irst derivative of g**4/28 - 8*g**3/7 + 45*g**2/14 + 48*g - 37. Let c(t) be the first derivative of w(t). What is k in c(k) = 0?
1, 15
Let v(d) be the first derivative of -d**4 - 64*d**3/3 + 1920*d**2 + 73728*d + 11379. Factor v(a).
-4*(a - 32)*(a + 24)**2
Let c(z) be the first derivative of -z**6/18 + z**5 - 53*z**4/12 + 7*z**3/3 + 15*z**2 - 330. What is d in c(d) = 0?
-1, 0, 3, 10
Let v(c) be the third derivative of 1/120*c**5 - c**3 + 0*c - 156*c**2 + 1/48*c**4 + 0. Determine f so that v(f) = 0.
-4, 3
Let v(z) be the first derivative of -z**6/1080 - z**5/40 - 7*z**4/36 - 4*z**3 + 7*z - 283. Let f(b) be the third derivative of v(b). Let f(i) = 0. What is i?
-7, -2
Let h(y) be the first derivative of -841*y**4/8 + 812*y**3/3 + 115*y**2/4 + y + 4457. Factor h(s).
-(s - 2)*(29*s + 1)**2/2
Let q = 289 + -284. Let w(a) = -3*a**2 - 51*a + 48. Let i(y) = -2*y**2 - 50*y + 47. Let h(u) = q*w(u) - 6*i(u). Factor h(x).
-3*(x - 14)*(x - 1)
Let m(l) = l**3 - 27*l**2 - 26*l - 53. Let d be m(28). Find z, given that -24*z**2 + 59*z**2 + 4*z - 4*z**d - 21*z**2 - 14*z**4 = 0.
-1, -2/7, 0, 1
Suppose -j - 3*o - 1 = -2, 0 = -3*j - 5*o + 7. Suppose -j*v + 14 = -2*y, 5*v + 5*y + 2 = -3. Suppose 8*t + 12*t + 7 - 22*t + 5 - 2*t**v = 0. Calculate t.
-3, 2
Let n(m) be the third derivative of -m**8/20160 + m**7/630 + 121*m**5/60 + 16*m**2 + 6*m. Let s(f) be the third derivative of n(f). Factor s(j).
-j*(j - 8)
Suppose -2*o - q = 3*q + 4, -3*q - 1 = 2*o. Solve 751*a**3 + 16*a**2 - 4*a**o - 751*a**3 = 0 for a.
-2, 0, 2
Let x(z) be the third derivative of 0 + 0*z + 1/225*z**5 + 0*z**3 - 1/900*z**6 + 0*z**4 + 11*z**2. Determine o so that x(o) = 0.
0, 2
Let j(y) be the first derivative of 5*y**6/6 - 25*y**5 + 205*y**4/2 + 90*y**3 - 1215*y**2/2 - 945*y + 3232. Suppose j(g) = 0. What is g?
-1, 3, 21
Suppose 3*x - 61*g - 7 = -62*g, 5*x - 9 = -3*g. Let q be ((-518)/(-168) - 3)*x/1. What is a in -q*a - 1/4*a**5 - a**2 + 1/2*a**4 + 1/2 + 1/2*a**3 = 0?
-1, 1, 2
Let v(i) be the first derivative of 0*i + 72 + 1/9*i**3 + 13/3*i**2. Determine z, given that v(z) = 0.
-26, 0
Suppose -i + 27*i = -i - 19*i. Let g(p) be the second derivative of 0*p**2 + 1/126*p**7 + 0*p**3 - 1/90*p**6 + 0*p**4 - 25*p + 0*p**5 + i. Factor g(l).
l**4*(l - 1)/3
What is u in 1/7*u**3 - 128/7 + 24/7*u + 18/7*u**2 = 0?
-16, -4, 2
Let s(a) be the second derivative of 7*a**4/66 - 239*a**3/33 - 210*a**2/11 + 6530*a. Factor s(n).
2*(n - 35)*(7*n + 6)/11
Factor 242/7 - 8/7*i**3 + 178/7*i**2 - 1012/7*i.
-2*(i - 11)**2*(4*i - 1)/7
Factor 0 - 2/7*n**2 + 1072/7*n.
-2*n*(n - 536)/7
Let l(n) be the second derivative of -n**6/480 + 7*n**5/240 - 7*n**4/48 + n**3/3 - 29*n**2/2 - 65*n. Let p(k) be the first derivative of l(k). Factor p(x).
-(x - 4)*(x - 2)*(x - 1)/4
Let n(g) be the second derivative of g**4/66 + 40*g**3/11 + 119*g**2/11 + 61*g + 39. Factor n(u).
