140))/1. Let p(i) be the second derivative of 0 + 0*i**r + 11*i - 4/3*i**4 - 14/15*i**6 + 0*i**2 + 16/5*i**5. Factor p(o).
-4*o**2*(o - 2)*(7*o - 2)
Let c(y) be the first derivative of -y**6/15 - 26*y**5/25 - 9*y**4/10 + 74*y**3/15 + 2*y**2 - 48*y/5 - 1382. Find z such that c(z) = 0.
-12, -2, -1, 1
Suppose 39*l = 12*l + 18468. Let s = -679 + l. Factor -20/9*x**2 - 10/9*x**4 - 2/9 - 2/9*x**s - 20/9*x**3 - 10/9*x.
-2*(x + 1)**5/9
Let z(d) be the second derivative of -d**6/24 - 5*d**5/6 - 85*d**4/24 - 20*d**3/3 + 20*d**2 + 25*d. Let m(y) be the first derivative of z(y). Factor m(j).
-5*(j + 1)**2*(j + 8)
Let x be ((-264)/(-7) + -2)/(6/42). Let w be 28/30 + (-150)/x. Factor w*u**2 + 0 - 2/9*u - 1/9*u**3.
-u*(u - 2)*(u - 1)/9
Suppose 954 = -127*o + 617*o - 516. Determine d so that -30*d**o + 345/2*d + 27 + 501/2*d**2 = 0.
-2/5, -1/4, 9
Determine l, given that -544/5*l + 3502/5*l**3 - 2002/5*l**2 - 54/5*l**5 + 184/5 - 1086/5*l**4 = 0.
-23, -1/3, 2/9, 1, 2
Let m be 3*(1 - 4) + 1. Let k(h) = 2*h**3 + 16*h**2 + h + 8. Let o be k(m). Suppose -1/3 + 1/3*j**2 + o*j = 0. What is j?
-1, 1
Let r(h) = 2*h**2 + h - 1. Suppose 0 = 40*y - 179 + 579. Let g(t) = 5*t**2 + 36*t - 37. Let z(n) = y*r(n) + 5*g(n). Find f, given that z(f) = 0.
-35, 1
Let q be (572985/(-428))/119*(-8)/50. Solve -q*j**3 - 24/5*j**2 - 1/5*j**4 + 0 - 16/5*j = 0.
-4, -1, 0
Let g(h) = -12*h**3 + 46*h**2 - 194*h. Let m(k) = 7*k**3 - 23*k**2 + 96*k. Let o(b) = -3*g(b) - 5*m(b). Determine y, given that o(y) = 0.
0, 6, 17
Let i be (2952/1025)/(32/60). Solve 6/5*x**2 + i*x - 3 = 0.
-5, 1/2
Let m = 97/10 - 1741/180. Let s(b) be the second derivative of -m*b**4 + 0 + 0*b**2 + 2/9*b**3 - 10*b. Suppose s(h) = 0. What is h?
0, 4
Suppose -69 - 3*x**3 + 69*x**2 - 73*x**2 + 135*x - 59*x**2 = 0. What is x?
-23, 1
Let o(a) be the third derivative of 5*a**5/6 + 265*a**4/24 - 105*a**3/2 - 1724*a**2. Determine y so that o(y) = 0.
-63/10, 1
Let n(o) = -29*o**2 + 3079*o - 1164356. Let i(l) = -84*l**2 + 9234*l - 3493066. Let d(k) = 9*i(k) - 26*n(k). Let d(h) = 0. Calculate h.
763
Let w(v) be the first derivative of -v**7/840 - v**6/240 + v**5/30 - v**2/2 - 59*v - 31. Let u(d) be the second derivative of w(d). Factor u(t).
-t**2*(t - 2)*(t + 4)/4
Suppose -17*z = 14*z - 93. Suppose 4*o - 1 = -z*r - 17, 5*r - 5*o = 20. Factor r*j - 1/5*j**4 + 0 + 0*j**2 + 0*j**3 + 1/5*j**5.
j**4*(j - 1)/5
Suppose -36 = -639*k + 621*k. Let j(y) be the third derivative of 2*y**k + 0*y + 0*y**4 + 2/15*y**3 + 0 - 1/300*y**5. Factor j(n).
-(n - 2)*(n + 2)/5
Let x be (-4865)/(-5) - (-12 + 4 + 1). Let k = x + -978. Let 1/10*y**4 - 1/2*y**k + 0*y + 2/5 + 0*y**3 = 0. What is y?
-2, -1, 1, 2
Let p = -2/63413 - 134245317/126826. Let w = p + 1072. Suppose 2/3*z**2 + 6*z + w = 0. What is z?
