 z, given that c(z) = 0.
-1, 6
Suppose 55524082*a - 1/2*a**5 + 27434285*a**2 - 435481/2*a**3 + 27871484 + 572*a**4 = 0. Calculate a.
-1, 382
Let d(c) be the second derivative of c**6/80 - 21*c**5/160 + 1662*c. Find r such that d(r) = 0.
0, 7
Let s = -5511 + 5511. Let h(l) be the second derivative of 0*l**2 + 1/3*l**4 + 17*l + s + 1/5*l**5 + 0*l**3. What is g in h(g) = 0?
-1, 0
Let z(k) = k**3 - 5*k**2 + 4*k - 35. Let c be z(9). Let u be (3 + (-34)/20)*c/10. Factor u*a**2 + 13*a + 1.
(13*a + 2)**2/4
Let p(n) be the first derivative of -n**6/2 + 5*n**5 - 18*n**4 + 24*n**3 + 8*n**2 - 48*n - 1030. What is z in p(z) = 0?
-2/3, 2, 3
Suppose -35 = 5*u - b, 0 = 5*u + 4*b + 16 + 44. Let f be ((-4)/u)/(38/(-8) - -5). Suppose 5/2*d**3 + 0*d - 5/4*d**4 + 0*d**f + 0 = 0. Calculate d.
0, 2
Let h(u) be the second derivative of 3*u**5/20 + 47*u**4/4 + 88*u**3 + 258*u**2 - 10576*u. Factor h(t).
3*(t + 2)**2*(t + 43)
Let n(s) be the third derivative of s**5/15 - 11*s**4/3 + 80*s**3 - 770*s**2. Let n(u) = 0. Calculate u.
10, 12
Factor -510*w**2 + 185*w**3 + 153*w**3 + 1026*w - 514 + 152*w**3 - 492*w**3.
-2*(w - 1)**2*(w + 257)
Suppose -180 = 122*l - 110*l. Let w be (16/(-24))/(l/9). Let -w*r - 2/5*r**2 + 4/5 = 0. What is r?
-2, 1
Let r(p) be the second derivative of 7*p**7/15 + 287*p**6/25 - 10*p**5 - 376*p**4/5 - 1088*p**3/15 - 144*p**2/5 - 1579*p - 1. Let r(h) = 0. What is h?
-18, -1, -2/7, 2
Let m = -1/450339 - -15911981/1351017. Suppose -98/9*f**3 - m*f**5 + 0 + 208/9*f**4 + 0*f - 4/9*f**2 = 0. What is f?
-2/53, 0, 1
Let m(f) be the first derivative of -f**5/45 + 14*f**4/9 - 392*f**3/9 - 9*f**2 + f - 35. Let c(b) be the second derivative of m(b). Solve c(g) = 0 for g.
14
Let c(w) = -w**2 - 10*w + 44. Let s be c(-13). Suppose 0 = 2*o + 3*q - s, 4*q = -5 + 1. Solve -18*b**4 - 2*b**5 + 2*b**2 + o*b**3 + 16*b**4 - 2*b**3 = 0 for b.
-1, 0, 1
Suppose 457*a = 800 + 686 - 115. Let v(g) be the second derivative of 8/3*g**a + 1/3*g**4 + 32*g + 0 + 8*g**2. Find i such that v(i) = 0.
-2
Let k = 34801/18558 + -201/2062. Factor -k*j + 2/9*j**3 + 0 - 14/9*j**2.
2*j*(j - 8)*(j + 1)/9
Let j(v) be the third derivative of 0 + 0*v**3 - v**2 + 66*v + 1/30*v**5 + 0*v**4 + 1/240*v**6. Factor j(l).
l**2*(l + 4)/2
Let l(v) = -v**2 - 1944*v - 1888. Let j(s) = 486*s + 471. Let n(i) = -11*j(i) - 3*l(i). Factor n(z).
3*(z + 1)*(z + 161)
Let i = 764926/7 - 109268. Factor -625/7 - 1/7*f**2 - i*f.
-(f + 25)**2/7
Let l(t) be the first derivative of -t**7/210 + t**6/120 + t**5/2 - 123*t**2 + 14. Let u(p) be the second derivative of l(p). Factor u(h).
-h**2*(h - 6)*(h + 5)
Suppose 150 = -2*x + 2*l, x - l = -4*l - 95. Let z = x - -82. Suppose 19*s**3 + 0*s + 3 - 23*s**2 + z*s - 4*s**4 + 3*s = 0. What is s?
