2
Let b = 3019 + 3449. Let q be (1 - 1) + (-49)/(b/(-120)). Factor 2/11*u**3 + 14/11*u - 6/11 - q*u**2.
2*(u - 3)*(u - 1)**2/11
Suppose 127 = -p - 3*g, 18*p - 17*p + 4*g = -128. Let c be p*(-5)/(-140) + 5. Determine d, given that 2/7 - 6/7*d**2 - c*d = 0.
-1, 1/3
Suppose 2*t - 33 = -m, 0 = -56*t + 59*t + 3*m - 42. Suppose 1210*k**3 + k**2 + 4*k - t*k**2 - 1196*k**3 = 0. Calculate k.
0, 2/7, 1
Let c(r) be the third derivative of -140*r**2 - 3/8*r**4 - 1/20*r**5 + 0*r - r**3 + 0. Factor c(h).
-3*(h + 1)*(h + 2)
Let h = -7975/2 - -271321/68. Let p = h + -30/17. Factor 0*a**3 + p*a**2 + 0*a + 0 - 3/4*a**4.
-3*a**2*(a - 1)*(a + 1)/4
Factor -801/5*a + 1/5*a**2 + 160.
(a - 800)*(a - 1)/5
Let o(y) be the third derivative of -4*y**7/945 + 97*y**6/1080 - 5*y**5/9 + y**4/6 + 154*y**2. Factor o(s).
-s*(s - 6)**2*(8*s - 1)/9
Let v(f) be the second derivative of -f**5/50 + 37*f**4/10 - 209*f**3 + 605*f**2 + 67*f + 16. Find j, given that v(j) = 0.
1, 55
Let x = 975964 - 975961. Factor -135*i**2 - 93/2 + 3/2*i**4 - 42*i**x - 138*i.
3*(i - 31)*(i + 1)**3/2
Let h = -108 - -106. Let t(v) = -v**4 - 2*v**3 - v**2 + 2*v + 6. Let z(i) = i**3 + i**2 - i + 1. Let d(n) = h*z(n) + t(n). Factor d(m).
-(m - 1)*(m + 1)*(m + 2)**2
Factor 21*s**2 + 151 - 434 + 146 - 3*s**4 + 137 - 18*s**3.
-3*s**2*(s - 1)*(s + 7)
Let c(z) be the first derivative of z**3/36 + 47*z**2/24 - 17*z - 1297. Determine d, given that c(d) = 0.
-51, 4
Solve -98/13*v - 2/13*v**2 - 60 = 0 for v.
-39, -10
Factor 0 - 224*g**3 + 0*g - 2/3*g**4 - 18816*g**2.
-2*g**2*(g + 168)**2/3
Let u = 1729156 + -1981612609/1146. Let f = u - -4/191. Factor 5/6*p**2 + f*p**3 - 3/2 + 1/2*p.
(p - 1)*(p + 3)**2/6
Let r(g) = g**2 - 2*g. Let j(f) be the second derivative of 2*f**4/3 + 2*f**3/3 - 15*f**2/2 + 63*f. Let w(q) = -j(q) + 3*r(q). Factor w(y).
-5*(y - 1)*(y + 3)
Let h(r) be the third derivative of -3*r + 0 - 15/14*r**4 + 100/7*r**3 - r**2 - 9/70*r**5 - 1/280*r**6. Factor h(a).
-3*(a - 2)*(a + 10)**2/7
Let s(x) be the third derivative of x**7/1260 - x**6/36 + 59*x**5/180 - 5*x**4/4 + 9*x**3/4 + 755*x**2. Factor s(p).
(p - 9)**2*(p - 1)**2/6
Suppose -i + 4*y = 2, y - 3*y - 14 = -2*i. Factor 12 - 44*p**2 + 64*p + i - 6 - 34*p**3 - 2*p**3.
-4*(p - 1)*(p + 2)*(9*p + 2)
Let 61 + 383*n + 45*n**3 + 360*n - 900*n**2 - 31 - 108 - 874*n**2 = 0. What is n?
1/5, 2/9, 39
Let i(x) be the first derivative of -x**6/120 - x**5/60 + x**4/24 + x**3/6 - x**2 + 25*x - 38. Let h(j) be the second derivative of i(j). Factor h(w).
-(w - 1)*(w + 1)**2
Suppose 9 = 2*w - 3*c, 4*w = -3*c - 6 + 51. Let b(p) = -20*p. Let t(j) = j**2 + 41*j. Let f(r) = w*b(r) + 4*t(r). Factor f(g).
4*g*(g - 4)
Let h be (-4)/(-12)*(-45)/(-3). Let c(i) be the second derivative of 5/4*i**h + 10*i**2 - 5/4*i**4 + 0 - 1/6*i**6 - 21*i - 25/6*i**3. Let c(b) = 0. Calculate b.
