 1
Suppose 74*d - 85*d = -22. Let u be (5 + d + -6)*72/8. Factor 0 + u*o**3 + 3/2*o**5 - 6*o**2 - 6*o**4 + 3/2*o.
3*o*(o - 1)**4/2
Let l = 758 - 786. Let y be ((-12)/(-21))/(l/(-196)). Determine q, given that 0 + 2/3*q**3 + 0*q - 1/3*q**2 - 1/3*q**y = 0.
0, 1
Let i = 724 - 898. Let a be i/(-54) + (-8)/36. Solve 4/7 + 10/7*k + 8/7*k**2 + 2/7*k**a = 0 for k.
-2, -1
Let z(i) be the third derivative of -1/1470*i**7 + 1/84*i**4 + 1/420*i**5 + 1/2352*i**8 + 0*i - i**2 - 27 + 0*i**3 - 1/280*i**6. Factor z(t).
t*(t - 2)*(t - 1)*(t + 1)**2/7
Determine d, given that 0 + 2*d**2 + 0*d - 9/2*d**3 + 5/2*d**4 = 0.
0, 4/5, 1
Let s(y) = -y**4 - 2*y**2 - y + 1. Let d(j) = -6*j**4 + 86*j**3 + 147*j**2 - 591*j + 343. Let h(i) = d(i) - 7*s(i). Solve h(o) = 0.
-84, -4, 1
Let h(g) be the third derivative of g**8/1344 + g**7/1008 + 91*g**5/60 + 139*g**2. Let v(t) be the third derivative of h(t). Factor v(z).
5*z*(3*z + 1)
Let k(i) be the first derivative of i**4/28 + i**3/14 - 3*i**2/7 - 256*i + 133. Let v(p) be the first derivative of k(p). Find y such that v(y) = 0.
-2, 1
Suppose 16*l - 83 = 61. Let t be (-90)/(-650)*30/l. Let 0 - 2/13*r**3 + 8/13*r**2 - t*r = 0. What is r?
0, 1, 3
Let p(g) be the third derivative of 18*g + 1/1260*g**7 - 1/48*g**4 + 0 + 0*g**3 - 1/72*g**5 + 3*g**2 - 1/720*g**6. Factor p(f).
f*(f - 3)*(f + 1)**2/6
Factor -43 + 88*h**3 - 80 - 2*h**4 + 123.
-2*h**3*(h - 44)
Let r(a) = 7*a**3 - 27*a**2 - 120*a - 112. Let p(i) = 14*i + 194. Let d be p(-14). Let f(n) = -n**3 - n**2. Let x(c) = d*r(c) - 18*f(c). Solve x(h) = 0.
-14, -2
Suppose 2*k = -7*j + 47, 86*k - 89*k + 11 = 2*j. Let q(n) be the second derivative of -7/60*n**4 + 11/30*n**3 + j*n + 1/100*n**5 + 0 - 1/2*n**2. Factor q(c).
(c - 5)*(c - 1)**2/5
Let c = 45641/140 - 326. Let z(i) be the third derivative of 0 + 0*i - 27*i**2 + 3/14*i**3 + 1/28*i**4 - c*i**5. Determine j, given that z(j) = 0.
-1, 3
Let j(o) = 6*o**2 + 1115*o + 1174. Let v(c) = 2*c**2 + 372*c + 390. Let p(m) = 4*j(m) - 13*v(m). Factor p(d).
-2*(d + 1)*(d + 187)
Solve -29491*r**2 - 29479*r**2 + 58966*r**2 - 712*r + 716 = 0.
-179, 1
Let a = -32900 + 32904. Let d(w) be the second derivative of -32*w - 1/33*w**a + 0 + 1/110*w**5 + 0*w**3 + 0*w**2. What is u in d(u) = 0?
0, 2
Let v = -287 - -3733/13. Let w = 2556 - 2553. Factor -54/13*m - v*m**w + 54/13 + 18/13*m**2.
-2*(m - 3)**3/13
Let w(j) be the first derivative of 225*j**4/22 - 60*j**3/11 + 12*j**2/11 + 24*j - 47. Let k(y) be the first derivative of w(y). Solve k(z) = 0 for z.
2/15
Suppose 11*n + 7727 = 7749. Suppose 28/13*i - 2/13*i**n + 0 = 0. Calculate i.
0, 14
Suppose -5*n - 4040 = -4070. Factor -3/8*z**2 + 51/8 - n*z.
-3*(z - 1)*(z + 17)/8
Let m(j) be the first derivative of -j**6/270 + 17*j**5/90 - 5*j**4/3 - 4*j**3/3 - 10*j + 100. Let w(g) be the third derivative of m(g). Factor w(v).