-9/2
Solve -1/2*o**2 + 126 + 18*o = 0 for o.
-6, 42
Let j(x) be the first derivative of -153/4*x**4 - 55/3*x**3 + 25*x**2 + 116 - 5/6*x**6 + 0*x - 53/5*x**5. Let j(a) = 0. Calculate a.
-5, -1, 0, 2/5
Let f(h) be the first derivative of 3*h**6/65 + 4*h**5/65 - 11*h**4/156 + h**3/39 - 83*h**2/2 - 50. Let k(x) be the second derivative of f(x). Factor k(w).
2*(w + 1)*(6*w - 1)**2/13
Let x be 12/(-4 - -2) - (67 - -5)/(-9). Let s(z) be the second derivative of -1/21*z**4 - 44/21*z**3 - 242/7*z**x - 3*z + 0. Factor s(d).
-4*(d + 11)**2/7
Suppose -1 = f, -2*w + f = -39 - 122. Suppose 5*r**5 - 186*r + 277*r + w*r**2 - 251*r + 80 - 25*r**4 + 20*r**3 = 0. Calculate r.
-2, 1, 2
Let z(p) be the second derivative of p**8/11760 + p**7/4410 + 37*p**4/12 + 58*p - 1. Let i(j) be the third derivative of z(j). Solve i(a) = 0 for a.
-1, 0
Suppose -18 = 8*p + 30. Let k be 6 + (-5 - (p - -4)). Factor -4*s**5 - 13*s**3 - 59*s**k - 52*s - 21 + 9 - 88*s**2 - 28*s**4.
-4*(s + 1)**4*(s + 3)
Let g = -339 - -340. Suppose -v = -g, 5*x - 10 + 0 = 5*v. Factor 3/5*r + 3/5*r**x + 6/5*r**2 + 0.
3*r*(r + 1)**2/5
What is i in -4/3*i**4 + 0 + 8/3*i - i**3 + 1/3*i**5 + 10/3*i**2 = 0?
-1, 0, 2, 4
Suppose 3*u = -12, -2*b + 3524 = -2*u + 248. Factor -1632 + 3266 - b + x**2 - 19*x.
x*(x - 19)
Let t(a) be the first derivative of a**4 + 0*a + 1/120*a**6 - 13*a**3 + 18 - 3/20*a**5 + 0*a**2. Let h(b) be the third derivative of t(b). Factor h(w).
3*(w - 4)*(w - 2)
Suppose 3326 + 41 = 249*f - 368. Let l(w) be the second derivative of -1/2*w**3 - 1/12*w**4 - w**2 + f*w + 0. Factor l(k).
-(k + 1)*(k + 2)
Let u be (-55)/(-2) - 0 - 8/16. Suppose 10*n - u = 5*n + t, 10 = -5*t. Suppose 10*i**3 - 4*i**4 + 3*i**4 + 6*i**2 + n*i - 15*i - 8 + 3*i**4 = 0. Calculate i.
-4, -1, 1
Let s(n) = 19*n**3 + 32*n**2 + 41*n - 77. Let l(b) = 5*b**3 + 7*b**2 + 11*b - 19. Let o(y) = -30*l(y) + 8*s(y). Factor o(c).
2*(c - 1)*(c + 1)*(c + 23)
Suppose -3*s + 240 = 225. Factor -3*x**s - 54*x**2 - 33*x**3 + 6*x**5 + 0*x**5 - 24*x.
3*x*(x - 4)*(x + 1)**2*(x + 2)
Let v be (-16 - -1)*(-139)/4170. Solve -v*w + w**2 + 1/2*w**3 - 1 = 0.
-2, -1, 1
Let r be -3 + (-204)/(-66) + (-1)/11. Let s(b) be the second derivative of 1/10*b**2 - 1/60*b**4 + r - 8*b + 0*b**3. Factor s(w).
-(w - 1)*(w + 1)/5
Determine c, given that -87/5*c + 87/5*c**3 - 93/5*c**2 + 3/5*c**4 + 18 = 0.
-30, -1, 1
Factor 309/7*n**2 + 46/7*n**3 + 1/7*n**4 - 5184/7*n + 8748/7.
(n - 6)*(n - 2)*(n + 27)**2/7
Let r(y) be the second derivative of -2*y**5/5 - y**4 + 16*y**3/3 - 6*y**2 - 32*y - 50. What is x in r(x) = 0?
-3, 1/2, 1
Suppose 2*c - 5*t - 52 = 0, -3*c + 28 = 7*t - 2*t. Suppose 16 - 3*n**3 - 2*n + 20*n - 15*n**2 - c = 0. Calculate n.
