 y(z) be the third derivative of 0 + 0*z**3 + 205*z**2 - 23/240*z**6 - 143/120*z**5 - 121/48*z**4 - 1/420*z**7 + 0*z. What is m in y(m) = 0?
-11, -1, 0
Factor -245/4 - 119/4*t - 19/4*t**2 - 1/4*t**3.
-(t + 5)*(t + 7)**2/4
Suppose 40*b = 19*b + 168. Suppose -4*r = -b, h - 3*r + 2*r = 0. Factor -1/5 - s + s**3 + 1/5*s**h.
(s - 1)*(s + 1)*(5*s + 1)/5
Let l(c) = -c**3 + 22*c**2 + 18*c + 91. Let s be l(23). Let a be (-152)/s + 2 - 7. Find f such that 16/3 + a*f**2 - 16/3*f = 0.
2
Let p be -2 + -2 + (-9)/(-1). Suppose 4 = 3*x - p. Factor 2*i**5 - 72*i**x + 155*i**3 - 8*i**4 - 71*i**3 - 8*i**2 + 2*i.
2*i*(i - 1)**4
Let w(z) = 81*z + 85. Let j = -1056 + 1055. Let b be w(j). Factor -b*i**2 + 12/5*i + 0 + 4/5*i**4 + 4/5*i**3.
4*i*(i - 1)**2*(i + 3)/5
Factor 40/7 - 11/7*y**3 + 1/7*y**4 - 68/7*y + 6*y**2.
(y - 5)*(y - 2)**3/7
Let p(d) be the first derivative of d**4/8 - 13*d**3/3 + 109*d**2/4 - 42*d - 5777. Solve p(l) = 0 for l.
1, 4, 21
Let d(c) be the third derivative of 0 - 123*c**2 + 1/84*c**7 + 25/8*c**4 + 6*c**3 - 1/30*c**6 - 79/120*c**5 + 0*c. Factor d(j).
(j - 3)**2*(j + 4)*(5*j + 2)/2
Let b(s) be the first derivative of s**6/36 - 8*s**5/15 - s**4/3 + 64*s**3/9 + 4*s**2/3 - 128*s/3 + 5863. Let b(u) = 0. What is u?
-2, 2, 16
Let s(g) be the second derivative of -g**7/630 + g**5/90 - g**3/18 + 63*g**2/2 - 13*g + 2. Let f(z) be the first derivative of s(z). Let f(h) = 0. Calculate h.
-1, 1
Let p = 41 + -71. Let u = 32 + p. Suppose m**u - 2*m**2 + 2*m**2 + 2*m**2 = 0. What is m?
0
Suppose 0 = -68*k + 36*k. Let r(o) be the third derivative of k*o**7 + 1/420*o**6 - 3*o**2 + 0*o**3 - 1/168*o**4 + 0*o**5 + 0*o + 0 - 1/2352*o**8. Factor r(z).
-z*(z - 1)**2*(z + 1)**2/7
Let d(t) = t**2 - 5. Let y be d(-2). Let b be y + (-8)/(-12) + 20/6. Let 5*o**3 + b*o**4 + 12*o - 9*o**3 - 5*o**3 = 0. What is o?
-1, 0, 2
Let b be 4 - ((21/203)/(135/(-90)) - (-1420)/406). Factor 12/7 + 4*r + 20/7*r**2 + b*r**3.
4*(r + 1)**2*(r + 3)/7
Suppose 0 = 5*v - 3*x - 57, v + x - 5*x = 25. Let a be (92/690)/(1/v). Solve -2/5*y**3 + 8/5 + a*y**4 - 14/5*y**2 + 0*y + 2/5*y**5 = 0 for y.
-2, -1, 1
Let g(i) be the second derivative of -169*i**8/1680 + 13*i**7/210 - i**6/90 + 13*i**3/6 - i**2/2 + 55*i. Let l(d) be the second derivative of g(d). Factor l(c).
-c**2*(13*c - 2)**2
Let y(o) be the first derivative of 2*o**4 + 0*o + 24*o**3 + 1/15*o**5 - 9*o**2 + 13. Let f(n) be the second derivative of y(n). Solve f(u) = 0 for u.
-6
Suppose 117 = -2*i - 5*p, 5*i + 5*p + 17 + 253 = 0. Let o = -5 - i. Factor -3*h**2 + 2*h**3 - 46 + 2*h**4 + o - 5*h**2 - 8*h.
2*h*(h - 2)*(h + 1)*(h + 2)
Let g = -2860 + 1040. Let f be (2 + -1)*-6 + (-11180)/g. Determine p, given that 0*p - 1/7*p**2 + f*p**3 + 0 = 0.
