first derivative of -7/8*v**2 + 1/12*v**3 + 3/2*v + 56. Suppose i(m) = 0. Calculate m.
1, 6
Factor 4/5*z**2 + 0 - 2/5*z**3 + 0*z - 2/5*z**4.
-2*z**2*(z - 1)*(z + 2)/5
Let q(f) = -2*f**3 + 2502*f**2 - 776250*f + 773750. Let s(y) = 2*y**3 - 2500*y**2 + 776251*y - 773753. Let l(x) = 5*q(x) + 6*s(x). Solve l(z) = 0.
1, 622
Let j be 55/6 - (-15)/(-90) - -4. Factor 5*k + 0*k**2 + 12*k**2 - j*k**2.
-k*(k - 5)
Suppose 10 - 91 = -3*a. Let t be ((-30)/(-4))/(a/18). Determine c, given that 20*c + t*c**2 + 23*c - 53*c = 0.
0, 2
Let a(t) be the second derivative of -t**9/22680 - t**8/5040 + t**7/3780 + t**6/540 - 5*t**4 - 22*t. Let s(v) be the third derivative of a(v). Factor s(n).
-2*n*(n - 1)*(n + 1)*(n + 2)/3
Let x(s) be the second derivative of s**4/114 - 35*s**3/57 + 196*s**2/19 - 4*s - 6. Factor x(w).
2*(w - 28)*(w - 7)/19
Let j(k) be the first derivative of k**6/12 - 17*k**5/10 - 79*k**4/8 - 103*k**3/6 - 21*k**2/2 + 2048. Determine w so that j(w) = 0.
-2, -1, 0, 21
Let y be (-297 + 291)/(30/(-32)*2). Let 0*c**2 - y*c**3 + 4/5 + 12/5*c = 0. What is c?
-1/2, 1
Let u(q) = -4*q**5 + 485*q**4 - 487*q**3 + 6*q**2 + 6*q. Let f(d) = 2*d**5 - 484*d**4 + 486*d**3 - 4*d**2 - 4*d. Let w(t) = 6*f(t) + 4*u(t). Solve w(p) = 0.
-242, 0, 1
Let o(w) be the second derivative of 2*w**7/105 - 4*w**6/75 - 37*w**5/25 - 82*w**4/15 - 32*w**3/5 + 208*w + 10. Solve o(p) = 0 for p.
-3, -2, -1, 0, 8
Suppose -20*x - 31 = -71. Factor 817*r**x - 5*r**4 + 34*r - 20*r**3 - 782*r**2 + 16*r.
-5*r*(r - 2)*(r + 1)*(r + 5)
Let q(y) = 15*y**3 - 39*y. Let g(o) = -10*o**3 - 8*o - 1 + 13*o**3 + 1. Let c = 288 - 283. Let b(a) = c*q(a) - 24*g(a). What is f in b(f) = 0?
-1, 0, 1
Let q(i) = -16*i**3 + 152*i**2 + 780*i + 1220. Let p(x) = -19*x**3 + 162*x**2 + 780*x + 1219. Let u(s) = -4*p(s) + 5*q(s). Solve u(f) = 0 for f.
-3, 34
Let s(d) be the second derivative of d**4/42 + 67*d**3/21 + 192*d**2/7 - 960*d. Solve s(o) = 0 for o.
-64, -3
Let l be (-47215)/(-855) - 4/18. Factor l*s - 158*s**2 + 68*s**2 + 21*s + 4*s - 22 - 3 + 40*s**3 - 5*s**4.
-5*(s - 5)*(s - 1)**3
Let l = 1/161 + -70681/322. Let z = 220 + l. Factor z - 1/2*g - 1/2*g**2 + 1/2*g**3.
(g - 1)**2*(g + 1)/2
Let d(t) = -15*t**3 - 3016*t**2 + 31*t + 2888. Let v(b) = -5*b**3 - 1005*b**2 + 10*b + 965. Let h(i) = -5*d(i) + 16*v(i). Find w such that h(w) = 0.
-200, -1, 1
Let c(t) be the third derivative of t**5/210 - 617*t**4/42 + 380689*t**3/21 + 1625*t**2. Determine h, given that c(h) = 0.
617
Let x(b) be the second derivative of 2*b - 5*b**3 + 42 + 0*b**2 - 1/6*b**4. Determine j so that x(j) = 0.
-15, 0
Suppose y = 25*y - 216. Suppose 27*k - 21*k = -y*k. Factor 3/7*w**2 - 3/7*w + k.
3*w*(w - 1)/7
Let h be ((-3)/10)/(112/84). Let d = h - -159/40. Factor 3/8*t**4 + 81/4*t + 81/8 + 27/2*t**2 + d*t**3.