-6, 0, 1
Let y(o) be the third derivative of 3/20*o**6 + 0 + 4/15*o**5 + 4*o - 1/21*o**7 - 1/48*o**8 - 11/24*o**4 - 18*o**2 - o**3. Let y(t) = 0. Calculate t.
-2, -1, -3/7, 1
Let o = 935 + -935. Let k(t) be the third derivative of 5/6*t**3 + 5/12*t**4 + 4*t**2 - 1/12*t**5 + o*t + 0 - 1/12*t**6. Find z such that k(z) = 0.
-1, -1/2, 1
Let h(f) be the third derivative of -f**5/120 - 185*f**4/48 - 91*f**3/2 + 1178*f**2 + 2*f. Factor h(i).
-(i + 3)*(i + 182)/2
Let m(q) be the first derivative of -4/7*q - 8/21*q**3 + 5/7*q**2 + 20 + 1/14*q**4. Solve m(g) = 0.
1, 2
Let f(w) be the second derivative of -w**5/4 + 95*w**4/12 + 2064*w - 3. Let f(o) = 0. Calculate o.
0, 19
Suppose 21*w = 27*w - 174. Suppose w = -39*u + 40*u. Suppose -13*j + 5*j**2 + 16 + 33*j + 10*j + u = 0. Calculate j.
-3
Let s(j) = -11*j - 284. Suppose 8*q - 68 = -0*v + 2*v, -q + 132 = -5*v. Let k be s(v). Factor 40 + 20*a + 5/2*a**k.
5*(a + 4)**2/2
Let k = 1201 - 557. Let s = -642 + k. Let -3/7*n**4 + 54/7*n + 9/7*n**s + 0 - 12/7*n**3 = 0. Calculate n.
-3, 0, 2
Let c(a) be the third derivative of 0*a**3 + 0*a**4 - 2/5*a**5 - 1/30*a**6 + 19*a**2 + 0 + 2/105*a**7 + 0*a. Solve c(x) = 0.
-2, 0, 3
Suppose -24/5 - 14/5*c**4 + 6/5*c**3 + 2/5*c**5 + 38/5*c**2 - 8/5*c = 0. What is c?
-1, 1, 2, 6
Find h, given that 29*h**3 + 8*h**4 - 4*h**5 - 24*h**2 - 234*h - 227*h + 461*h - 9*h**3 = 0.
-2, 0, 1, 3
Find o such that -1536/5 + 4/5*o**3 + 128*o - 88/5*o**2 = 0.
6, 8
Let p(o) be the first derivative of o**6/6 - 87*o**5/5 + 85*o**4/4 + 29*o**3 - 43*o**2 + 4115. Find h, given that p(h) = 0.
-1, 0, 1, 86
Let l(c) be the third derivative of c**5/360 + 5*c**4/6 - 121*c**3/36 - 39*c**2 + 7*c + 4. Factor l(v).
(v - 1)*(v + 121)/6
Let m = 157465 - 2361973/15. Factor -4/5*s**2 - m*s**3 + 0 - 2/3*s.
-2*s*(s + 1)*(s + 5)/15
Suppose 34470*k = 34472*k. Let z(s) be the second derivative of 1/2*s**3 + 3/4*s**2 + 1/8*s**4 + 13*s + k. Find v, given that z(v) = 0.
-1
Let y(h) be the second derivative of 79*h + 0*h**2 + 5/3*h**4 + 0 - 4*h**3 + 1/5*h**5. Factor y(b).
4*b*(b - 1)*(b + 6)
Let x(n) be the third derivative of n**6/120 - 161*n**5/60 + 319*n**4/24 - 53*n**3/2 + 873*n**2. Suppose x(r) = 0. Calculate r.
1, 159
Solve 0 - 2/7*k**3 + 0*k - 2592/7*k**2 = 0.
-1296, 0
Let n(l) be the second derivative of 529*l**7/42 + 506*l**6/15 + 219*l**5/10 - 11*l**4/3 + l**3/6 + 3279*l. Find x, given that n(x) = 0.
-1, 0, 1/23
Let g(f) be the first derivative of -2/3*f**4 + 0*f + 20/27*f**3 + 4/45*f**5 + 0*f**2 - 48. Find d, given that g(d) = 0.
0, 1, 5
Let w(y) = 41*y**3 + 160 + 345*y**4 - 344*y**4 - 174*y + 8*y - 30*y**2. Let c(i) = -i**4 - i**3 + i. Let z(p) = -6*c(p) - w(p). Suppose z(d) = 0. What