-4*(v - 15)*(v - 2)/3
Let p = -249 - -253. Let b be (-88)/(-352) + 2/(p*2). What is f in 1/2*f**2 + 3/2*f - 3/2*f**3 - 1 + b*f**4 = 0?
-1, 1, 2
Factor -19*d**2 - 6808512*d**3 + d - 43*d**2 + 31*d**4 + 6808510*d**3 + 31 + d**5.
(d - 1)**2*(d + 1)**2*(d + 31)
Let i(w) = -60*w**5 - 162*w**4 - 9*w**3 - 15*w**2 + 30. Let h(u) = -45*u**5 - 121*u**4 - 7*u**3 - 11*u**2 + 22. Let s(b) = -15*h(b) + 11*i(b). Factor s(a).
3*a**3*(a + 2)*(5*a + 1)
Let p(c) be the second derivative of -7*c - 1/15*c**3 + 1/90*c**4 + 2/15*c**2 + 0. Factor p(m).
2*(m - 2)*(m - 1)/15
Let v(l) = -l**3 + 10*l**2 + 36*l + 33. Let n be v(13). Let q be (-9)/(-24)*(-4)/n. Solve 5*t**2 + 15/4*t**4 - 25/4*t**3 + q - 7/8*t**5 - 15/8*t = 0 for t.
2/7, 1
Let q be ((-2)/(-4))/(15/(127 + -7)). Let k(l) be the second derivative of -4/3*l**2 - 1/9*l**q + 0 + 2/3*l**3 + 7*l. Find t, given that k(t) = 0.
1, 2
Let w(n) = -4*n**2 - 65*n + 69. Let f(y) = 4*y**2 + 41*y - 8 - 2*y**2 - 18 - 9*y - 8. Let m(l) = 7*f(l) + 4*w(l). Solve m(o) = 0 for o.
-19, 1
Let f(s) = 9*s**3 + 27*s**2 + 54*s + 30. Let w(k) = 8*k**3 + 27*k**2 + 55*k + 31. Let d = -290 + 296. Let h(n) = d*w(n) - 5*f(n). Factor h(b).
3*(b + 1)*(b + 2)*(b + 6)
Let l(i) be the third derivative of i**7/420 - 31*i**6/240 - 131*i**5/40 - 689*i**4/48 - 82*i**3/3 - 25*i**2 + 68. Factor l(f).
(f - 41)*(f + 1)**2*(f + 8)/2
Let h(a) = 45*a**4 - 380*a**3 - 495*a**2 + 770*a + 40. Let b(t) = 20*t**4 - 169*t**3 - 220*t**2 + 342*t + 18. Let c(d) = 20*b(d) - 9*h(d). Solve c(v) = 0.
-2, 0, 1, 9
Let w = 1609 + -1609. Let v(z) be the second derivative of w + 0*z**6 - 9/20*z**5 + 1/14*z**7 + 0*z**3 + 2*z + 0*z**2 + 1/2*z**4. Factor v(b).
3*b**2*(b - 1)**2*(b + 2)
Suppose -2*d = -3*t + 2166, -3514*t + 3510*t = d - 2910. Find n, given that 33*n**2 - t*n + 5324 - 1/2*n**3 = 0.
22
Let o = 1/271 - -2161/1897. Let h be 17/(3213/(-180))*660/(-550). Factor -h*d - o - 2/7*d**2.
-2*(d + 2)**2/7
Let m(p) = -20*p**2 + 688*p. Let y(b) = -4*b**2 + 138*b. Let f(z) = -3*m(z) + 14*y(z). Factor f(x).
4*x*(x - 33)
Let c(x) be the third derivative of 0*x + 1/15*x**5 - 177*x**2 + 0 + 88/3*x**3 + 5/2*x**4. Find b, given that c(b) = 0.
-11, -4
Let v(w) be the first derivative of 3*w**4 - 2252*w**3/3 - 384*w**2 + 3008*w - 11872. Determine p so that v(p) = 0.
-4/3, 1, 188
Let q(o) be the third derivative of -o**6/320 + 17*o**5/40 + 9*o**2 + 63. Find j, given that q(j) = 0.
0, 68
Let o(y) be the first derivative of -y**6/36 + 2*y**5/5 - 49*y**4/24 + 11*y**3/3 + 8*y**2/3 - 16*y + 425. What is r in o(r) = 0?
-1, 2, 3, 4
Let u(y) be the third derivative of y**8/1680 - y**7/315 + y**6/180 - 79*y**4/24 - 8*y**2 + 5. Let d(h) be the second derivative of u(h). Solve d(k) = 0 for k.