3*(t + 1)*(t + 3)**3/8
Suppose -5*x = 4*y + 388, 7*x - 5*y + 294 = 3*x. Let b = 82 + x. Factor -13 - 4*d**3 - 26 - b*d**4 + 2*d**4 + 16*d + 24*d**2 + 7.
-4*(d - 2)*(d - 1)*(d + 2)**2
Let r(g) be the first derivative of 10*g**3 + 0*g + 5/2*g**2 + 10/3*g**6 + 12*g**5 + 164 + 65/4*g**4. What is y in r(y) = 0?
-1, -1/2, 0
Let -15916*z - 1909*z**2 - 1819*z**2 + 3730*z**2 + 31664882 = 0. What is z?
3979
Let v(p) be the first derivative of -p**5/5 - 5*p**4/3 - 16*p**3/3 + 17*p**2 + 237. Let c(n) be the second derivative of v(n). Let c(u) = 0. Calculate u.
-2, -4/3
Determine h so that -2/21*h**4 - 24/7*h + 6/7*h**3 + 8/21*h**2 + 0 = 0.
-2, 0, 2, 9
Let o(a) = -a**3 + a + 1. Let r(c) = 3*c**4 + 9*c**3 + 18*c**2 + 15*c + 6. Let s be (4 - 6)/(1*(-8)/12). Let l(t) = s*o(t) - r(t). Factor l(p).
-3*(p + 1)**4
Let a(u) be the third derivative of -u**5/15 - 41*u**4/6 - 220*u**3 - 2500*u**2. Determine j, given that a(j) = 0.
-30, -11
Let g be (2 - 1)*(12 + 27 + -15). Factor -20 + g*o**2 + 2 + 17*o - 23*o**2.
(o - 1)*(o + 18)
Find g, given that g + 13*g - 272 - 22*g + 4*g**2 + 2*g - 46*g = 0.
-4, 17
Let v = 120 - 116. Let 3*a - v*a + a**3 - 4*a**2 + 3*a + a = 0. What is a?
0, 1, 3
Solve -1/2*p**4 + 5*p + 12 - 5*p**3 - 23/2*p**2 = 0 for p.
-6, -4, -1, 1
Let q(t) be the third derivative of -t**7/2520 - t**6/120 - 13*t**4/12 - 18*t**2. Let j(y) be the second derivative of q(y). Factor j(o).
-o*(o + 6)
Let n be (-6*1/(-18))/(2/162). Find o such that -3*o**5 + 14*o**3 + 24*o**2 - 42*o**3 + 59*o**4 - o**5 - n*o**4 - 24*o**3 = 0.
0, 1, 6
Let y(u) be the first derivative of -u**6/21 - 2*u**5/7 - 5*u**4/14 + 10*u**3/21 + 6*u**2/7 + 1133. Find r, given that y(r) = 0.
-3, -2, -1, 0, 1
Let s(z) be the first derivative of 2*z**5/95 - 5*z**4/38 + 8*z**3/57 + 3288. Factor s(o).
2*o**2*(o - 4)*(o - 1)/19
Let v(s) = -s**3 - s - 6. Let g be v(0). Let i be (-21)/3*((g - -2) + 2). Factor -11 + 8*z**2 + 15 + 6*z - i*z - 4*z**2.
4*(z - 1)**2
Determine r so that -3308/5*r + 1367858/5 + 2/5*r**2 = 0.
827
Factor -2654/7*j - 467/7*j**2 + j**3 - 720/7.
(j - 72)*(j + 5)*(7*j + 2)/7
Find c, given that 3/4*c**2 - 621/2 - 1239/4*c = 0.
-1, 414
Let u(j) be the second derivative of -27*j + 8/7*j**3 + 0 + 1/105*j**6 + 11/21*j**4 + 9/7*j**2 + 4/35*j**5. Suppose u(w) = 0. What is w?
-3, -1
Let y(s) = -139*s**2 + 5682*s - 2690435. Let f(j) = 52*j**2 - 1894*j + 896812. Let g(r) = 8*f(r) + 3*y(r). Factor g(t).
-(t - 947)**2
Let i(s) be the first derivative of -8/15*s - 26/5*s**3 + 27/10*s**4 - 31 + 8/3*s**2. Factor i(j).
2*(j - 1)*(9*j - 2)**2/15
Suppose 0 = -156*m + 95 + 217. Let s(k) be the first derivative of -5/6*k**6 + 6250/3*k**3 + 25*k**5 - 625/2*k**4 + 15625*k - 23 - 15625/2*k**m. Factor s(w).
