hird derivative of 0*x**4 + 1/105*x**5 - x + 0*x**7 + 0*x**3 + 0 + 1/140*x**6 - 1/1176*x**8 - 8*x**2. Find w such that k(w) = 0.
-1, 0, 2
Let x = -4974 - -4978. Let m(z) be the second derivative of 2/7*z**2 - 12*z - 1/42*z**x + 0 - 1/21*z**3. What is g in m(g) = 0?
-2, 1
Suppose -3*o = -4*p + 262, 30*p - 4*o - 59 = 29*p. Let m = p - 601/9. Factor 2/9*w + 0 - m*w**2.
-2*w*(w - 1)/9
Find t such that -88 + 272/3*t + 2/3*t**3 - 74/3*t**2 = 0.
2, 33
Let z = 561583/3 + -187190. Factor 1/6*b**2 - 5/2*b + z.
(b - 13)*(b - 2)/6
Let k(l) be the third derivative of -l**8/112 - 36*l**7/35 - 259*l**6/8 + 18*l**5/5 + 162*l**4 + 2*l**2 - 4*l - 233. Suppose k(x) = 0. Calculate x.
-36, -1, 0, 1
Suppose 2*s + 4*f - 32 = 0, 4*s + 3*f + f - 72 = 0. Suppose -s = -0*p - 2*p - 5*i, -3*i = 2*p - 28. Factor 29*m**3 + 5*m**4 + 0 + p*m - 34*m**3 + 0 - 20*m**2.
5*m*(m - 2)*(m - 1)*(m + 2)
Let h(j) be the first derivative of -58 + 12*j - 15/2*j**2 + j**3. Find n such that h(n) = 0.
1, 4
Let g be -2*1 + (-14366)/(-4928). Let s = g + -11/32. Find j such that -16/7*j**2 - s + 20/7*j = 0.
1/4, 1
Suppose -10613 = 8*c - 3618*c + 217. Suppose 3*x**2 + 9*x + 0 + 1/4*x**c = 0. Calculate x.
-6, 0
Let n(r) be the second derivative of 25*r**7/84 + 53*r**6/120 + 3*r**5/80 + 2791*r. Suppose n(w) = 0. Calculate w.
-1, -3/50, 0
Let w(r) = 17*r**3 + 952*r**2 + 26*r - 995. Let u(d) = 2*d**3 + 112*d**2 + 3*d - 117. Let s(t) = -86*u(t) + 10*w(t). Factor s(o).
-2*(o - 1)*(o + 1)*(o + 56)
Let v(c) be the second derivative of 0 + 1/4*c**4 - 15*c - 16*c**3 + 384*c**2. Suppose v(t) = 0. What is t?
16
Suppose -m - 2 = -4*d, -2*m = -7*m - d + 32. Factor -13 + m*q**2 - 96*q + 25 - 50*q + 6*q**2 + 352*q**2.
2*(7*q - 2)*(26*q - 3)
Let r(f) be the second derivative of -1/35*f**6 + 1/14*f**4 - 93 + 1/70*f**5 + 1/147*f**7 + 0*f**2 - 2/21*f**3 - f. Determine q so that r(q) = 0.
-1, 0, 1, 2
Let o(m) = m**3 + 11*m**2 + 20*m - 29. Let z be o(-8). Solve 0 + 1/3*f**2 - 1/3*f**z + 0*f = 0.
0, 1
Let u = -17742 + 17747. Let f = -314/5 + 63. Factor -46/5*v**2 - u*v**4 - 12/5*v - f - 12*v**3.
-(v + 1)**2*(5*v + 1)**2/5
Let h(x) be the second derivative of x**7/35 + x**6/120 - x**5/10 - x**4/24 + 14*x**2 - 34*x. Let w(j) be the first derivative of h(j). Factor w(i).
i*(i - 1)*(i + 1)*(6*i + 1)
Let u(q) be the second derivative of -q**6/10 + 588*q**5/5 - 101781*q**4/2 + 8576956*q**3 + 272871705*q**2/2 - 3054*q. Factor u(l).
-3*(l - 263)**3*(l + 5)
Let p(g) be the first derivative of -g**5/30 - 5*g**4/12 - 2*g**3 - 70*g**2 - 117. Let h(q) be the second derivative of p(q). Factor h(w).
-2*(w + 2)*(w + 3)
Let w(r) be the second derivative of 34*r**6/15 + 52*r**5/5 - 422*r**4/3 + 664*r**3/3 + 42*r**2 - 79*r + 23. Suppose w(o) = 0. What is o?
