/2
Let b(n) = n**5 + 24*n**4 + 73*n**3 + 38*n**2 - 16*n. Let u(a) = -a**5 - 24*a**4 - 71*a**3 - 39*a**2 + 12*a. Let f(d) = -3*b(d) - 4*u(d). Factor f(t).
t**2*(t + 1)*(t + 2)*(t + 21)
Let y(h) be the first derivative of h**4/26 + 3494*h**3/13 + 9156027*h**2/13 + 10663719446*h/13 + 1175. Determine o, given that y(o) = 0.
-1747
Let c(u) be the third derivative of -u**5/270 + 229*u**4/108 - 454*u**3/27 + u**2 - 1484. Factor c(i).
-2*(i - 227)*(i - 2)/9
Let n(d) be the third derivative of -1/70*d**7 - 170*d**2 + 0 + 1/20*d**5 + 1/20*d**6 + 0*d - 1/4*d**4 + 0*d**3. Factor n(b).
-3*b*(b - 2)*(b - 1)*(b + 1)
Let c(d) be the first derivative of -2/21*d**3 - 5/7*d**2 + 166 + 12/7*d. Factor c(l).
-2*(l - 1)*(l + 6)/7
Let r(c) be the first derivative of -2*c**6/3 - 32*c**5/5 + 7*c**4 + 200*c**3/3 - 96*c**2 - 369. Determine k so that r(k) = 0.
-8, -3, 0, 1, 2
Let s be ((-792)/(528/(-8)))/((-1 + 10/3)*2). Factor -2/7*r**4 - 16/7*r**3 + 0 + s*r**2 + 0*r.
-2*r**2*(r - 1)*(r + 9)/7
Let f = 126/73 + 2781/292. Let g(w) be the first derivative of -f*w**2 - 75/4*w**4 + 20*w**3 - 6 + 3*w - 7/4*w**6 + 9*w**5. What is t in g(t) = 0?
2/7, 1
Factor 8472/5*c - 3/5*c**3 + 8484/5 + 2109/5*c**2.
-3*(c - 707)*(c + 2)**2/5
Let t = 856776/373 - 2297. Let m = 1567/5595 + t. Factor -2/15*d**2 + m + 2/15*d.
-2*(d - 2)*(d + 1)/15
Solve 0 - 49/4*o**5 + 10563/4*o**4 + 215*o**2 + 0*o - 1506*o**3 = 0 for o.
0, 2/7, 215
Let z(c) = c**2 + 10*c - 117. Let q be z(-17). Suppose v - o = 84, 2*v + 3*o - 86 - 87 = 0. Factor -87*i**2 + v*i - 43 - 13*i**q + 28.
-5*(4*i - 1)*(5*i - 3)
Let w = 734149/872556 - 14/3827. Let j = w + -5/57. Factor 5/4*h**2 + 1/4*h + j*h**3 - 1/4.
(h + 1)**2*(3*h - 1)/4
Let i be 17/(-1)*(-8 + (-2 - -9)). Suppose 0 = 79*j - i*j - 248. Factor 1/4*p**2 + j + 2*p.
(p + 4)**2/4
Suppose 20*r = 15*r + 10. Let -9*z**r + 1159*z**3 - 2*z - 3 - 7*z - 1162*z**3 = 0. What is z?
-1
Let a = -159 + 164. Find t such that 96 - a*t + t - 32*t + 68*t**2 - 65*t**2 = 0.
4, 8
Factor 8/5 + 4/5*v**2 - 14/5*v + 2/5*v**3.
2*(v - 1)**2*(v + 4)/5
Let c = -5656 - -5661. Let s(g) be the third derivative of 0 + 4*g**3 + 7/40*g**6 + 0*g + 1/70*g**7 + 17*g**2 + 9/10*g**c + 5/2*g**4. Factor s(n).
3*(n + 1)*(n + 2)**3
Let w(o) = 2*o**3 + 12*o - 12. Let s be w(1). Let x be 3 - 3*3/9. Suppose 2*q**s + 64*q**3 - 58*q**3 - 4*q + 0*q**x = 0. Calculate q.
-1, 0, 2/3
Let b(t) = -23*t + 120. Let f be b(5). Let p(i) be the second derivative of 0 - 1/20*i**f + 12*i + 5/2*i**2 - 11/6*i**3 + 7/12*i**4. Factor p(j).
-(j - 5)*(j - 1)**2
Let w = 419 - 4573/11. Let u = 1332 - 1330. Factor 48/11*z**u - 28/11*z + 10/11*z**4 - w*z**3 + 6/11.
2*(z - 1)**3*(5*z - 3)/11
Let r(m) = m + 90. Let n be r(-17). Let y = n - 71. Suppose 8/5*j - 4/5*j**y + 0 = 0. What is j?