-5*(w - 5)**5
Let w be -17 + 20 - (-1 + 0). Factor -3*h**w - 502*h**2 + 3 - 20*h + 0*h**4 + 7*h**4 + 4*h**3 + 490*h**2 - 11.
4*(h - 2)*(h + 1)**3
Let s(a) = a**2 - 98*a - 496. Let l be s(-5). Let f(d) be the first derivative of 46 + l*d**4 - 8*d**2 + 0*d - 92/5*d**5 + 32/3*d**3 + 4*d**6. Solve f(i) = 0.
-1/2, 0, 1/3, 2
Let p(s) be the third derivative of 0*s - 1/20*s**5 + 0 - 7/24*s**4 - 35*s**2 - 1/3*s**3. Let j(i) = -3*i**2 - 9*i - 3. Let x(b) = 2*j(b) - 3*p(b). Factor x(v).
3*v*(v + 1)
Let b(n) = 10*n**2 - 9*n + 3. Suppose 3 = 2*v + r - 0, -5*v = 5*r - 5. Let i(s) = -20*s**2 + 17*s - 7. Let h(a) = v*i(a) + 5*b(a). Factor h(q).
(q - 1)*(10*q - 1)
Let u(d) be the first derivative of d**3/3 + 181*d**2/2 + 358*d + 5574. Factor u(t).
(t + 2)*(t + 179)
Let w be (0 + -1)*(-5 + -2) - 1066/(-9020)*-55. What is k in k**3 + 5/4*k**2 + 1/4*k**4 + w*k + 0 = 0?
-2, -1, 0
Let h(f) = f**2 + 114. Let o be h(0). Suppose 7*d + o = 10*d. Factor -27*v**3 - d*v + 72*v**2 - 27*v - 12*v**2 + 53*v.
-3*v*(v - 2)*(9*v - 2)
Suppose 24*a**3 - 435*a**4 - 422*a**4 + 67*a - 198*a**2 + 859*a**4 + 334*a - 77*a = 0. What is a?
-18, 0, 3
Let x(z) = -3*z**4 + z**3 - z**2 + 2. Let o(r) = -10*r**4 + 20*r**3 - 72*r**2 - 16*r + 74. Let w(q) = -o(q) + 4*x(q). Let w(u) = 0. What is u?
-11, -1, 1, 3
Let b(n) be the first derivative of -n**3/21 + 57*n**2/14 + 2248. Determine u so that b(u) = 0.
0, 57
Let x(y) be the first derivative of 78 - 10/3*y**2 - 20/3*y - 5/9*y**3. What is p in x(p) = 0?
-2
Let j(p) be the first derivative of -54 + 16/9*p**3 - 1/3*p**4 + 8*p**2 + 0*p. Factor j(u).
-4*u*(u - 6)*(u + 2)/3
Suppose 53*z - 259 = 16*z. Let c(n) be the third derivative of -22*n**2 + 0*n**3 + 0 + 1/20*n**5 - 1/56*n**6 + 0*n - 3/56*n**4 + 1/490*n**z. Factor c(u).
3*u*(u - 3)*(u - 1)**2/7
Let i(y) = -875*y**3 - 5238*y**2 - 7815*y + 92. Let z(t) = t**2 + 1. Let a(n) = i(n) - 2*z(n). Suppose a(o) = 0. Calculate o.
-3, 2/175
Let y(g) = g**2 - 42*g + 322. Let m be y(32). Let -3*z - 9*z + 50 - z**m - 37*z = 0. What is z?
-50, 1
Let k(f) be the first derivative of -1/6*f**6 - 22 - 9/2*f**2 - 16/3*f**3 - 7/2*f**4 - 6/5*f**5 - 2*f. Let k(b) = 0. Calculate b.
-2, -1
Let g be (15 + -54 + 41)*2. Let g*j - 15/4 - 1/4*j**2 = 0. Calculate j.
1, 15
Let x(m) be the first derivative of m**5/12 - 35*m**4/24 + m**2/2 - 69*m + 75. Let u(k) be the second derivative of x(k). Factor u(j).
5*j*(j - 7)
Factor -450623*u**2 - 10*u + 1 - 1 + 451008*u**2.
5*u*(77*u - 2)
Let i(r) be the third derivative of -r**5/80 + 187*r**4/32 - 185*r**3/4 + 203*r**2. Let i(x) = 0. Calculate x.
2, 185
Factor -2/9*y**3 + 7011904/9 - 1165120/3*y - 588*y**2.
-2*(y - 2)*(y + 1324)**2/9
Let s(i) be the second derivative of i**6/16 + 9*i**5/20 - 17*i**4/4 + 6*i**3 - 139*i**2 - 2*i - 102. Let r(