0, 1
Suppose -72 - 16*q**3 - 59*q + 1134*q**2 - 834*q**2 - 153*q = 0. What is q?
-1/4, 1, 18
Let w = 176 - 173. Let 4*m**5 - 1029*m - 147*m**w - 144*m**3 + 66*m**4 - 7*m**5 + 394*m**2 + 1076*m**2 - 213*m**3 = 0. Calculate m.
0, 1, 7
Determine d so that 2*d**2 + 2*d**4 + 28*d + 0*d**2 + 4*d - 24*d**2 - 2*d**2 = 0.
-4, 0, 2
Let l(b) be the first derivative of 4*b**5/5 - 3*b**4 + 8*b**2 - 1346. Solve l(i) = 0.
-1, 0, 2
Let d(g) be the first derivative of -1/6*g**4 + 32/9*g**3 + 103 + 0*g**2 + 0*g. Let d(r) = 0. Calculate r.
0, 16
Let d(a) be the third derivative of -9*a**8/224 - 43*a**7/40 - 681*a**6/80 - 54*a**5/5 - 4*a**4 - 58*a**2 - 24. Find j such that d(j) = 0.
-8, -1/2, -2/9, 0
Let x(y) be the third derivative of y**5/90 - 143*y**4/18 + 95*y**3/3 - 3744*y**2. Factor x(w).
2*(w - 285)*(w - 1)/3
Let j be (4/8)/(-63*(-6)/432). Factor -80/7*m - 96/7 + j*m**3 - 8/7*m**2.
4*(m - 6)*(m + 2)**2/7
Let x(a) = -36*a**2 + 9*a. Suppose 20 = 43*b - 39*b. Let p(r) = 7*r**2 - 2*r. Let z(c) = b*x(c) + 24*p(c). Factor z(k).
-3*k*(4*k + 1)
Let h be (-1)/(((-12)/(-9))/(-1)). Let x = 38181 + -38179. Factor h*r**x + 0 + 1/4*r**4 - 5/4*r**3 + 9/4*r.
r*(r - 3)**2*(r + 1)/4
Let l(z) = -28*z**2 - 784*z. Let s be ((-10)/2)/(1/4). Let k(n) = -4*n**2 - 112*n. Let j(h) = s*k(h) + 3*l(h). Factor j(t).
-4*t*(t + 28)
Factor -744/5*p - 742/5 - 2/5*p**2.
-2*(p + 1)*(p + 371)/5
Solve 5*p**3 - 2*p**2 - 97*p + 4*p**3 - 100*p - 2*p**4 + 113*p + 7*p**3 = 0.
-2, 0, 3, 7
Let s(r) = 53*r**2 + 467*r + 366. Let y be s(-8). Suppose -34/3*q**4 + 46/3*q**2 + 4/3*q**5 - y*q**3 + 134/3*q + 20 = 0. What is q?
-1, 3/2, 10
Let r(i) be the second derivative of -1/12*i**4 + 25/6*i**3 - 12*i**2 - 123*i + 0. Find y such that r(y) = 0.
1, 24
Let p(j) be the second derivative of -4*j + 0*j**2 + 5/12*j**4 - 45/2*j**3 - 6. Factor p(m).
5*m*(m - 27)
Let y(o) = o**2 - 3*o - 104. Let v be y(12). Factor -v - 1 - 38*z + 10 - 20 - 22 - z**2.
-(z + 1)*(z + 37)
Let h(v) be the second derivative of v**7/6300 + 2*v**6/675 - v**5/100 + 4*v**3/3 - 3*v**2/2 + 59*v. Let i(y) be the second derivative of h(y). Factor i(p).
2*p*(p - 1)*(p + 9)/15
Let z = -4561163/3 - -1520388. Factor 1/3 + 1/3*x - 1/3*x**3 - z*x**2.
-(x - 1)*(x + 1)**2/3
Let v(b) be the second derivative of -b**4/4 - 41*b**3/2 + 129*b**2 - 545*b. Factor v(h).
-3*(h - 2)*(h + 43)
Let b(f) be the second derivative of f**6/6 - 3*f**5/4 - 35*f**4/6 + 10*f**3 + 100*f**2 - 29*f + 25. What is z in b(z) = 0?
-2, 2, 5
Let b(t) = -t**2 + 16383*t + 213152. Let z be b(-13). Factor 2/11*x**z + 32/11*x**3 - 72/11*x**2 + 0 + 0*x.
2*x**2*(x - 2)*(x + 18)/11
Let a = -120 + 169. Suppose a = 5*v + 24. Find t, given that 5*t - v*t**4 + 3*t**3 - 7*t**2 + 12*t**4 - 3*t - 5*t**5 = 0.