-7, -1/17, 1, 3
Let r = 28 + -12. Suppose -d + r = 2*z + 5, 5*d - z = 55. Let k(f) = 26*f**2 - 19*f. Let j(i) = 9*i**2 - 6*i. Let t(g) = d*j(g) - 4*k(g). Factor t(n).
-5*n*(n - 2)
Factor -s**2 - 49 - 738 - 452*s - 200 + 87.
-(s + 2)*(s + 450)
Let v be ((-6)/18)/(106/159) - -2. Find c such that -3/2*c - v*c**2 + 3/2*c**3 + 3/2 = 0.
-1, 1
Let w(x) be the first derivative of x**5/5 + 439*x**4/4 + 289*x**3 - 3055*x**2/2 + 1748*x + 10586. Factor w(d).
(d - 1)**2*(d + 4)*(d + 437)
Factor 49*r**2 - 16*r**3 - 598*r + 78*r + 26239 - 28267 + 15*r**3.
-(r - 26)**2*(r + 3)
Let o(q) be the first derivative of 5*q**6/6 - 19*q**5 - 65*q**4/2 + 580*q**3/3 + 220*q**2 - 800*q + 167. Suppose o(u) = 0. Calculate u.
-2, 1, 2, 20
Find a such that -534*a**4 + 677*a + 329*a**2 + 150 - a**5 - 722*a**3 + 52*a**3 - 3*a**5 + 55*a**2 - 3*a**5 = 0.
-75, -1, -2/7, 1
Let d(u) be the first derivative of -11/9*u**3 + 1/2*u**2 + 145 + 0*u. Factor d(g).
-g*(11*g - 3)/3
Suppose -20*c + 28 = -18*c. Let f be 3702/c - (-1 - 20/(-14)). Suppose 11*z**2 + 3 - 3 - 41*z**4 - f*z + 28*z**5 + 266*z = 0. Calculate z.
-2/7, -1/4, 0, 1
Let f(z) = 10*z - 36. Let x be f(5). Let i = 8 - -2. Factor -x*l**4 + 96*l**2 + 5*l**5 - i*l**3 - 156*l**2 + 34*l**4 + 45*l.
5*l*(l - 1)**2*(l + 3)**2
Let v(n) = -10*n**2 - 42*n + 196. Let g(k) = -8*k**2 - 42*k + 196. Let u(m) = 6*g(m) - 5*v(m). Factor u(t).
2*(t - 14)*(t - 7)
Suppose 20 = -2*s, 9*s - 5*s = 8*p - 56. Determine a, given that -1156/7*a - 136/7*a**p - 4/7*a**3 + 0 = 0.
-17, 0
Let s(o) be the third derivative of o**5/75 - 41*o**4/30 + 52*o**3/5 + 2366*o**2. Let s(k) = 0. Calculate k.
2, 39
Let y(k) be the third derivative of -k**8/56 + 31*k**7/105 - 47*k**6/30 + 10*k**5/3 - 2*k**4 + 1380*k**2. Determine n, given that y(n) = 0.
0, 1/3, 2, 6
Let p be (24780/5880)/((-1)/(-4)) - 16. Let s be (-12)/28*-1*3. Factor -s*m - p - 3/7*m**2.
-3*(m + 1)*(m + 2)/7
Let f(i) be the third derivative of -1/120*i**6 + 1/180*i**5 + 1/36*i**4 - 9*i**2 - 1/630*i**7 + 0*i**3 + 3 + 1/1008*i**8 + 0*i. Let f(j) = 0. What is j?
-1, 0, 1, 2
Let o(d) be the second derivative of -6*d - 17/15*d**4 + 18/5*d**2 + 2/25*d**5 - 4/3*d**3 - 2. Determine n, given that o(n) = 0.
-1, 1/2, 9
Let o be -1 + 56/10 + (-16)/(-40). Let m = 79 + -75. Suppose -12*h**2 + h**o - 4*h**3 - 3*h**4 + 3*h**5 + 15*h**m = 0. Calculate h.
-3, -1, 0, 1
Let x(h) be the third derivative of -53*h**5/6 + 2375*h**4/24 - 60*h**3 + 110*h**2. Let g(p) = 59*p**2 - 264*p + 40. Let k(i) = 55*g(i) + 6*x(i). Factor k(a).
5*(a - 4)*(13*a - 2)
Let m(n) be the second derivative of n**7/630 - n**6/45 - n**4/4 + n**2 + n - 35. Let d(l) be the third derivative of m(l). Factor d(a).
4*a*(a - 4)
Solve 3/4 + 363/8*a**2 - 369/8*a = 0 for a.
2/121, 1
Let t(n) be the first derivative of -n**6/810 - 31*n**5/270 + 16*n**4/27 - 2*n**3/3 + 8*n**2 + 144. Let g(q) be the third derivative of t(q). Factor g(v).
