-122, -1, -1/2
Let m(i) be the third derivative of -i**8/224 + 3*i**7/70 + 7*i**6/40 - 9*i**5/10 - 85*i**4/16 - 21*i**3/2 - 43*i**2 + 1. Determine c, given that m(c) = 0.
-2, -1, 3, 7
Let i(q) be the first derivative of q**5/20 + q**4/2 - 6*q**3 + 263*q**2/2 - 255. Let g(x) be the second derivative of i(x). Suppose g(f) = 0. Calculate f.
-6, 2
Let f(h) be the third derivative of -h**8/448 - 17*h**7/40 - 1857*h**6/80 - 2581*h**5/20 - 841*h**4/4 - 10*h**2 - 42*h + 5. Let f(y) = 0. What is y?
-58, -2, -1, 0
Factor -4/3*y**2 + 8/3*y + 20.
-4*(y - 5)*(y + 3)/3
Let q(p) = -3*p**3 + 2025*p**2 + 510065*p + 5. Let y(j) = j**3 - j**2 - 3*j - 1. Let r(c) = q(c) + 5*y(c). Factor r(x).
2*x*(x + 505)**2
Let x(q) be the first derivative of q**6/21 + 12*q**5/35 - 2*q**4 - 220*q**3/21 - 117*q**2/7 - 80*q/7 + 2011. Solve x(h) = 0.
-8, -1, 5
Let j(t) be the third derivative of -t**6/420 + 13*t**5/210 - 13*t**4/21 + 20*t**3/7 + 2240*t**2. Factor j(x).
-2*(x - 6)*(x - 5)*(x - 2)/7
Suppose -8*y + 15 = -17. Solve -7*n - 4*n**3 - 2*n**3 - n**5 + 11*n - 2*n**2 + 2*n**y + 3*n**5 = 0.
-2, -1, 0, 1
Let d = 166 + -163. Factor d*w**5 - 7*w**5 + 3*w**5 - 3*w**3 + 4*w**3.
-w**3*(w - 1)*(w + 1)
Let t(c) be the third derivative of c**7/11340 - c**6/1080 - 37*c**4/24 + 111*c**2. Let q(g) be the second derivative of t(g). Determine s, given that q(s) = 0.
0, 3
Let q(f) be the first derivative of -f**7/210 - f**6/10 - 7*f**5/15 + 11*f**3/3 - 7*f - 35. Let g(z) be the third derivative of q(z). What is l in g(l) = 0?
-7, -2, 0
Let -116/5*r**2 + 2/5*r**4 + 112/5*r**3 + 114/5 - 112/5*r = 0. Calculate r.
-57, -1, 1
Factor -2*y**4 + 111*y - 107*y + 2*y**2 - y**3 + 2*y**5 - 9*y**3 + 4*y**3 + 0*y**2.
2*y*(y - 2)*(y - 1)*(y + 1)**2
Let x be 8/108 + 205/(-54)*(-22)/110. Let z(k) be the first derivative of -14 + 4/9*k**3 - x*k**2 - 1/12*k**4 + 2/3*k. Factor z(t).
-(t - 2)*(t - 1)**2/3
Let y(v) = v**2 + 3*v - 7. Let s be y(-5). Let g(f) be the first derivative of -2 - 3*f + 3/2*f**4 + 4*f**3 - 9/5*f**5 - s*f**2. Let g(c) = 0. What is c?
-1, -1/3, 1
Let n(y) be the first derivative of 4*y**3/9 + 15536*y**2/3 + 60341824*y/3 - 10042. Suppose n(a) = 0. Calculate a.
-3884
Factor 39 - 5*k**2 + 82*k - 39 - 153*k - 114*k.
-5*k*(k + 37)
Let u = 3314 - 3314. Let d(z) be the second derivative of 0 + 0*z**4 + 1/30*z**3 - 1/50*z**5 + u*z**2 + 15*z + 0*z**6 + 1/210*z**7. Factor d(f).
f*(f - 1)**2*(f + 1)**2/5
Let h(g) be the first derivative of 5/2*g**4 + 65 - 20*g - g**5 + 5*g**3 - 10*g**2. Factor h(n).
-5*(n - 2)**2*(n + 1)**2
Suppose -4*z - 164*g - 40 = -168*g, 5*g - 50 = -2*z. Find h, given that 1/2*h**5 + z*h - 1/2*h**2 + 1/2*h**4 - 1/2*h**3 + 0 = 0.
-1, 0, 1
Solve 974 - 695*s**3 - 4165*s + 1147 - 676 + 564*s**2 - 4161*s**2 - 20*s**4 - 2688*s**2 = 0.