-1, 1, 4
Let q(x) = x**2 + 14*x - 60. Let d(w) = -4*w**2 - 41*w + 178. Suppose 111 = -5*c + 2*z, -32*z = -4*c - 31*z - 87. Let m(r) = c*q(r) - 6*d(r). Factor m(v).
3*(v - 8)**2
Factor 2/9*j**2 - 812/9 - 10/3*j.
2*(j - 29)*(j + 14)/9
Factor -675*q**2 - 198*q**3 - 256 - 126*q**3 - 229*q - 225*q**2 - 603*q.
-4*(q + 1)*(9*q + 8)**2
Let u = -1356114 + 6780598/5. Factor -u*b**2 + 0*b + 1/5*b**4 + 12/5*b**3 + 0.
b**2*(b - 2)*(b + 14)/5
Let l(s) be the second derivative of 25/12*s**4 + 0 + 0*s**2 - 1/4*s**5 - 1/6*s**6 - 76*s - 5/2*s**3. Factor l(m).
-5*m*(m - 1)**2*(m + 3)
Let w(a) be the first derivative of 17 + 0*a**2 + 0*a - 16/9*a**3 + 1/6*a**4. Find n, given that w(n) = 0.
0, 8
Let f = -77 - -63. Let z be (-24)/f - 2 - (-64)/28. Factor o**z - 3*o + 9*o + 5 + 4.
(o + 3)**2
Let w(n) be the third derivative of -5*n**5/12 - 435*n**4/8 + 1925*n**3/3 - 9*n**2 - 281*n. Factor w(i).
-5*(i + 55)*(5*i - 14)
Let k(p) = -p - 4. Let r be k(-8). Factor -8*a**2 - 16*a**3 - 32*a**4 + 8*a**r + 22*a**4 - 6*a**2.
-2*a**2*(a + 1)*(a + 7)
Let b = 24 - 20. Suppose -5*n = l - 7, -b*n - 1 - 5 = -5*l. Suppose 7*c**4 - 16*c**l + 10*c**3 - 17*c**4 + 8*c**4 + 8*c = 0. Calculate c.
0, 1, 2
Suppose 81*b**2 + 1570*b**3 + 31 + 195*b**4 - 1550*b - 42 + 99*b**2 - 371 + 7 - 20*b**5 = 0. Calculate b.
-5, -1, -1/4, 1, 15
Determine i, given that -11686*i**2 + 11752*i**2 + i - 10*i = 0.
0, 3/22
Factor 240*s**2 + 147*s + s**4 + 2*s**3 - 1089 - 917*s + 23*s**3 - 55*s**3 + 48*s**2.
(s - 11)**2*(s - 9)*(s + 1)
Let f = -4035 + 4036. Let r(k) be the first derivative of 2/21*k**3 + 1/7*k**2 - 1/14*k**4 + f - 2/35*k**5 + 0*k. Factor r(p).
-2*p*(p - 1)*(p + 1)**2/7
Factor -332/7*x**3 + 16/7*x**4 + 0 + 0*x + 240/7*x**2.
4*x**2*(x - 20)*(4*x - 3)/7
Let b be (4 - -9 - 10) + (-2)/(-1). Let r be 1 - (-3 - b/(-10)*0). Let -4 + 22*k**2 + 3/4*k**4 - 45/4*k**5 - r*k + 34*k**3 = 0. What is k?
-1, -2/3, 2/5, 2
Let i(x) = 7*x**2 + 161*x + 996. Let b(k) = -48*k**2 - 1128*k - 6920. Let h(q) = -3*b(q) - 20*i(q). Factor h(d).
4*(d + 6)*(d + 35)
Suppose 4*s + 3*y = 17 + 6, 5*s = -2*y + 27. Solve 7*z**5 - 98*z**2 - 3*z**s + 694*z - 100*z**3 + 32 - 682*z - 18*z**4 = 0.
-2, -1, 1/2, 8
Suppose 2*c = -0*c + 9*c. Let b(w) = w + 52. Let f be b(c). Let -f*q**3 - 8*q**2 + 12 - 16*q**4 + 4*q**5 + 12 + 4*q**3 + 66*q - 22*q = 0. Calculate q.
-1, 1, 6
Let u(a) = -2*a - 25. Let x be u(-11). Let b be (x + 3)/(6/(-3)). Solve 5*w**4 + b*w**3 + 6*w**3 + 3 - 6*w - 2*w**4 - 6 = 0 for w.
-1, 1
Factor -1/10*b**3 + 2/5*b**2 - 2/5*b + 0.
-b*(b - 2)**2/10
Factor 10/7*k**2 - 1880/7 - 4696/7*k.