-1/4, 1, 3
Let a be (-23 - -16) + 5 - -2. Let h(r) be the second derivative of 12*r + 2/5*r**2 - 1/60*r**4 + 0 + a*r**3. Factor h(d).
-(d - 2)*(d + 2)/5
Let x(b) be the first derivative of -b**6/600 - b**5/12 - b**4/5 + b**2 + 13*b - 212. Let l(h) be the second derivative of x(h). Factor l(o).
-o*(o + 1)*(o + 24)/5
Let z = -2374/165 + 752/33. Suppose -25 = -0*h - 5*h. Factor 9/5 - 4/5*i**3 + h*i**2 - z*i.
-(i - 3)**2*(4*i - 1)/5
Suppose f = -1 + 5. Let m = -55692 - -111385/2. Factor m*g**2 + 0*g + 0 - 1/4*g**f + 1/4*g**3.
-g**2*(g - 2)*(g + 1)/4
Let o(x) be the second derivative of 5*x**4/12 - 715*x**3/6 + 1050*x**2 - x + 1166. Determine j, given that o(j) = 0.
3, 140
Let v(c) be the first derivative of 2*c**5/55 + 63*c**4/22 - 2*c**3/11 - 17*c**2 + 252*c/11 + 2853. Find y such that v(y) = 0.
-63, -2, 1
Factor 277*l**2 - 83952 + 12035 - 279*l**2 - 800*l - 8083.
-2*(l + 200)**2
Factor -27*a - 3/8*a**3 - 42 - 45/8*a**2.
-3*(a + 4)**2*(a + 7)/8
Let x = 745604/3 + -248518. What is j in -8 + 2/3*j**3 + x*j - 28/3*j**2 = 0?
1, 12
Let u(v) be the first derivative of v**6/45 + 7*v**5/15 + 25*v**4/18 + 4*v**3/3 + 132*v - 123. Let a(d) be the first derivative of u(d). Factor a(o).
2*o*(o + 1)**2*(o + 12)/3
Let b be -4 + 8/(448/(-31736)). Let v = 571 + b. Factor v*r - 1/7*r**2 - 1/7.
-(r - 1)**2/7
Let r = 16 - 31/2. Let l be (-54)/72*78/(-117). Factor -r + s - l*s**2.
-(s - 1)**2/2
Let m be ((-2)/3)/(26/(-663)). Suppose t + 2*t = -a + m, 4*t + 9 = 5*a. Let -13*o**2 + 65*o**4 - 13*o**3 - 35*o**4 - 3*o - 33*o**t = 0. Calculate o.
-3, -1, -1/3, 0
Let a(n) be the first derivative of n**4/72 - n**3/12 + n**2/6 - 151*n - 106. Let w(v) be the first derivative of a(v). Solve w(u) = 0 for u.
1, 2
Suppose 875*c**4 + 42*c**3 + 132000 + 36600*c + 899*c**4 - 1777*c**4 + 3060*c**2 = 0. What is c?
-10, 44
What is d in -9*d**3 - 11227*d**5 + 37*d**3 + 11229*d**5 + 18*d**4 = 0?
-7, -2, 0
Solve -48/5*i**2 - 2/5*i**3 + 0 - 46/5*i = 0 for i.
-23, -1, 0
Factor 210*x**3 - 510770*x**2 - 78*x**4 + 9*x**5 - 28 + 510518*x**2 - 2 + 141*x.
3*(x - 5)*(x - 1)**3*(3*x - 2)
Factor -59/2*x**2 - 29*x + 0 - 1/2*x**3.
-x*(x + 1)*(x + 58)/2
Let a = -1836362/3 - -612121. What is j in -4/3*j**4 + 0*j + 0 - a*j**3 + 2*j**2 - 1/3*j**5 = 0?
-3, -2, 0, 1
Suppose 12 = 2*y + 3*v, -5 = -5*y - 3*v + 16. Determine g so that -19*g**3 - 5*g**y + 17*g**3 - 30*g**2 - 18*g**3 + 20 + 15*g = 0.
-1, 4/5
Let t(r) be the first derivative of 4*r**3/3 - 589*r**2/3 + 196*r/3 - 544. Factor t(y).
2*(y - 98)*(6*y - 1)/3
Let x(r) be the second derivative of -2*r**7/21 + 44*r**6/15 - 109*r**5/5 + 16*r**4 + 120*r**3 - 24*r - 3. Let x(i) = 0. Calculate i.
-1, 0, 2, 6, 15
Let u(h) be the first derivative of h**3/21 + 54*h**2/7 + 212*h/7 - 199. Find a, given that u(a) = 0.