-17, -1, 1/4
Let w = -1/176 - 5/88. Let i = 55/144 - w. Determine g so that -4/9*g + i*g**3 + 0*g**2 + 2/9 - 2/9*g**4 = 0.
-1, 1
Factor -2*u**3 + 21 - 14*u - 21*u**2 + 5*u + 6*u + 5*u**3 + 0*u.
3*(u - 7)*(u - 1)*(u + 1)
Factor -230/3*d - 578/15*d**2 - 574/15 - 2/15*d**3.
-2*(d + 1)**2*(d + 287)/15
Let b be 13/((-104)/(-72)) - 297/44. Factor b*z**3 - 21/2*z**2 + 6*z + 0.
3*z*(z - 4)*(3*z - 2)/4
Let s(n) be the first derivative of 28 + 0*n**2 - 1/24*n**4 - 1/6*n**3 + 5*n. Let g(h) be the first derivative of s(h). Factor g(m).
-m*(m + 2)/2
Let l = -226 + 53. Let t = 176 + l. Factor 5/4*c**4 + 15/4*c**2 - 15/4*c**t + 0 - 5/4*c.
5*c*(c - 1)**3/4
Solve -4068/7*q - 4066/7 - 2/7*q**2 = 0 for q.
-2033, -1
Let r = 301563/24130 - -31/12065. Find w such that 5/2*w**5 + r*w**4 + 0 - 25/2*w**2 - 10*w + 15/2*w**3 = 0.
-4, -1, 0, 1
Let r(a) = 106*a**2 - 2241*a + 319. Let l be r(21). Suppose -14/11*o**3 + 0*o + 0 + 2/11*o**l + 20/11*o**2 = 0. What is o?
0, 2, 5
Let n be (-131)/(35632/13504) + 52. Let t be (-8)/34*3/(-2). Factor -n*c + 14/17 - t*c**2.
-2*(c + 7)*(3*c - 1)/17
Let n = 55783/139420 - 3/27884. Factor 14/5*k**2 + 0*k + 0 + n*k**3.
2*k**2*(k + 7)/5
Suppose -41/4*o + 1/8*o**3 - 13 + 23/8*o**2 = 0. What is o?
-26, -1, 4
Factor 515*l**2 + 3*l**5 + 317*l**2 + 408*l**3 + l**5 - 7 + 223 + 708*l + 72*l**4.
4*(l + 1)**3*(l + 6)*(l + 9)
Let g be 36/(-20)*(45 + 7600/(-168)). Factor -5/7*v - g - 3/7*v**3 + 11/7*v**2.
-(v - 3)*(v - 1)*(3*v + 1)/7
Let x be (-20)/(-16) + (-114)/(-152). Let l be x/6 - (529/69)/(-23). Factor -2/9*z**2 + l*z + 0.
-2*z*(z - 3)/9
Suppose -j - 13 = -5*c, 5*c = 3*j + 3 + 6. Let l be j*(-18)/63 - (-74)/56. Factor l*s**2 + 1/4*s**3 - 1/4*s - 3/4.
(s - 1)*(s + 1)*(s + 3)/4
Let f(t) = 3*t**3 - 550*t**2 - 574*t + 21. Let o(p) = -p**3 + 275*p**2 + 288*p - 12. Let m(z) = -4*f(z) - 7*o(z). Factor m(s).
-5*s*(s - 56)*(s + 1)
Let b(h) = h**3 + h**2 + 2*h + 4. Let t be b(4). Let v be 23/t + (-22)/(-8). Factor v*x**2 - 6*x - 10*x + 0*x**2 + x**2 + 12.
4*(x - 3)*(x - 1)
Let v(a) be the first derivative of -68 - 5/4*a**4 - 6/5*a**5 + 0*a + 1/3*a**3 + 0*a**2. Factor v(x).
-x**2*(x + 1)*(6*x - 1)
Let w = -68037/35 - -9721/5. Let j(x) be the first derivative of -5/7*x**4 - 8 + 2/7*x - 5/7*x**2 - 1/21*x**6 + 20/21*x**3 + w*x**5. Factor j(d).
-2*(d - 1)**5/7
Find b, given that 0 - 61/4*b**4 + 0*b + 0*b**2 + 1/4*b**5 + 15*b**3 = 0.
0, 1, 60
Determine g so that -432*g**2 - 5*g**5 + 28*g + 2132*g - 20891*g**3 + g**5 + 136*g**4 + 20423*g**3 = 0.
-2, 0, 3, 30
Let l = -11665 + 23331/2. Let i(x) be the third derivative of -1/60*x**5 + 0 + 0*x - l*x**3 + 1/6*x**4 + 4*x**2. Solve i(j) = 0.