2*(k - 470)*(5*k + 2)/7
Let j(y) = y**2 - 613*y + 7214. Let a be j(12). Determine w so that -169/8 + 195/8*w + 1/8*w**3 - 27/8*w**a = 0.
1, 13
Factor -129*w**2 + 27147 - 13572 + 2*w - 13575.
-w*(129*w - 2)
Let x(k) = -30*k**3 - 40*k**2 - 14*k - 5. Let o(c) = -c**3 - 2*c**2 - c - 1. Let t = 200 - 180. Let u(j) = t*o(j) - 4*x(j). Factor u(i).
4*i*(5*i + 3)**2
Find n, given that -18*n - 2/7*n**3 + 0 - 32/7*n**2 = 0.
-9, -7, 0
Factor 369/8*y - 371/4 + 1/8*y**2.
(y - 2)*(y + 371)/8
Let h(w) be the first derivative of 3*w**6/56 - 9*w**5/70 + w**4/14 - w**3/3 + 5*w - 8. Let t(k) be the third derivative of h(k). Determine i so that t(i) = 0.
2/15, 2/3
Let q(y) be the third derivative of 0*y - 4/735*y**7 + 0 + 13/140*y**6 + 207*y**2 - 59/105*y**5 + 8/7*y**4 + 32/21*y**3. Determine s so that q(s) = 0.
-1/4, 2, 4
Determine s, given that -228/11*s**3 + 0 - 3024/11*s - 2088/11*s**2 + 6/11*s**5 + 42/11*s**4 = 0.
-6, -2, 0, 7
Let h be (-11088)/(-4032) + 2/8. Let 6*s**4 + 0*s + 18/5*s**h + 0 - 12/5*s**2 = 0. What is s?
-1, 0, 2/5
Let v(h) be the second derivative of -2*h**6/15 - 43*h**5/5 - 535*h - 1. Solve v(c) = 0 for c.
-43, 0
Let i(b) be the first derivative of b**6/12 + b**5/2 + 7*b**4/8 - b**3/6 - 2*b**2 - 2*b - 199. Let i(x) = 0. What is x?
-2, -1, 1
Suppose -4*k = u - 85, 5*k + 3*u - 75 = 2*k. What is g in -37 - 5*g**4 - k*g**3 - 340*g**2 - 650*g - 228 - 4*g**3 - 110 - 46*g**3 = 0?
-5, -3, -1
Let -3024*y + 834*y**3 + 4*y**5 + 128*y**4 + 1872*y**2 + 140*y**3 + 212*y**3 - 881*y**3 + 715*y**3 = 0. What is y?
-21, -6, 0, 1
Factor 578/11 + 50/11*u**3 - 290/11*u**2 + 238/11*u.
2*(u + 1)*(5*u - 17)**2/11
Let k(d) be the third derivative of 2/15*d**5 - 30 - 21/80*d**6 - 4/105*d**7 - d**2 + 0*d - 1/672*d**8 + 4/3*d**4 + 0*d**3. What is v in k(v) = 0?
-8, -1, 0, 1
Suppose 11448 = -17*i + 53*i. Let j = 322 - i. Factor 4/5*x**j + 0 + 12/5*x**3 + 4/5*x + 12/5*x**2.
4*x*(x + 1)**3/5
Suppose -53*z - 35*z = -15*z. Let y(u) be the first derivative of 3/14*u**4 - 16 + 0*u + z*u**2 - 2/21*u**3. What is o in y(o) = 0?
0, 1/3
Let y be (-15 + 12970/864)*4. Let p(l) be the second derivative of 0 - y*l**4 - 12*l - 1/18*l**3 + 0*l**2. Factor p(q).
-q*(5*q + 3)/9
Let q be -11*(-40)/220*1. Let l(z) be the first derivative of -3*z + 24 + 1/6*z**3 + 1/4*z**q. Determine a so that l(a) = 0.
-3, 2
Let n(i) be the first derivative of -1/34*i**4 - 143/17*i**2 - 6 + 50/51*i**3 - 338/17*i. Solve n(c) = 0.
-1, 13
Suppose -3*z + 8700 - 1629 = 0. Factor -z*l**2 - 15*l + 2356*l**2 - 5*l.
-l*(l + 20)
Let n(t) = -7*t**4 - 13*t**3 - 17*t**2 + 5*t + 4. Let h(i) = -2*i**4 - i**3 - 4*i**2 - i + 1. Let k(m) = 4*h(m) - n(m). Find g such that k(g) = 0.
-1, 0, 1, 9
Factor 0*q + 0 + 57*q**3 + 3/2*q**4 - 120*q**2.
3*q**2*(q - 2)*(q + 40)/2
Suppose -9 = -a, 5*q - 183 = 25*a - 15*a - 12*a. Find r, given that 3/2*r**4 - 33/4*r**3 - 30*r**2 + 3/4*r**5 - 12 - q*r = 