0, 1
Let x(q) be the third derivative of -q**5/240 + 767*q**4/96 - 383*q**3/12 + q**2 + 2*q + 855. Determine w so that x(w) = 0.
1, 766
Suppose 2*l - n + 7 = 0, -158*n + 157*n = 2*l - 15. Let -35/2*w**4 + 45/2*w**3 - 15/2*w**5 - 15*w + 35/2*w**l + 0 = 0. Calculate w.
-3, -1, 0, 2/3, 1
Let s be 14 + (559/(-65) - 1). Let a = 229 - 226. Factor 8/5*v + 0 - 6/5*v**a - s*v**2.
-2*v*(v + 4)*(3*v - 1)/5
Factor -135000 - 1800*y**2 + 50*y**3 - 1/2*y**4 + 27000*y.
-(y - 30)**3*(y - 10)/2
Let f be (7/133)/((-30)/(-57)). Let x(g) be the second derivative of g**3 + 2*g**2 + 0*g**4 + 0 - 4*g - f*g**5. Determine l, given that x(l) = 0.
-1, 2
Suppose 4*w = 11*a - 5*a - 11*a, 3*a - 4*w = 32. Let 16/5*t**a + 12/5*t**2 - 26/5*t**3 + 0 + 0*t - 2/5*t**5 = 0. What is t?
0, 1, 6
Suppose -6 = i, -22*l + 28*l - 120 = 5*i. Let z(u) be the second derivative of -6/5*u**2 + 0 - 1/3*u**3 - l*u - 1/30*u**4. Factor z(p).
-2*(p + 2)*(p + 3)/5
Let g be -31 - (5 - (2 - -4)*1). Let k be g/(-50) - (1356/210 - 6). Solve -2/7 + 1/7*v - k*v**3 - 1/7*v**4 + 3/7*v**2 = 0 for v.
-2, -1, 1
Let c(w) be the second derivative of -w**7/840 - w**6/120 + w**4/6 + 2*w**3/3 - 197*w**2/2 + 163*w. Let l(y) be the first derivative of c(y). Factor l(g).
-(g - 2)*(g + 2)**3/4
Let n(t) be the second derivative of 80*t**7/189 + 104*t**6/45 + 53*t**5/10 + 178*t**4/27 + 43*t**3/9 + 2*t**2 + 41*t + 10. Find k, given that n(k) = 0.
-1, -3/4, -2/5
Let z(a) be the third derivative of -a**6/360 - a**5/18 + 3*a**4/8 + 2*a**3 + 754*a**2. Find k, given that z(k) = 0.
-12, -1, 3
Let x(m) be the third derivative of 18/5*m**5 + 1/35*m**7 + m**2 + 12*m**4 + 0*m + 58 + 64/3*m**3 + 31/60*m**6. Factor x(t).
2*(t + 1)*(t + 4)**2*(3*t + 4)
Let f(s) = 3 - 516*s**2 + 518*s**2 - 8 + 9*s. Let z(u) = -5*u**2 - 17*u + 8. Let x(q) = -5*f(q) - 3*z(q). Factor x(d).
(d + 1)*(5*d + 1)
Let a(y) be the third derivative of 3*y + 2/105*y**7 - 784/3*y**3 + 0 + 70/3*y**4 + 29/30*y**6 + 74/5*y**5 - 2*y**2. Factor a(x).
4*(x - 1)*(x + 2)*(x + 14)**2
Let s = 17158 + -17122. Let v(c) be the first derivative of 1/45*c**5 - 1/6*c**4 + s + 0*c + 4/9*c**3 - 4/9*c**2. Solve v(z) = 0 for z.
0, 2
Let i = 23624 - 23624. Factor -1/2*l**3 - 1/2*l**2 + i + 0*l.
-l**2*(l + 1)/2
Let j = 247 - 161. Find k such that -830*k**2 + 1986*k**3 - 2 - 136*k**2 - j*k - 2868*k**3 = 0.
-1, -1/21
Let v be (7*6/420)/((-40)/(-75)). Let l(t) be the first derivative of -26 - v*t**4 + 3/2*t**3 - 15/8*t**2 + 0*t. Factor l(p).
-3*p*(p - 5)*(p - 1)/4
Let f be (24/(-44))/((-187331)/4070 + 46). Solve -f - 5/3*u**2 - 65/3*u = 0.
-12, -1
Find a such that -1/2*a**4 + a**2 - 1/2 + 0*a + 0*a**3 = 0.
-1, 1
Determine w, given that -25/2*w**2 + 10 + 5/2*w**4 - 85*w - 85/4*w**5 + 425/4*w**3 = 0.
