(k - 20)*(k + 5)/5
Let r(w) = w**5 + 2*w**4 - w**2 - w - 1. Let g(b) = 5*b**5 + 19*b**4 - 42*b**3 + 4*b**2 + 37*b - 23. Let d(t) = g(t) - 2*r(t). Factor d(x).
3*(x - 1)**3*(x + 1)*(x + 7)
Let t(z) be the third derivative of 0*z**4 + 0 - z - 1/240*z**6 + 3/40*z**5 + 12*z**2 + 0*z**3. Factor t(r).
-r**2*(r - 9)/2
Let u(j) be the first derivative of -122 + 116/27*j**3 + 5/18*j**4 - 44/9*j + 31/9*j**2. Determine q, given that u(q) = 0.
-11, -1, 2/5
Suppose 1/8*k**3 - 75 + 61/8*k**2 - 1/8*k**4 + 35/8*k = 0. Calculate k.
-5, 3, 8
Suppose -31 = -20*u + 9. Let b(k) = -k**2 + 27*k + 61. Let o be b(-2). Solve 2/7*x**o + 2/7*x - 4/7*x**u + 0 = 0 for x.
0, 1
Suppose 92338*r - 87474*r - 108*r**2 + 37544 + 286*r**2 + 2*r**3 = 0. Calculate r.
-38, -13
Let i(s) be the second derivative of -s**5/20 - 3*s**4/8 + 5*s**3 + 177*s**2/2 - 19*s. Let z(w) be the first derivative of i(w). Solve z(q) = 0.
-5, 2
Solve 72*h - 15*h + 96*h**2 - 99*h**2 - 400 + 190 = 0.
5, 14
Let m(f) be the first derivative of -3*f**6/4 + 111*f**5/40 - 117*f**4/32 + 15*f**3/8 - 3*f**2/16 - 1378. Suppose m(i) = 0. Calculate i.
0, 1/12, 1
Suppose b - 223 = 3*l, 23*l - 22*l - 2*b + 66 = 0. Let m be (-57)/l*(-8)/(4/(-2)). Factor 20/3 - 14/3*t**m + 16*t**2 - 18*t.
-2*(t - 1)**2*(7*t - 10)/3
Let c(u) be the second derivative of 11*u**5/4 + 175*u**4/12 + 5*u**3 + 161*u + 3. Let c(g) = 0. What is g?
-3, -2/11, 0
Let d(l) be the first derivative of 1/7*l**2 + 0*l**4 - 1/140*l**5 + 15 - 3*l + 1/14*l**3. Let h(t) be the first derivative of d(t). Factor h(k).
-(k - 2)*(k + 1)**2/7
Let w(n) = 2*n**2 + 27*n + 5. Let m be w(-13). Let o = m + 23. Find z, given that -2*z**2 + 38*z**5 - o*z**4 + 15*z**3 + 37*z**5 - 3*z**2 - 70*z**5 = 0.
0, 1
Let 343/3 - 7/6*u**2 + 2399/6*u = 0. Calculate u.
-2/7, 343
Let n be (-3090)/(-927)*(4 - (-51)/(-15)). Factor -20/7*p + 2/7*p**n - 48/7.
2*(p - 12)*(p + 2)/7
Suppose -25*j - 466 + 541 = 0. Let a(u) be the first derivative of -24*u - 4*u**2 - 2/9*u**j + 5. Suppose a(o) = 0. Calculate o.
-6
Let a be (-18)/(-270)*(0 - 3) - 1034/(-220). Let h(i) be the first derivative of 6*i - 4 - a*i**2 + 0*i**3 + 3/4*i**4. Factor h(g).
3*(g - 1)**2*(g + 2)
Let l = -1181799/8 + 147726. What is n in l*n**3 - 3/8*n**5 + 0 + 3*n**2 + 3/2*n - 3/4*n**4 = 0?
-2, -1, 0, 2
Suppose 3180*j = -3170*j + 6343*j. Solve 0 + 0*h + 1/3*h**4 + j*h**2 - h**3 = 0.
0, 3
Let f(y) = y**2 - 5*y - 12. Let a be f(-2). Suppose -2*h - 13 = -a*g + 5, 6 = -g - 2*h. Factor g + 4*r**2 + 23 + 16*r - 11.
4*(r + 2)**2
Let u = -47/1022 + 2116703/3066. Let k = -690 + u. Determine p, given that -k*p**2 + 4/3*p + 5/3 = 0.
-1, 5
Let d(u) be the second derivative of u**4/48 - 5*u**3 + 450*u**2 + u + 1. Determine v so that d(v) = 0.