0, 2
Suppose -11*s + 2497 = -2511 + 4986. Factor -2*w**s + 2/9*w**3 - 14/9 + 10/3*w.
2*(w - 7)*(w - 1)**2/9
Let n = 2581/10897 - 1/641. Let g = 746693/17 - 43923. Factor 0 - n*r + g*r**3 - 2/17*r**2.
2*r*(r - 2)*(r + 1)/17
Let a be (8 - 83/10)*-90. Suppose l - 9 = -2*l. Suppose -z**2 - 9 - 4*z - 10 - l*z**2 + a = 0. What is z?
-2, 1
Let i(j) be the first derivative of -j**6/36 + 4*j**5/15 + j**4/3 - 31*j**3/3 + 147*j**2/4 - 45*j - 2497. Determine g so that i(g) = 0.
-5, 1, 3, 6
Let b(v) be the second derivative of -v**6/90 + v**5/30 + 559*v**4/36 - 2926*v**3/9 + 882*v**2 - 4*v + 233. Suppose b(n) = 0. What is n?
-27, 1, 14
Let f(b) = 4*b**3 + 5*b + 9*b - b**2 + 11*b + 4 - 26*b. Let l(w) = w**3 + 1. Let g(h) = f(h) - 3*l(h). Find d, given that g(d) = 0.
-1, 1
Determine c, given that 37 + 5*c**2 - 747 - 382*c - 323*c = 0.
-1, 142
Let z = -32628 + 33012. Factor -32*t - z - 2/3*t**2.
-2*(t + 24)**2/3
Solve -w**2 + 39*w**2 - w**3 + 1890 - 1890 - 325*w = 0 for w.
0, 13, 25
Let g(c) be the second derivative of c**5/10 - 8*c**4 + 92*c**3/3 + 670*c. Factor g(n).
2*n*(n - 46)*(n - 2)
Let t(k) be the third derivative of 68*k**2 - 25/12*k**4 - 15/2*k**3 + 0 - 1/12*k**5 + 0*k. What is h in t(h) = 0?
-9, -1
Let p(a) be the third derivative of -a**5/210 + a**4/6 - 13*a**3/21 + 570*a**2. Determine m so that p(m) = 0.
1, 13
Let k(w) = -2*w + 19. Let h be k(-6). Suppose 0 = 4*j - h - 77. Factor 10*r + 8 - j*r**2 + 11*r - 2.
-3*(r - 1)*(9*r + 2)
Let v(p) be the third derivative of p**6/120 + 5*p**5/12 + 25*p**4/8 - 375*p**3/2 - 1601*p**2. Factor v(t).
(t - 5)*(t + 15)**2
Let u = 1494933/2 - 747459. Suppose 1/2*c**3 - u*c**2 + 15/2 - 1/2*c = 0. Calculate c.
-1, 1, 15
Suppose 0*w + 5*w = w. Let r be ((-12)/(-18))/(8/6)*w. Factor 0*a**2 + 3/2*a**4 + r - 6*a + 9/2*a**3.
3*a*(a - 1)*(a + 2)**2/2
Suppose 0 = -10*h - 738*h. Let h*u - 4/7*u**2 + 0*u**4 - 6/7*u**3 + 0 + 2/7*u**5 = 0. What is u?
-1, 0, 2
Let n(l) = l**3 - 83*l**2 + 48*l - 24. Let f(w) = -82*w**2 + 48*w - 20. Let u(k) = 6*f(k) - 5*n(k). Let u(x) = 0. What is x?
-16, 0, 3/5
Let h = 1544734/5 + -308942. Determine a, given that -h*a - 2/5*a**2 - 22/5 = 0.
-11, -1
Solve 119*b - 2*b**4 + 102*b**2 + 403*b**3 - 202*b**3 - 225*b**3 - 240 + 45*b = 0 for b.
-15, -2, 1, 4
Let l = -53/21 - -5/14. Let z = l - -233/102. Factor -2/17*q + 2/17*q**2 + 2/17*q**3 - z.
2*(q - 1)*(q + 1)**2/17
Determine k so that 31/12*k**2 + 7/2*k - 1/12*k**4 + 0 - k**3 = 0.
-14, -1, 0, 3
Let w(m) be the second derivative of -6*m - 20*m**3 - 3 + 90*m**2 - 1/12*m**5 + 25/12*m**4. Solve w(t) = 0 for t.
3, 6
Let u(h) be the first derivative of -5*h**4/4 + 1400*h**3/3 - 96585*h**2/2 - 198810*h + 7869. Factor u(k).
