
1, 6
Let d be 19/38*136/1. Solve -28*k - 8*k + d*k**5 - 38*k**4 + 82*k**5 + 89*k**3 - 48*k**2 - 145*k**5 = 0.
-2/5, 0, 2, 3
Let p(r) be the second derivative of 0 - 1/14*r**7 + 0*r**3 + 0*r**4 + 0*r**5 + 41*r + 1/10*r**6 + 0*r**2. Factor p(k).
-3*k**4*(k - 1)
Let q(x) be the first derivative of 0*x - 3*x**2 - 53 - 20/9*x**3 - 1/6*x**4. Find y, given that q(y) = 0.
-9, -1, 0
Let k = 106961 + -106959. Factor -12/7 - 24/7*q + 6/7*q**3 + 3/7*q**4 - 9/7*q**k.
3*(q - 2)*(q + 1)**2*(q + 2)/7
Let j = -613429 + 613431. Solve 22/3*a + 5/2 - 1/6*a**4 + 7*a**2 + j*a**3 = 0 for a.
-1, 15
Let j(q) be the second derivative of -5*q**4/12 + 215*q**3/2 - 41*q + 7. Solve j(z) = 0 for z.
0, 129
Let m(x) be the third derivative of 3*x**6/40 - 253*x**5/20 + 333*x**4/8 - 83*x**3/2 - 1228*x**2. Factor m(z).
3*(z - 83)*(z - 1)*(3*z - 1)
Let s(k) = -11*k - 206. Let a be s(-26). Determine t, given that -4*t**2 - 173 + a + 20*t + 77 = 0.
1, 4
Let j = -3507 + 3509. Let f(a) be the first derivative of a**4 + 2 + j*a**2 - 8/3*a**3 + 0*a. Suppose f(y) = 0. Calculate y.
0, 1
Let n(t) be the third derivative of -11/12*t**4 + 0 - 3*t**2 - 16*t + 1/15*t**5 + 5/3*t**3. Let n(b) = 0. Calculate b.
1/2, 5
Suppose 0 = -24*u + 25*u, 4*o = -5*u. Let n be (-2 + o)/(10 - (-988)/(-95)). Let -2/13*h**3 - 2/13*h**n + 0*h + 0 - 4/13*h**4 + 0*h**2 = 0. Calculate h.
-1, 0
Find t, given that 11815*t - 11142*t**2 - 67253*t + 62208 - 4*t**5 + 13362*t**2 + 184*t**4 - 3204*t**3 - 29234*t + 23268*t**2 = 0.
1, 9, 12
Solve 121 + 38*n - 601 + 52*n - 4*n**2 - 2*n = 0.
10, 12
Determine f, given that 288 - f**2 - 8*f**2 - 238*f + 283 + 6*f**2 - 411 = 0.
-80, 2/3
Let p(w) be the third derivative of 2*w**7/245 - 1479*w**6/280 + 1289*w**5/70 - 105*w**4/8 - 184*w**3/7 - 1359*w**2 - 2. Determine l, given that p(l) = 0.
-1/4, 1, 368
Let q(m) be the first derivative of m**6/2 - 168*m**5/5 + 81*m**4 + 2*m**3 - 327*m**2/2 + 162*m + 266. Let q(u) = 0. Calculate u.
-1, 1, 54
Let f = 42022/531 + -4656/59. Suppose -14/9*a**2 + 14/9*a + 10/3 + f*a**3 = 0. Calculate a.
-1, 3, 5
Let c(r) be the first derivative of -3*r**5/35 - 111*r**4/28 + 11*r**3 - 117*r**2/14 - 2267. Determine p, given that c(p) = 0.
-39, 0, 1
Let k = 17155/7 - 154171/63. Factor -4/9*q**5 - k*q**3 + 0*q + 20/9*q**4 + 16/9*q**2 + 0.
-4*q**2*(q - 2)**2*(q - 1)/9
Let a be ((-240)/(-990)*-11)/((-10)/9). Let u(z) be the first derivative of a*z**2 - 3*z**4 + 22/15*z**3 - 2*z**5 - 8/5*z + 46. Let u(g) = 0. What is g?
-1, 2/5
Let f(i) = -5*i**2 - 4*i + 4. Let l(q) = -6*q**2 - 5*q + 5. Let m(a) = -5*f(a) + 4*l(a). Let v be m(2). Factor d**5 - 150*d**3 + 0*d**4 + 3*d**v + 152*d**3.
d**3*(d + 1)*(d + 2)
Factor 1791*j**2 + 3082*j**2 + 563*j**2 - 1172*j - 4 - 4 + 0.
4*(9*j - 2)*(151*j + 1)
Let v(f) be the second derivative of f**6/10 + 24*f**5/5 - 219*f**4/4 + 169*f**3 - 228*f**2 + 2162*f. Find g such that v(g) = 0.
