0, 1
Let n = 317 - 315. Determine x, given that 93*x - 54*x**2 - x**4 - 3*x**3 - n*x**4 + 6*x**4 + 53*x - 120 + 10*x = 0.
-5, 2
Let t(h) be the first derivative of h**6/30 - 25*h**2 - 2*h + 46. Let k(a) be the second derivative of t(a). Factor k(v).
4*v**3
Suppose -19*f + 60 + 168 = 0. Let g be (-2 + 0)/((-4)/22). Solve 8*s**2 - 4*s**3 - 4*s - 1 - g + f = 0.
0, 1
Let r(u) be the third derivative of 0*u - 1/420*u**6 - 4/105*u**5 + 0 + 0*u**3 - 1/7*u**4 + 20*u**2. Find s such that r(s) = 0.
-6, -2, 0
Let l be ((-77658)/(-455))/((-30)/(-260)). Factor l + 344/5*u + 4/5*u**2.
4*(u + 43)**2/5
Suppose 3*a - 10 = -4*j, 5*j - 5*a = -0*a - 5. Let f be j - -26 - (-14)/7. Factor f*n - 16*n + 3*n + 4*n**2.
4*n*(n + 4)
Let t = -10600/7 + 1516. Let x(u) be the second derivative of 0 - 15*u - 216/7*u**2 + t*u**3 - 1/28*u**4. Factor x(n).
-3*(n - 12)**2/7
Let g(x) be the first derivative of 10*x**6/3 + 236*x**5/5 + 121*x**4 - 236*x**3/3 - 252*x**2 + 6000. Let g(y) = 0. What is y?
-9, -14/5, -1, 0, 1
Suppose 4*p + 3 = -17. Let c(t) = 3*t**3 + 12*t**2 - 87*t - 92*t + 177*t - 2. Let g(l) = 5*l**3 + 25*l**2 - 5*l - 5. Let v(z) = p*c(z) + 2*g(z). Factor v(y).
-5*y**2*(y + 2)
Let g(v) be the second derivative of -v**4/4 + 13*v**3/2 - 33*v**2 + 575*v. Let g(y) = 0. What is y?
2, 11
Let m be (3/36)/(2/4). Suppose 210 + 600 - 210 = 150*z. Determine s, given that 1/2*s**3 + 0*s + 0 + 1/3*s**2 + m*s**z = 0.
-2, -1, 0
Let x(h) be the third derivative of -h**7/210 - 113*h**6/10 - 51076*h**5/5 - 11543176*h**4/3 - 365*h**2 - 5*h. Suppose x(i) = 0. What is i?
-452, 0
Let x be -3 + (22 - 4) - 3. Suppose x*o = 12 + 24. Factor -9*i**3 - 6*i**o + 11*i**3 + 8*i**2.
-4*i**2*(i - 2)
Let r(f) be the second derivative of 10*f**4/3 - 29*f**3/6 - 26*f**2 - f - 22. Let i(c) = 7*c**2 - 5*c - 9. Let g(p) = -34*i(p) + 6*r(p). Factor g(b).
2*(b - 3)*(b + 1)
Suppose -7*u + 56 = 4*j, j + 16 = -6*u + 8*u. Let r(t) be the first derivative of 2/27*t**3 + 39 + u*t + 4/3*t**2. Factor r(s).
2*(s + 6)**2/9
Factor -559 + 32*b**2 - 24*b**3 - 12*b**2 + 13*b + 23*b**3 + 15*b - 1009.
-(b - 14)**2*(b + 8)
Let v(k) be the first derivative of 0*k**2 + 65 + 0*k**4 + 0*k**3 + 5/6*k**6 + 0*k + k**5. Suppose v(x) = 0. What is x?
-1, 0
Let w(k) be the first derivative of k**5/330 + 3*k**4/44 - 12*k**3/11 - 42*k**2 + 240. Let g(i) be the second derivative of w(i). Factor g(p).
2*(p - 3)*(p + 12)/11
Let r(c) be the second derivative of -c**5/30 - 2*c**4/3 - 7*c**3/3 - 19*c**2/2 - 17*c. Let t(i) be the first derivative of r(i). Let t(x) = 0. What is x?
-7, -1
Let -60*u**2 + 2576*u + 1/3*u**3 + 33856/3 = 0. Calculate u.
-4, 92
Let h = 47 + 8. Factor 22 - h*r**2 + 18*r**2 - 20*r + 14*r**2 + 21*r**2.
-2*(r - 1)*(r + 11)
Suppose -43*p**3 + 139*p**2 - 43*p**2 + 5*p**5 - 108*p**2 + 111*p**2 - 11*p**4 - 18*p = 0. Calculate p.