-5*(k - 141)**2*(k + 2)
Let f(q) be the second derivative of 9/20*q**5 - 2*q - 3*q**2 - 2 + 5/3*q**4 - 23/6*q**3. Factor f(u).
(u - 1)*(u + 3)*(9*u + 2)
Determine o so that 380/3*o + 256 - 2/3*o**2 = 0.
-2, 192
Let i = 1998157 + -1998077. Find u such that -3833/3*u**3 - 1421*u - 4/3*u**5 - 7019/3*u**2 - i*u**4 - 841/3 = 0.
-29, -1, -1/2
Let i(j) be the second derivative of -j**7/42 + j**6/3 - 7*j**5/12 - 3*j**2 + 8*j. Let r(x) be the first derivative of i(x). Suppose r(s) = 0. Calculate s.
0, 1, 7
Let 124*j**3 - 221*j**3 + 47*j**3 + 57*j**2 - 80*j - 85*j**4 + 15*j**5 + 130*j**3 + 43*j**2 = 0. What is j?
-1, 0, 2/3, 2, 4
Factor -45*w - 162 + 1/3*w**3 + 4*w**2.
(w - 9)*(w + 3)*(w + 18)/3
Let i be (2/4)/(5/2). Let y = 108747/35 - 21748/7. Suppose i*p + 0 + 1/5*p**4 - 1/5*p**2 - y*p**3 = 0. Calculate p.
-1, 0, 1
Let m be (-2 + (-4 - -5))*(-5 - -3). Determine p so that -7*p**2 - p + 2*p**m + 5*p**3 - 7*p - 2*p = 0.
-1, 0, 2
Let l(a) = -a**3 - 44*a**2 - 81*a + 119. Let n be l(-42). Let o be 9/90*n*-5. Suppose -7/2*w**3 - o*w**2 - w**4 - w + 0 = 0. What is w?
-2, -1, -1/2, 0
Suppose -34*x**2 + 17768*x**3 - 47 + 2*x**4 + 124*x**2 - 8*x - 17732*x**3 - 73 = 0. What is x?
-15, -2, 1
Suppose -16*y - 4*y = -60. Factor -74*u**3 + 38*u**3 + 32*u**y + 20*u**4.
4*u**3*(5*u - 1)
Let j(k) be the second derivative of k**6/300 + 11*k**5/150 + k**4/6 + 39*k**2 + 21*k - 1. Let v(c) be the first derivative of j(c). Factor v(p).
2*p*(p + 1)*(p + 10)/5
Let z(c) be the first derivative of -c**5/330 - c**4/132 + 28*c**2 - 191. Let d(n) be the second derivative of z(n). Solve d(m) = 0.
-1, 0
Suppose -5*b = 10, 0 = -i - 19*b + 18*b + 10. Suppose 3*f = 2*s - 11, 2*s - 6*s + i = 4*f. Determine y so that -10 + 30*y - 65/2*y**2 + 15*y**3 - 5/2*y**s = 0.
1, 2
Suppose -3*a - 162*a = 420*a - 1755. Find m such that 0*m + 0 + 0*m**2 - 1/4*m**5 - 1/2*m**a + 3/4*m**4 = 0.
0, 1, 2
Let s(c) = -c**2 - 7*c + 12. Let t(v) = 7*v**2 + 43*v - 75. Suppose 16 = 2*u + 4*n, 5*u - 24 = 2*n + 4. Let h(g) = u*t(g) + 39*s(g). Factor h(d).
3*(d - 3)*(d - 2)
Suppose -1/4*y**2 - 70 + 61/4*y = 0. Calculate y.
5, 56
Let c(q) = q**2 + 2. Let r(w) = -2*w**2 + 21*w + 104. Let o(d) = -12*c(d) - 4*r(d). Factor o(k).
-4*(k + 10)*(k + 11)
Let d(c) be the first derivative of c**7/2940 - 23*c**6/1260 + 43*c**5/420 - c**4/4 + c**3 + 26*c + 3. Let o(b) be the third derivative of d(b). Factor o(n).
2*(n - 21)*(n - 1)**2/7
Let t = -6381222115/833 + 7660539. Let h = -312/49 + t. Solve -2/17 - 46/17*q**2 + 48/17*q**4 - h*q**5 + 14/17*q**3 + 18/17*q = 0.
-1, 1/4, 1
Let n(d) = d**3 - 72*d**2 + 1201*d - 226. Let b be n(46). Factor -1/6*q**2 + 1/2*q**b + 0*q**3 + 1/3*q**5 + 0*q + 0.
q**2*(q + 1)**2*(2*q - 1)/6
Let l(j) be the first derivative of j**4/4 - 10*j**3 - j**2 + 63*j + 124. Let w be l(30). Factor -x**2 - 5/3*x + 25/9 - 1