-4*(v - 1)*(v + 32)/9
Let r be 5 - 4 - ((-760)/(-7980) + 38/42). Let 32/5*s**5 + r*s + 48/5*s**4 + 2/5*s**2 + 18/5*s**3 + 0 = 0. Calculate s.
-1, -1/4, 0
Suppose 0 = -2*r - 181 - 31. Let p be (-42)/(-231) + r/(-22). Factor 35/4*s**p + 15*s**4 - 5/2*s**2 + 0*s + 15/4*s**3 + 0.
5*s**2*(s + 1)**2*(7*s - 2)/4
Let c be (81/(-162))/((9/36)/((-2)/12)). Let f(s) be the first derivative of 5 + 0*s - c*s**6 + 0*s**2 + 3/2*s**4 - 4/3*s**3 + 0*s**5. Solve f(q) = 0 for q.
-2, 0, 1
Let r(u) = 8*u**3 + 188*u**2 - 1143*u - 1344. Let c(s) = -2*s**3 - 62*s**2 + 382*s + 448. Let a(t) = 7*c(t) + 2*r(t). Suppose a(l) = 0. What is l?
-1, 14, 16
Let p(m) = -44*m**2 + 608*m - 2336. Let c(u) = -18*u**2 + 244*u - 935. Let l(g) = 12*c(g) - 5*p(g). Factor l(d).
4*(d - 23)*(d - 5)
Suppose -2*b - 17 = 188*q - 185*q, 27 = -4*b - 5*q. Factor 1/2*c**3 + c + 0 - 3/2*c**b.
c*(c - 2)*(c - 1)/2
Let t(o) be the first derivative of 0*o + 1/26*o**4 + 1/13*o**2 - 4/39*o**3 - 15. Factor t(n).
2*n*(n - 1)**2/13
Let z(h) = -5*h**3 + h**2 + 20*h - 2. Let r(g) = 3*g**3 - g**2 - 11*g + 1. Let i(w) = -7*r(w) - 4*z(w). Let i(v) = 0. Calculate v.
1
Let p(d) be the first derivative of -d**4/18 - 274*d**3/27 + 278*d**2/9 - 777. Determine j so that p(j) = 0.
-139, 0, 2
Let l be (-100)/20 + (-26)/(-5). Let k be (4 - 16/4)/(2 + -4). Factor 1/5*x**4 + l*x**2 + k*x + 0 + 2/5*x**3.
x**2*(x + 1)**2/5
Suppose 8*v + 4*v + 107 - 143 = 0. Let r(s) be the second derivative of 19*s + 1/8*s**v + 0*s**2 + 0 - 1/48*s**4. Determine q, given that r(q) = 0.
0, 3
Let u be (-24)/(-54) - 7090/(-612). Let n = u - 196/17. Factor 1/6*o**4 - n + 1/6*o**5 - 11/6*o - o**3 - 7/3*o**2.
(o - 3)*(o + 1)**4/6
What is g in 1482548/9*g**2 + 190/3*g**4 - 1260806*g + 2/9*g**5 + 52948/9*g**3 - 12777422/9 = 0?
-97, -1, 7
Factor 204 + 3/4*d**2 - 207/2*d.
3*(d - 136)*(d - 2)/4
Suppose 13*y - 295453 + 66211 = 0. Factor -7*s - 248*s**2 + 2*s + y + s - 17634.
-4*s*(62*s + 1)
Let p be -105 - 17595/(-138) - (9 + 1). Factor -p - 5*t - 1/2*t**2.
-(t + 5)**2/2
Let z be (-105)/(-33) + 120/(-660). Suppose -5*m + 20 = 0, -a - z*m - 6 = -5*m. Suppose 1/4*r**a - r + 3/4 = 0. What is r?
1, 3
Suppose 466*b + 714 = 508*b. Let z(k) be the second derivative of 1/4*k**4 + 0*k**2 - 1/3*k**3 - 1/20*k**5 + b*k + 0. Suppose z(r) = 0. Calculate r.
0, 1, 2
Let g(k) = -k**3 - 10*k**2 + k - 1. Let m(s) = -11*s**3 + 382*s**2 + 431*s + 60. Let b(q) = 2*g(q) + m(q). Factor b(t).
-(t - 29)*(t + 1)*(13*t + 2)
Let q(g) be the third derivative of 0 - 10*g**2 - 10*g**3 - 5/3*g**4 - 1/12*g**5 + 0*g. Suppose q(o) = 0. What is o?
-6, -2
Let i(w) be the first derivative of -w**7/1995 + w**6/285 - w