60
Let d(k) be the second derivative of -k**5/180 - k**4/9 - 59*k**2/2 - 5*k + 3. Let c(t) be the first derivative of d(t). Factor c(a).
-a*(a + 8)/3
Let r(c) be the first derivative of 2*c**6/9 - 1132*c**5/15 + 20719*c**4/3 - 395332*c**3/9 + 311360*c**2/3 - 309136*c/3 + 1359. Solve r(w) = 0 for w.
1, 2, 139
Let a(v) = -v**2 - 30*v + 44. Let n(i) = -i**2 - 61*i + 97. Let o(q) = 7*a(q) - 4*n(q). Suppose o(f) = 0. Calculate f.
10/3, 8
Let c(s) be the third derivative of -s**8/21 + 31*s**7/15 - 457*s**6/20 - 140*s**5/3 + 49*s**4/3 - 588*s**2 + s. Find p, given that c(p) = 0.
-1, 0, 1/8, 14
Factor 0 - 185*g + 1/2*g**3 - 369/2*g**2.
g*(g - 370)*(g + 1)/2
Let s be -1 + 0 + 9 - (-103 + 109). Let z(o) be the first derivative of -8/5*o**3 - 2/15*o + 4/5*o**s + 22. Factor z(x).
-2*(6*x - 1)**2/15
Let s be 22/(-10)*-29 - (-16)/(-20). Let t = s + -59. Factor 2*m**2 + m + 0*m**3 + 0*m**2 - 1 + m**5 - t*m**3 + 2*m**3 - m**4.
(m - 1)**3*(m + 1)**2
Let d(a) be the second derivative of 3*a**5/40 - 397*a**4/8 - 797*a**3/4 - 1197*a**2/4 + 2*a + 1669. What is j in d(j) = 0?
-1, 399
Let w(y) be the second derivative of 1/90*y**6 - 1/6*y**3 + 0*y**2 - 1/36*y**4 + 2 + 1/20*y**5 + 48*y. Solve w(c) = 0.
-3, -1, 0, 1
Let q(a) = -a**3 + 63*a**2 + 113*a - 253. Let i be q(-3). Factor 280/19*g + 2/19*g**i + 9800/19.
2*(g + 70)**2/19
Let l(z) be the second derivative of -z**7/2100 - z**6/300 + 18*z**4 - 212*z. Let k(o) be the third derivative of l(o). Factor k(i).
-6*i*(i + 2)/5
Let y(u) = -u**3 - 4*u**2 - u + 2. Let k(q) = 8*q**3 + 32*q**2 + 16*q - 8. Let a(x) = k(x) + 9*y(x). Factor a(j).
-(j - 2)*(j + 1)*(j + 5)
Suppose -3*h + 7 = 2*k, 5*k = -0*k + h + 9. Suppose -35*a + 615 + 3*a**k - 71*a + 34*a - 183 = 0. Calculate a.
12
Let w(t) be the first derivative of t**5/30 - t**4/3 + t**3 + 6*t**2 - 2*t - 38. Let n(c) be the second derivative of w(c). Suppose n(o) = 0. What is o?
1, 3
Let j(f) be the second derivative of f**5/60 + 6*f**4 + 648*f**3 + 2*f + 211. Let j(a) = 0. Calculate a.
-108, 0
Let q(d) be the third derivative of d**5/300 - 11*d**4/120 - 2*d**3 - 25*d**2 + 7. Factor q(o).
(o - 15)*(o + 4)/5
Let f = 7452 - 7444. Let q(x) be the second derivative of 0 + 0*x**2 + 0*x**3 - 1/28*x**4 + f*x. Factor q(p).
-3*p**2/7
Suppose 4*c - 84*g + 81*g = 23, 0 = c + 2*g + 8. Let b(a) be the first derivative of 2/3*a**6 - 4/3*a**3 + 4 + 0*a**c + 0*a + 4/5*a**5 - a**4. Factor b(o).
4*o**2*(o - 1)*(o + 1)**2
Let m(g) be the second derivative of 17/42*g**4 - g**3 - 1/105*g**6 + 0*g**2 - 55 + 1/14*g**5 + g. Let m(w) = 0. Calculate w.
-3, 0, 1, 7
Let c(w) be the second derivative of 0 - 81*w + 0*w**2 + 51/40*w**5 - 2*w**4 + w**3 - 1/4*w**6. Suppose c(x) = 0. What is x?
0, 2/5, 1, 2
Let l = -74 - -115. Suppose 0 = -4*n + l - 33. Let 3*i**2 + 4*i**2 - 5*i - 4 - n*i**2 - 6*i**2 = 0. What is i?