2*(u + 1)*(u + 119)/11
Suppose 6*c - 4*c = 5 + 11, -3*r - 16 = -2*c. What is f in 0*f + 11/2*f**5 - f**3 + 9/2*f**4 + r*f**2 + 0 = 0?
-1, 0, 2/11
Solve 0 - 2/9*i**5 - 10/9*i**3 + 0*i**2 + 0*i - 4/3*i**4 = 0 for i.
-5, -1, 0
Let w be -31 + (-4572)/(-720)*5. Solve -9/4*s**2 + 0*s - w*s**3 + 0 + 3/2*s**4 = 0 for s.
-1, 0, 3/2
Let w be ((-243)/(-26) + (-12027)/1266)/(-1). Find t, given that 2/13*t**3 - w*t - 4*t**2 + 4 = 0.
-1, 1, 26
Let s = 1117/7 - 1077/7. Let y be (((-60)/(-25))/2)/(13 + 806/(-65)). Find m such that -6/7*m**3 - s*m + 4*m**y + 16/7 = 0.
2/3, 2
Let g = 820 + -837. Let x(z) = -z**2 - 11*z + 106. Let p be x(g). Solve 0*l + 4/7*l**5 + 12/7*l**3 + 12/7*l**p + 0 + 4/7*l**2 = 0.
-1, 0
Let u(b) be the third derivative of -b**8/1008 - 4*b**7/315 - b**6/30 + b**5/90 + 13*b**4/72 + b**3/3 - 142*b**2. Find s, given that u(s) = 0.
-6, -1, 1
Let i be ((-3)/(-19 + 7 + 13))/(-1). Solve -2/5*c**i + 46/5*c**2 + 98/5*c + 10 = 0 for c.
-1, 25
Let f(n) be the third derivative of -n + 1/540*n**6 + 1/54*n**5 + 4/27*n**3 - 23*n**2 + 0 + 2/27*n**4. Solve f(a) = 0.
-2, -1
Let c(z) be the third derivative of 10*z**2 - 1/210*z**7 + 1/27*z**3 - z + 0 + 11/216*z**4 - 11/1080*z**6 + 7/540*z**5. Suppose c(a) = 0. Calculate a.
-1, -2/9, 1
Let k be 1252/(-6)*(-45)/(-48) + -4. Let q = 200 + k. Factor 3/8 + 3/4*g + q*g**2.
3*(g + 1)**2/8
Let o(s) be the third derivative of -s**6/400 + 77*s**5/120 + s**4/80 - 77*s**3/12 - 127*s**2 + 9*s - 2. Determine v so that o(v) = 0.
-1, 1, 385/3
Determine z so that -2/5*z**4 + 8/5*z - 2 - 8/5*z**3 + 12/5*z**2 = 0.
-5, -1, 1
Let g be ((-19128)/27895)/((-3)/20). Factor -12/7*u**2 + 8/7*u**3 + 4/7*u**4 - g*u - 16/7.
4*(u - 2)*(u + 1)**2*(u + 2)/7
Let y(f) = 2 - 28*f - 4*f**2 - 5219*f**3 + 5218*f**3 + 20*f**2. Let w be y(14). What is h in -2/7*h**4 - 4/7*h - 8/7*h**3 - 10/7*h**w + 0 = 0?
-2, -1, 0
Let d(f) be the second derivative of -f**5/5 - 17*f**4/3 - 20*f**3 + 805*f. Find k such that d(k) = 0.
-15, -2, 0
Factor -1/4*z**2 + 33/4*z - 115/2.
-(z - 23)*(z - 10)/4
Let u(m) be the first derivative of 0*m**2 - 2/9*m**3 + 135 + 0*m + 1/6*m**4. Determine o, given that u(o) = 0.
0, 1
Let p be (-6)/(-20) + 111*(-31)/(-930). Let g(d) be the second derivative of 0 - 1/16*d**3 + 1/160*d**5 - 9/8*d**2 + 1/24*d**p - 13*d. Factor g(m).
(m - 2)*(m + 3)**2/8
Let x(n) be the second derivative of 0*n**4 + 15*n + 3/20*n**5 + 0*n**3 + 0*n**2 + 1/120*n**6 - 6. Factor x(d).
d**3*(d + 12)/4
Let i(s) be the third derivative of s**7/168 - 13*s**5/48 + 5*s**4/8 + 526*s**2 + 2. Solve i(v) = 0 for v.