-3, 0, 1/5, 2, 3
Let g(c) be the first derivative of -2/27*c**3 + 4*c - 47 - 7/9*c**2. Factor g(o).
-2*(o - 2)*(o + 9)/9
Let h(c) be the second derivative of -c**5/120 + 7*c**3/36 - c**2/2 + c + 71. Suppose h(o) = 0. What is o?
-3, 1, 2
Let z(s) be the first derivative of 2*s**3 + 36 + 198*s + 12*s**2 - 246*s - 3*s**3 + 30. Factor z(c).
-3*(c - 4)**2
Let l(n) be the first derivative of -n**3 + 1296*n**2 - 559872*n - 2942. Solve l(w) = 0.
432
Let y be (-5913)/(-459) + (-12)/(-6 - -10). What is b in 88/17 - y*b + 6/17*b**3 + 50/17*b**2 = 0?
-11, 2/3, 2
Let j(a) be the third derivative of a**7/105 + 17*a**6/6 + 535*a**5/2 + 17000*a**4/3 + 160000*a**3/3 + 11*a**2 + 25. Factor j(b).
2*(b + 5)**2*(b + 80)**2
Determine j, given that 260 - 167 - 88 + 5120*j**2 + 320*j = 0.
-1/32
Determine c, given that 5*c**2 - 106281 - 818*c + 105371 - 87*c = 0.
-1, 182
Suppose 574 - 222 = 176*z. Factor 15/4*c**3 + 0*c - 3*c**4 + 3/4*c**5 + 0 - 3/2*c**z.
3*c**2*(c - 2)*(c - 1)**2/4
Let x(u) = -10*u - 36. Let n be x(-4). Suppose n*y**2 - 6*y - 80 - 2*y**2 - 2*y + 0*y**2 + 2*y**3 + 72 = 0. What is y?
-2, -1, 2
Let l(y) = -y**3 + 3*y**2 - 6. Let h be l(0). Let u(f) = -7*f**2 + 58*f - 835. Let q(i) = 5*i**2 - 58*i + 837. Let t(c) = h*q(c) - 4*u(c). Solve t(a) = 0.
29
Let w be 26117/39 - 2/(-6) - -2. Determine i so that -31*i**3 + 77*i**2 + w*i + 35*i**3 + i**2 - 784 + 30*i**2 = 0.
-14, 1
Suppose -3*h - 45 = -4*c, 2*h = 34026*c - 34022*c - 30. Factor -9/8*d**2 - 3/8*d**5 + 15/8*d**3 - 3/8*d**4 + 0 + c*d.
-3*d**2*(d - 1)**2*(d + 3)/8
Let d = 360/13 + -284721/10283. Let s = d + 2361/3164. Find x such that 0*x**2 + s*x - x**3 - 1/4 = 0.
-1, 1/2
Let v(l) be the second derivative of l**5/20 - 193*l**4/6 + 38009*l**3/6 - 72962*l**2 + 5317*l. Suppose v(c) = 0. Calculate c.
4, 191
Let q(c) = c - 14. Let s be q(13). Let b be (-3 - -7 - 5)*(-5 - s). Factor -v**2 + 50*v**b - 106*v**4 - v**3 + v + 57*v**4.
v*(v - 1)**2*(v + 1)
Let p(m) = 356*m + 42367. Let z be p(-119). Factor 0 + 1/2*x**4 + 1/2*x**5 + 0*x - 1/2*x**2 - 1/2*x**z.
x**2*(x - 1)*(x + 1)**2/2
Suppose -229 = -5*q + 3*r, -3*q - 4*r + 164 = q. Let o(n) = -n + 46. Let b be o(q). Factor -22/3*f + 2/3*f**4 - 2/3*f**3 - 6*f**b - 8/3.
2*(f - 4)*(f + 1)**3/3
Let z(d) = 2*d**5 + d**4 - d**3 - d**2 - 1. Let o = -205 - -211. Let y(g) = -17*g**5 + 19*g**4 + 6*g**3 + 6*g**2 + 6. Let h(c) = o*z(c) + y(c). Factor h(x).
-5*x**4*(x - 5)
Suppose 44 = -3*g + 25*g. Find x such that -592*x**3 + 306*x**3 - 242*x**4 - 44*x**g - 2*x**2 - 2*x = 0.
-1, -1/11, 0
Find v such that -5827396/7 - 4/7*v**2 - 9656/7*v = 0.
-1207
Let q(s) be the third derivative of s**5/4 - 20*s**3/3 - 8*s**2 - 4. Let f = -4 + -1. Let o(u) = 7*u**2 - 20. Let h(j) = f*o(j) + 2*q(j). Factor h(t).