1, 3
Let t(y) = -4*y**3 + 4*y**2 - 2*y + 4. Let i = 83 - 69. Let b(g) = 13*g**3 - 12*g**2 + 7*g - 14. Let k(p) = i*t(p) + 4*b(p). Solve k(c) = 0 for c.
0, 2
Let s(x) = 26*x**4 - 383*x**3 + 24*x**2 + 1454*x + 817. Let f(c) = -3*c**4 + 48*c**3 - 3*c**2 - 180*c - 102. Let m(v) = -51*f(v) - 6*s(v). Factor m(r).
-3*(r - 2)*(r + 1)**2*(r + 50)
Determine j, given that -2*j**5 - 19/3*j**4 + 0*j - 2/3*j**2 - 5*j**3 + 0 = 0.
-2, -1, -1/6, 0
Let l(h) = 30*h**2 + 10236*h - 4458273. Let s(p) = -13*p**2 - 5124*p + 2229136. Let c(u) = -4*l(u) - 9*s(u). Factor c(v).
-3*(v - 862)**2
Let o(b) = -11*b + 13. Let g be o(1). Let 319 - 1377*a**g - 19 - 840*a + 47*a**3 - 296*a**3 - 12*a**4 = 0. What is a?
-10, -1, 1/4
Let u(g) be the first derivative of 2*g**3/21 + 2564*g**2/7 + 3287048*g/7 + 1440. Let u(w) = 0. Calculate w.
-1282
Let k be ((-1)/(-20))/(132342/(-2070) - -64). Factor k*s - 7 + 1/4*s**2.
(s - 4)*(s + 7)/4
Factor 1/3*c**3 + 140/3*c**2 - 427/3*c + 286/3.
(c - 2)*(c - 1)*(c + 143)/3
Let a(w) be the first derivative of -3*w**4/8 - 71*w**3/2 + 435*w**2/4 - 219*w/2 + 1927. Factor a(z).
-3*(z - 1)**2*(z + 73)/2
Let d(v) be the first derivative of v**7/42 + v**6/50 - v**5/50 + 45*v - 74. Let y(m) be the first derivative of d(m). Let y(k) = 0. Calculate k.
-1, 0, 2/5
Suppose -4*s + j - 5 = 6*s, -5*s = -5*j + 25. Let g(q) be the second derivative of -25/6*q**3 + 15*q**2 + s + 5*q + 5/12*q**4. Factor g(m).
5*(m - 3)*(m - 2)
Let m = 2/274163 + 274159/548326. Determine v so that 0 - m*v**4 + 3/2*v**2 + v + 0*v**3 = 0.
-1, 0, 2
Let g(o) be the second derivative of -o**5/4 - 1605*o**4/4 + 3215*o**3/2 - 4825*o**2/2 + 3781*o - 1. Factor g(w).
-5*(w - 1)**2*(w + 965)
Let l(f) be the first derivative of f**3 - 183*f**2 + 11163*f + 236. Find s such that l(s) = 0.
61
Let g(m) be the second derivative of -1/42*m**5 + 1/42*m**4 - 2*m + 1/315*m**6 - 16 + 5/63*m**3 - 4/21*m**2. Suppose g(l) = 0. Calculate l.
-1, 1, 4
Let x(j) be the third derivative of 15/2*j**4 + 71/12*j**5 + 0 - j + 0*j**3 + 17/12*j**6 - 118*j**2 - 1/42*j**7. Solve x(r) = 0 for r.
-1, 0, 36
Let v = -1739 + 1741. Let d(l) be the third derivative of 0 - 1/30*l**6 + 0*l**3 + 0*l - 2*l**v + 0*l**5 + 0*l**4 - 2/105*l**7. Factor d(y).
-4*y**3*(y + 1)
Let j(h) be the second derivative of -5/6*h**4 - 4*h + 1/10*h**5 - 12 + 48*h**2 - 8/3*h**3. Suppose j(f) = 0. Calculate f.
-3, 4
Suppose 0 = 27*s + 380*s - 1221. Determine a so that -18/5*a**s - 3/5 + 18/5*a + 3/5*a**2 = 0.
-1, 1/6, 1
Let o(u) be the second derivative of -u**6/165 - u**5/10 - 25*u**4/66 + 13*u**3/11 + 126*u**2/11 - 6762*u. Find z such that o(z) = 0.
-7, -3, 2
Let p(k) be the first derivative of 0*k + 1/2*k**4 + 0*k**2 - 51 + 36*k**3. Factor p(b).
2*b**2*(b + 54)
Let a(w) be the first derivative of w**8/420 - w**7/70 + 7*w**3/3 - 4*w + 30. Let k(f) be the third derivative of a(f). Suppose k(b) 