-4, 0, 1, 3
Suppose 1834 = -2*s + 4*a + 1812, -a = -7. Let f(x) be the second derivative of 3/20*x**5 + 28*x - 5/3*x**s + 0*x**2 + 0 - 13/12*x**4. Factor f(d).
d*(d - 5)*(3*d + 2)
Let r(a) = 228*a + 28274. Let y be r(-124). Find w, given that -1/5*w**3 - 177/5*w**y - 205379/5 - 10443/5*w = 0.
-59
Let u(n) be the second derivative of 2/3*n**3 + 0 - 5/6*n**4 + 1/5*n**5 + 0*n**2 + 15*n. Factor u(g).
2*g*(g - 2)*(2*g - 1)
Let a(l) be the second derivative of -3/14*l**3 + 0*l**4 - 60*l + 3/140*l**5 + 1 + 3/7*l**2. Factor a(c).
3*(c - 1)**2*(c + 2)/7
Let o(m) be the second derivative of m**4/12 - 374*m**3/3 + 69938*m**2 - 33*m + 2. Let o(b) = 0. What is b?
374
Let d(q) = -21*q**3 + 51*q**2 - 2669*q + 17424. Let j(a) = 34*a**3 - 76*a**2 + 4002*a - 26136. Let f(o) = 8*d(o) + 5*j(o). Factor f(l).
2*(l - 11)**2*(l + 36)
Suppose g - 2 = -0*g - o, 4*o - 3 = -3*g. Suppose 4*p - 9 = -4*b + 7, g*b - 16 = -p. Find u such that 2*u**3 + 8*u**b - 12 + 44*u**2 + 2*u**3 + 20*u = 0.
-3, -1, 1/3
Let p = 51 + -49. Factor 69*h**3 - 45*h**3 - 14*h**4 + 80*h**p + 32*h + 40*h**2.
-2*h*(h - 4)*(h + 2)*(7*h + 2)
Let j(a) be the third derivative of -a + 3/70*a**7 + 1/60*a**6 + 0 - 1/336*a**8 + 63*a**2 - 3/10*a**5 - 1/24*a**4 + 3/2*a**3. Factor j(z).
-(z - 9)*(z - 1)**2*(z + 1)**2
Let f(t) be the second derivative of 4 + 10*t**2 - 1/2*t**5 + 1/6*t**6 + 10/3*t**3 - 5/4*t**4 + t. Determine v so that f(v) = 0.
-1, 2
Let u(j) be the first derivative of -2*j**3/3 - 4950*j**2 - 12251250*j - 8467. Find t, given that u(t) = 0.
-2475
What is h in 27*h**2 - 3*h**5 - 36 - 26*h - 22*h + 88557*h**4 + 51*h**3 - 88548*h**4 = 0?
-2, -1, 1, 6
Let u(y) be the second derivative of 6/13*y**2 + 10 + 5/39*y**3 - 1/78*y**4 + 3*y. Factor u(z).
-2*(z - 6)*(z + 1)/13
Suppose -3*p + 3*j + 0 = -3, -3*p - j = -11. Let -220*q**4 + 27*q**2 + 128*q**3 + 988*q**4 + 179*q**p - 19*q**3 = 0. What is q?
-3/16, 0
Let b(q) be the second derivative of q**5/210 + 5*q**4/84 + 4*q**3/21 - 120*q**2 - 2*q + 106. Let c(r) be the first derivative of b(r). Factor c(v).
2*(v + 1)*(v + 4)/7
Let l be (-1145)/(-4122)*(-2)/((-20)/189). Suppose -9/2*i - 3/4 + l*i**2 = 0. What is i?
-1/7, 1
Let n(d) = -d**3 + d**2 + d + 22. Let j be n(0). Let l = 30 - j. Find q such that 38*q**5 + 37*q**5 - 4*q**3 + l*q**4 - 117*q**5 + 38*q**5 = 0.
0, 1
Let t(s) be the first derivative of 3*s**2 - 5*s - 1/4*s**4 - 12 + 1/2*s**3. Let h(o) be the first derivative of t(o). Factor h(i).
-3*(i - 2)*(i + 1)
Let d(n) be the third derivative of 0 - 2*n - 1/168*n**8 + 0*n**3 + 2/105*n**7 + 0*n**4 + 22*n**2 - 1/15*n**5 + 1/60*n**6. Suppose d(f) = 0. Calculate f.
-1, 0, 1, 2
Suppose 0 = -7*p - 5*g + 21, -5*p + 4*g = -g - 15. Factor -3/2 - 3/8*j**4 + 39/8*j - 45/8*j**2 + 21/8*j**p.
-3*(j - 4)*(j - 1)**3/8
Let t be (0 - 2)/(1044/(-81) - -13). Let l be 15/20 + (4 - t/(-4)). Factor l*d**3 - 3*d**2