-4, -1
Let f = -47478 + 427306/9. Factor -f + 10/9*h**3 + 14/9*h - 2/9*h**4 - 2*h**2.
-2*(h - 2)*(h - 1)**3/9
Factor 2/3*y - 2/3*y**3 - 2*y**2 + 2.
-2*(y - 1)*(y + 1)*(y + 3)/3
Solve 1/2*z**5 + 11/2*z**4 - 355/2*z**2 + 3/2*z**3 - 700*z - 750 = 0.
-5, -2, 6
Let y(o) be the second derivative of 7*o**6/90 + 8*o**5/15 + 2*o**4/3 - 52*o**3/3 + o - 54. Let u(a) be the second derivative of y(a). Let u(j) = 0. What is j?
-2, -2/7
Let j be 42/5*2/(2/(-5)). Let b be 19/21 - (312/j + 7). Determine t so that 0 - 8/3*t + 4/3*t**2 - b*t**5 - 4/3*t**4 + 4*t**3 = 0.
-2, -1, 0, 1
Let q(p) = -1940*p - 85360. Let u be q(-44). Factor 4/3*z**4 + 140/3*z**2 - 196/3*z + u + 52/3*z**3.
4*z*(z - 1)*(z + 7)**2/3
Factor 97/11*s**2 - 2401/11 - 2303/11*s - 1/11*s**3.
-(s - 49)**2*(s + 1)/11
Let t = 1275527/9 - 141721. Factor -1/9*r**5 - 8/9 - 28/9*r - t*r**2 - 8/9*r**4 - 25/9*r**3.
-(r + 1)**2*(r + 2)**3/9
Suppose -450/11 - 2/11*s**2 - 452/11*s = 0. What is s?
-225, -1
Suppose -8*b + 10*b - 4 = 0. Suppose 44*p - 62*p**2 + 8 + 59*p**b + 39*p**2 = 0. Calculate p.
-1, -2/9
Suppose 4*r + g - 347 + 31 = 0, 3*r - 256 = 4*g. Suppose -t - 4*t = -r. Solve -t*o**2 - 8*o**5 - 13*o**4 + 3*o**4 + 56*o**2 + 8*o + 30*o**3 = 0 for o.
-2, -1, -1/4, 0, 2
Factor 6*u**3 + 0*u - 18/7*u**4 - 22/7*u**2 - 2/7*u**5 + 0.
-2*u**2*(u - 1)**2*(u + 11)/7
Let p(u) be the third derivative of -u**5/15 + 13*u**4/3 + 58*u**3 - 693*u**2. What is a in p(a) = 0?
-3, 29
Let f(q) be the first derivative of -q**7/6720 + q**6/960 + q**5/240 + 112*q**3/3 - 73. Let v(u) be the third derivative of f(u). Factor v(b).
-b*(b - 4)*(b + 1)/8
Let n(l) be the first derivative of -l**6/1800 + 29*l**5/600 + 31*l**4/60 + l**3 - 9*l - 131. Let b(x) be the third derivative of n(x). Factor b(q).
-(q - 31)*(q + 2)/5
Let j(t) = -30*t**2 + 324*t + 40695. Let d(r) = 3*r**2 - 32*r - 4069. Let n(u) = 21*d(u) + 2*j(u). Let n(z) = 0. Calculate z.
-33, 41
Let o(d) be the second derivative of -1/10*d**5 + 8*d**2 + 9 - 4/3*d**4 + 2*d + 1/3*d**3. Solve o(p) = 0.
-8, -1, 1
Suppose 2*f - 37 = -20 - 11. Factor 12/5*j**f + 0*j**2 - 4/5*j + 0 + 8/5*j**4.
4*j*(j + 1)**2*(2*j - 1)/5
Let s be (-10)/(-6)*(-41)/(1845/(-54)). Let d(r) be the first derivative of 0*r - r**3 - 15/2*r**s + 25. Factor d(i).
-3*i*(i + 5)
Factor 905 - 2565 - 746*v**2 - 3008*v + 2*v**3 - 1356.
2*(v - 377)*(v + 2)**2
Suppose 376*h - 3489 - 161 = -354*h. Factor -7/2*d - 1/2*d**2 - h.
-(d + 2)*(d + 5)/2
Let p(s) be the first derivative of s**3 + 85*s**2 + 7567*s - 11. Let o(n) = 10*n**2 + 508*n + 22700. Let i(g) = 2*o(g) - 7*p(g). Suppose i(l) = 0. Calculate l.
-87
Let y be (2/(-114))/(-6*(-1)/(-54)). Let n(c) be the first derivative of 17 - 2/57*c**3 - y*c**2 + 0*c. Factor n(q).
-2*q*(