-2, -1, 2/17, 1, 2
Let n(f) = -125*f**2 - 98*f - 22. Let x be 32 - 22 - (6 + 2). Let m(z) = -250*z**2 - 195*z - 45. Let r(g) = x*m(g) - 5*n(g). Factor r(q).
5*(5*q + 2)**2
Suppose 24*b - 120 = 9*b. Determine u so that -7*u**4 - b*u**2 - 4*u + 144*u**3 + 2 - 2 - 125*u**3 = 0.
-2/7, 0, 1, 2
Let f(w) be the third derivative of w**7/105 + 7*w**6/30 + 19*w**5/30 - 11*w**4/2 - 24*w**3 + 2*w**2 - 203*w. Suppose f(i) = 0. What is i?
-12, -3, -1, 2
Let f(y) = -3*y**3 + 65*y**2 - 179*y - 7. Let q be f(4). Solve q + 1/5*u**2 + 10*u = 0 for u.
-25
Determine u so that 2225/3 - 150*u + 1/3*u**2 = 0.
5, 445
Let i(m) = -m**2 + 107*m - 2212. Let s be i(28). Let a(h) be the third derivative of 1/3*h**4 + h**3 - 17*h**2 + s + 1/30*h**5 + 0*h. Factor a(d).
2*(d + 1)*(d + 3)
Let l(k) = -k**3 + 12*k**2 + 12*k - 11. Let b be l(13). Let p = -16 - b. Determine q so that -p*q**3 - 12*q**2 - 7*q + 4*q**4 + 19 + 5*q - 3 + 18*q = 0.
-1, 2
Let u = 6172218/7 + -881745. Factor 9/7*l + 6/7 + 0*l**2 - u*l**3.
-3*(l - 2)*(l + 1)**2/7
Suppose -2945*b = 4*g - 2935*b + 82, 0 = -3*b - 27. Determine l so that 2/9*l**g - 20/3 + 2/9*l = 0.
-6, 5
Let n(m) = -m**2 + 6*m + 7. Let l(t) = -t**2 + 17*t - 65. Let p be l(10). Let z be n(p). Factor -5 - u - u + 8 - z*u**2 + 11*u**2.
-(u - 1)*(u + 3)
Suppose 100*j**4 + 12*j**5 - 804*j**2 + 235*j - 95*j**3 + 704 - 333*j**3 + 276*j - 95*j = 0. Calculate j.
-11, -4/3, -1, 1, 4
Let a(h) be the second derivative of h**9/7560 - h**8/3360 + 5*h**4/6 - 15*h. Let w(v) be the third derivative of a(v). Determine q so that w(q) = 0.
0, 1
Suppose 771 - 681 = 30*t. Let o(r) be the second derivative of 0 - 6*r**2 - t*r + 9/20*r**5 + 7/4*r**4 + 0*r**3. Let o(z) = 0. What is z?
-2, -1, 2/3
Let i(w) = 3*w**2 + 39*w - 6. Let f(n) = -n**2 + 1. Suppose o - 61 = a + 3*a, 0 = -5*o - 5*a + 380. Let r = o - 72. Let l(u) = r*i(u) - 12*f(u). Factor l(t).
3*(t + 3)*(5*t - 2)
Let h be (-12)/108 + 76/36. Suppose 30*r**2 - 6*r**3 + 8*r**4 + 0*r**5 + 8*r - h*r**5 - 38*r**2 = 0. Calculate r.
-1, 0, 1, 2
Let h be (-24)/8 + ((-22288)/(-36) - 3). Let c = h - 612. Factor 1/9*x**2 + c*x + 25/9.
(x + 5)**2/9
Let c(u) = u**3 - u**2 + 26*u - 16. Let x be c(-6). Let l = 424 + x. Suppose l*d + 0 + 1/2*d**3 + 5/2*d**2 = 0. What is d?
-5, 0
Let x(p) be the third derivative of -p**8/1848 + p**7/1155 + 2*p**6/55 - 4*p**5/15 + 28*p**4/33 - 16*p**3/11 - 6541*p**2. Suppose x(z) = 0. Calculate z.
-6, 1, 2
Let p = 266 - 264. Suppose -18 + 93*z**p + 2 + 20*z**4 + 44*z**3 + 24*z**4 - 51*z**4 + 26*z = 0. Calculate z.
-1, 2/7, 8
Let x be 20/(-30)*6/4*-38. Let z = -33 + x. Factor -p**2 + z*p**2 + 11*p + 4*p**3 - 11*p.
4*p**2*(p + 1)
Factor -2/11*v**2 + 504/11*v - 502/11.
-2*(v - 251)*(v - 1)/11
Let m = 327659/436884 + 1/109221. Factor -21/4*k + m*k**2 + 9/2.
3*(k - 6)*(k - 1)/4
Let i be (-5 + (2 - -2))*-90.