-38, 1, 4
Let b = 76531/30 - 2551. Let n(w) be the second derivative of 1/42*w**7 - 30*w + 0*w**2 - b*w**6 + 1/3*w**3 - 3/20*w**5 + 1/12*w**4 + 0. Factor n(x).
x*(x - 2)*(x - 1)*(x + 1)**2
Let k(y) = -3*y**3 + 14*y**2 + 13*y - 24. Let h(t) = 2*t**3 - 7*t**2 - 7*t + 12. Let c = -48 - -43. Let w(d) = c*h(d) - 3*k(d). Find n, given that w(n) = 0.
-6, -2, 1
Let b(g) be the first derivative of g**6/75 - 3*g**5/50 - 7*g**4/30 + 9*g**3/5 - 18*g**2/5 - 95*g - 7. Let m(v) be the first derivative of b(v). Solve m(k) = 0.
-3, 1, 2, 3
Let d be (-2 + (-3)/6)/((-12)/24). Suppose 6*u = 19 + d. Determine w, given that 6*w - w**2 - 206*w**3 + 204*w**3 - u*w + w**4 = 0.
-1, 0, 1, 2
Factor -344*k**2 - 2848*k - 3031*k - 12*k**3 + 51 + 5659*k + 61.
-4*(k + 1)*(k + 28)*(3*k - 1)
Let a = 347294/5 - 68289. Let s = 1171 - a. Solve -39/5*f - 57/5*f**2 - s*f**4 - 9/5 - 33/5*f**3 = 0 for f.
-3, -1, -1/2
Let q(l) be the first derivative of -l**4/14 + 10*l**3/7 - 23*l**2/7 - 66*l - 4158. Factor q(x).
-2*(x - 11)*(x - 7)*(x + 3)/7
Let n(y) = -y**2 - y. Let b be n(-1). Suppose -5*s + 53 = -142*r + 143*r, 13*r = 4*s - 1. What is z in 3/2 + 3/4*z**r - 9/4*z + b*z**2 = 0?
-2, 1
Let h be (-60)/105 - 56841/(-21). Let f = h - 2701. Solve 1/7*i**2 + f - 12/7*i = 0.
6
Let 121*a - 190*a - 20*a**2 + 54 - 225*a**3 + 228*a**3 = 0. What is a?
-3, 2/3, 9
Let w(b) = -6*b**3 - 9*b**2 + 34*b + 41. Let a(t) = -7*t**3 - 7*t**2 + 44*t + 42. Let l(v) = 5*a(v) - 6*w(v). Find p, given that l(p) = 0.
-18, -2, 1
Let v(h) be the third derivative of -h**8/56 + 41*h**7/105 + 31*h**6/30 - 13*h**5/15 - 59*h**4/12 - 5*h**3 + 62*h**2 + 9*h. Solve v(m) = 0.
-1, -1/3, 1, 15
Let m(j) = j**3 - 8*j**2 - 59*j + 302. Let c be m(4). Factor 28/11*b - 2/11*b**c + 30/11.
-2*(b - 15)*(b + 1)/11
Let j(t) be the first derivative of -t**5/60 - t**4/6 - t**3/2 + 84*t**2 - 240. Let z(u) be the second derivative of j(u). Factor z(m).
-(m + 1)*(m + 3)
Find n, given that 20*n - 25 - 21*n**2 - 14*n**2 + 31*n**2 + 1 + 0*n = 0.
2, 3
Suppose -165*i = 4*q - 160*i + 63, 5*q = 5*i + 90. Factor 4/7*k**4 + 0 + 96/7*k - 188/7*k**2 + 88/7*k**q.
4*k*(k - 1)**2*(k + 24)/7
Suppose -2*d + 4*z = -30, 0*d = 5*d + 3*z - 10. Factor -95*o + 177*o - 60 + 5*o**3 - 122*o + d*o**2.
5*(o - 3)*(o + 2)**2
Let n = -6/34625 - 147640874/727125. Let v = n - -610/3. Factor -v*i**3 + 6/7*i + 0 + 4/7*i**2.
-2*i*(i - 3)*(i + 1)/7
Let c(w) = -48*w**2 + 48*w - 209*w**3 + 396*w**3 + 80 - 203*w**3. Let s(x) = -x**3 - x**2. Let a(l) = c(l) - 12*s(l). Determine m, given that a(m) = 0.
-10, -1, 2
Let f be 18 + -3 - (2 + 1). Let q be 14/f - (13 - 473/33). Find o, given that 0 + 5/4*o**4 + 0*o + 5/4*o**3 - q*o**2 = 0.