-106, -2
Find v, given that -5156/5*v + 44/5*v**2 + 936/5 = 0.
2/11, 117
Suppose 0 = 2*s - 6*s + r + 8, -2*s + 10 = -2*r. Let g(q) = -2*q**2 + q. Let z(o) = o**2 - 23*o. Let t(h) = s*z(h) + 3*g(h). Suppose t(u) = 0. Calculate u.
-4, 0
Let t(u) be the third derivative of -u**8/336 - 59*u**7/105 + 241*u**6/60 - 182*u**5/15 + 487*u**4/24 - 61*u**3/3 + 253*u**2. Factor t(s).
-(s - 1)**4*(s + 122)
Let v(k) = -k**5 - k**4 + k**3 - k**2 + k. Let a = 119 + -125. Let n(o) = 7*o**5 + 10*o**4 - o**3 + 8*o**2 - 6*o. Let m(d) = a*v(d) - n(d). Factor m(t).
-t**2*(t + 1)**2*(t + 2)
Let v = -717/41 - -3299/123. Let p(t) be the first derivative of -16*t + 12 + 1/6*t**4 + v*t**2 - 20/9*t**3. Determine l, given that p(l) = 0.
2, 6
Let i(f) be the third derivative of f**8/112 + 27*f**7/10 + 9207*f**6/40 + 25943*f**5/20 - 93*f**4 - 17298*f**3 - 1374*f**2. Solve i(k) = 0.
-93, -2, 1
Let l be (-1 + (-387)/15)/(29/1595). Let v = 1478 + l. Solve 0 + 0*i - 2/3*i**v - 8/3*i**3 + 10/3*i**2 = 0 for i.
-5, 0, 1
Let l(w) be the first derivative of -w**5/270 + w**4/36 - 2*w**3/27 - w**2/2 - 11*w - 54. Let h(b) be the second derivative of l(b). Factor h(f).
-2*(f - 2)*(f - 1)/9
Let d be (10/2)/(-267 + 268). Let l(w) be the second derivative of 1/56*w**7 + 0*w**3 + 0*w**2 + 0 - 4*w - 3/16*w**4 + 21/80*w**d - 1/8*w**6. Factor l(c).
3*c**2*(c - 3)*(c - 1)**2/4
Let d(j) be the second derivative of j**6/210 - 5*j**5/28 - j**4/84 + 25*j**3/42 + 51*j - 4. Factor d(l).
l*(l - 25)*(l - 1)*(l + 1)/7
Let u = -28771/2 - -14388. What is l in u*l**3 + 0*l**4 + 0 - 5/4*l**5 + 0*l**2 - 5/4*l = 0?
-1, 0, 1
Suppose -4 = -g - 5, 5*g + 5 = 4*x. Suppose x = -m - 4, -5*t + 2*m + m + 332 = 0. Factor 2*a + t + 0*a + 14*a + 4*a**2 + 16*a.
4*(a + 4)**2
Let f = -5938 + 53449/9. Let h(x) be the first derivative of -1/6*x**4 + 3 + f*x**3 - 1/15*x**5 + 0*x - 2/3*x**2. Suppose h(j) = 0. What is j?
-4, 0, 1
Let f(z) be the first derivative of z**5/15 + 7*z**4/2 + 36*z**3 + 8*z**2 + 2*z - 189. Let o(r) be the second derivative of f(r). Solve o(d) = 0 for d.
-18, -3
Let u(g) be the third derivative of -130*g - 25/336*g**8 + 1/6*g**6 + 2*g**2 + 5/24*g**4 - 1/2*g**5 + 0*g**3 + 1/7*g**7 + 0. Solve u(q) = 0 for q.
-1, 0, 1/5, 1
Let y(q) = q**3 + 28*q**2 + 74*q + 13. Let t be y(-16). Factor 3*l**2 + 3322 + 1889 + 288*l - 2879 + t + 2679.
3*(l + 48)**2
Let w(f) be the third derivative of 39/35*f**5 + 0*f - 169/210*f**6 - f**2 + 8/7*f**4 + 2 + 8/21*f**3. Determine z, given that w(z) = 0.
-2/13, 1
Let i be ((1 - 15) + 270/18)*2. Factor -12*u + 54 + 2/3*u**i.
2*(u - 9)**2/3
Let s be (-33600)/(-35750) + 2/(-65). Factor -6*o**2 + 32/11*o + s*o**3 + 24/11.
2*(o - 6)*(o - 1)*(5*o + 2)/11
Let m(n) be the third derivative of -405*n**5/4 + 30*n**4 - 32*n**3/9 - 139*n**2 + 3. Let