-5*(t - 2)*(t + 2)
Solve -4*s**4 + 30 + 42 + 3*s + 4*s**4 - s**4 - 81*s**2 - 3*s**3 + 10*s**4 = 0.
-8/3, -1, 1, 3
Find d, given that 21*d**2 - 52*d**2 - 45*d - 70*d**2 + 36*d - 109*d**2 = 0.
-3/70, 0
Let t(v) be the second derivative of -2/15*v**6 + 0 + 7/5*v**5 - 111*v + 12*v**2 - 5/3*v**4 - 14/3*v**3. Let t(m) = 0. What is m?
-1, 1, 6
Let m(l) be the first derivative of -1/3*l**6 + 65 + 6/5*l**5 + 3*l**2 - 2*l - 4/3*l**3 - l**4. Factor m(b).
-2*(b - 1)**4*(b + 1)
Let p(f) be the second derivative of f**7/21 - 37*f**6/15 + 42*f**5 - 832*f**4/3 + 1280*f**3/3 + 8744*f. Let p(b) = 0. What is b?
0, 1, 8, 20
Let v(i) be the third derivative of i**7/105 + i**6/6 + 29*i**5/30 + 5*i**4/3 + 1621*i**2. Factor v(w).
2*w*(w + 1)*(w + 4)*(w + 5)
Let k(c) = -16*c**4 + 29*c**3 - 96*c**2 + 50*c. Let g(a) = 3*a**4 - 6*a**3 + 19*a**2 - 10*a. Let q = 0 - -6. Let i(o) = q*k(o) + 33*g(o). Factor i(u).
3*u*(u - 5)*(u - 2)*(u - 1)
Let d be 10/6*(330/(-25))/(-11). Solve 5*u**2 - 4*u + 9*u**2 + 2*u**3 + 2*u**3 - 13*u**d - u**4 = 0.
-1, 0, 1, 4
Let p(a) be the first derivative of -2/3*a**5 + 0*a - 5/8*a**4 - 24 + 5/3*a**2 - 5/36*a**6 + 10/9*a**3. Determine x so that p(x) = 0.
-2, -1, 0, 1
Let y(j) be the first derivative of -9/10*j**2 - 50 + 1/6*j**6 + 12/25*j**5 - 2/3*j**3 + 1/5*j**4 - 2/5*j. Factor y(d).
(d - 1)*(d + 1)**3*(5*d + 2)/5
Let l(v) = 2*v - 9. Let n be l(7). Let c be (-264)/924 - (3 + (-216)/21). Factor -c*f**2 - 24*f - n + 25*f**2 + 13.
2*(3*f - 2)**2
Let w(o) = -o**3 - 7*o**2 - 4*o - 93. Let g be w(-8). Let f(y) be the first derivative of 8/3*y**g - 31 - 3/8*y**4 - 17/4*y**2 + 2*y. Factor f(p).
-(p - 4)*(p - 1)*(3*p - 1)/2
Let j(f) be the third derivative of f**5/60 - 3*f**3/2 - 10*f**2 - 39*f. Find y such that j(y) = 0.
-3, 3
Suppose -1499680 + 1499676 = -2*d. Determine b so that 3/4*b**d - 57/8*b + 3/8*b**3 - 15/2 = 0.
-5, -1, 4
Let m(n) = n**2 + 10*n - 12. Let t be m(-12). Suppose 4*q - t = 4*o, 4*q + 4*o + 6 = 5*q. Factor 2*p**2 - 4*p**q + 8*p - 6*p**2 - 4*p**2 + 4*p**3.
4*p*(p - 2)*(p - 1)
Let z = 1469/4581 - -58/4581. Let 2*x - 7/3*x**3 + 0 - z*x**4 + 1/3*x**5 + 1/3*x**2 = 0. What is x?
-2, -1, 0, 1, 3
Let d(f) be the first derivative of -6*f**2 - 90*f - 126 - 2/15*f**3. Determine k, given that d(k) = 0.
-15
Let a(l) be the third derivative of 11/180*l**5 - 3*l**2 - 1/6*l**4 + 1/1008*l**8 - 1/210*l**7 + 0*l + 33 - 1/360*l**6 + 2/9*l**3. Solve a(o) = 0 for o.
-2, 1, 2
Let o be -8 + 4/6*(-23 - -51 - 15). Factor 0 + 2/3*u - o*u**2.
-2*u*(u - 1)/3
Let c be 12 + ((-2)/4)/(7/(-70)). Let x = -13 + c. Factor 0 - 8/7*i**x + 0*i**3 - 4/7*i + 8/7*i**2 + 4/7*i**5.
4*i*(i - 1)**3*(i + 1)/7
Let h(j) = j**2 + 8*j + 19. Let r be h(-5). Suppose -4*a = -0*a 