-2, 0, 1
Let n be (-3 - (-338)/10) + (-12)/15. Factor 4*y**3 - 3*y**4 + 12*y**3 - 99*y**2 - n + 92*y + 23*y**3 + y.
-3*(y - 10)*(y - 1)**3
Let h = 902189 + -902187. Factor -24 - 162/7*a + 6/7*a**h.
6*(a - 28)*(a + 1)/7
Let g = -2/577 - 543/9809. Let z = g + 25/136. Let 1/8 - 1/8*d**3 + 1/8*d - z*d**2 = 0. Calculate d.
-1, 1
Let f(q) be the first derivative of -q**3/24 + 395*q**2/8 - 156025*q/8 + 556. Solve f(k) = 0 for k.
395
Suppose 0 = -5*r - 3*t + 9, 0*r - 5*t - 16 = -2*r. Let n = -3106 + 3143. Factor 0 + 6 - 34*h**3 + n*h**r - 9*h.
3*(h - 1)**2*(h + 2)
Let x = -6/17 - -122/153. Suppose 0 = 2*p + 3*z - 7*z - 22, -4*z = p + 13. Factor 2/9*g**4 + 2/9*g**p + x - 2/3*g**2 - 2/9*g.
2*(g - 1)**2*(g + 1)*(g + 2)/9
Suppose 9 = 5*c - 3*h - 10, -13 = c + 5*h. Let s = 141397/4 + -35349. Find x such that s*x**c + 3/2 + 5/4*x = 0.
-3, -2
Factor 81*m**2 - m**4 - 645*m**2 - 3*m**4 - 23*m**3 - 1596*m - 61*m**3 - 8*m**2 - 1584.
-4*(m + 3)**2*(m + 4)*(m + 11)
Factor 1503*m - 64*m**2 + 2951*m + 672 - 942*m + 60*m.
-4*(m - 56)*(16*m + 3)
Let q be (4 - 0)*(6/(-6) - 0). Let i be -4 + 65*q/(-40). Find j such that i*j - 3/2*j**3 + 4*j**2 - 3 = 0.
-1, 2/3, 3
Let h be 2/3 - 590/(-390)*-7. Let o = h + 2039/195. Find x, given that 0*x**2 - o*x**3 - 32/15*x**4 + 6/5*x**5 + 0 + 0*x = 0.
-2/9, 0, 2
Let c(v) = -27*v**3 - 75*v**2 - 4829*v - 4725. Let u(p) = -37*p**3 - 100*p**2 - 6439*p - 6300. Let h(o) = -19*c(o) + 14*u(o). Factor h(g).
-5*(g - 21)*(g + 1)*(g + 15)
Let u(z) = 5*z**3 - 87*z**2 + 307*z - 204. Let l(r) = 110*r**3 - 1915*r**2 + 6750*r - 4490. Let g(k) = 3*l(k) - 65*u(k). Determine n so that g(n) = 0.
1, 3, 14
Let g(k) = -29*k**2 - 51*k - 49. Let t(p) = 16*p**2 + 25*p + 24. Let o(i) = -5*g(i) - 9*t(i). Find v, given that o(v) = 0.
-29, -1
Let d(m) = 40*m**3 - 215*m**2 + 470*m + 680. Let n(r) = 49*r**3 - 214*r**2 + 469*r + 678. Let w(y) = 6*d(y) - 5*n(y). Find z, given that w(z) = 0.
-46, -1, 3
Let q(g) be the third derivative of -2/105*g**7 + 1/6*g**4 + 4 - 1/40*g**6 - 6*g**2 + 0*g**3 - 1/336*g**8 + 0*g + 1/15*g**5. Find m such that q(m) = 0.
-2, -1, 0, 1
Determine q, given that -12*q**3 - 184/15*q**2 - 56/15*q**4 - 62/15*q + 2/15*q**5 + 0 = 0.
-1, 0, 31
Let r be (-6)/(-36) + (-124)/(-93). Let 12*j**3 - 24 - r*j**4 - 33*j + 9/2*j**2 = 0. What is j?
-1, 2, 8
Let j(z) = 14*z + 122. Let n be j(-13). Let p be (90/n)/((-54)/8). Let 2/9*k + 0*k**4 + p*k**5 + 0*k**2 + 0 - 4/9*k**3 = 0. What is k?
-1, 0, 1
Let i be ((-74)/(-148))/(1/(-5))*(-7)/10. Solve -3/2*a + 1/4*a**2 - i = 0 for a.
-1, 7
Let z(t) = t**2 - t. Let i(x) = 8*x**2 - 464*x + 456. Let g(b) = i(b) - 5*z(b). Factor g(d).
3*(d - 152)*(d - 1)
Let y = 18402/50545 + -2/4595. Let -10/11*f**4 + 10/11*f**2 + 4/11*f**5 + 0*f**3 -