 d be 9*(-49)/((-29988)/51). Factor 21*z - 6 + 75/4*z**3 - 57/2*z**2 - 6*z**4 + d*z**5.
3*(z - 2)**3*(z - 1)**2/4
Let a be (130/117)/((5170/(-176) + 29)*2/(-9)). Factor -2/3*v**2 - 14*v - a.
-2*(v + 1)*(v + 20)/3
Let b(h) = h**3 + 11*h**2 + 18*h + 4. Suppose -4*q - 44 + 6 = -2*l, -q = 5*l + 4. Let y be b(q). Factor -3*o**3 - 11*o**3 - 5*o**y - 5*o**2 + 4*o**3.
-5*o**2*(o + 1)**2
Let z = -139685 + 139687. Determine x so that -13/6*x**3 + 5/6*x**4 + 13/6*x - 11/6*x**z + 1 = 0.
-1, -2/5, 1, 3
Let f(q) = -q**3 - 10*q**2 + 42*q - 2426. Let s be f(-19). Find p such that 45/2*p + 94*p**2 - s - 21*p**4 + 23*p**3 + 5/2*p**5 = 0.
-1, 2/5, 5
Suppose 20 = -s + 3*s - 4*c, 26 = 3*s - 5*c. Find b, given that 147 - 3*b**3 + 5*b**2 - 165*b + 40*b**s - 24*b = 0.
1, 7
Let r(j) = -15*j - 303. Let i be r(24). Let n = i + 5311/8. Factor n*t**4 + 3/8*t**3 + 0 + 0*t + 0*t**2.
t**3*(7*t + 3)/8
Let o be (-4)/((-1)/8*-20)*(-188)/32 - 8. Factor 2*g**3 - o + 22/5*g - 1/5*g**4 - 24/5*g**2.
-(g - 7)*(g - 1)**3/5
Let m(i) be the first derivative of -i**5/70 - i**4/7 - i**3/7 + 10*i**2/7 + 11*i - 19. Let p(c) be the first derivative of m(c). Factor p(z).
-2*(z - 1)*(z + 2)*(z + 5)/7
Let a be 5 + (-3)/((-5)/(-5)) + 0. Let h(g) = 12. Let w(r) = -2*r**2 - 10. Let c(q) = a*w(q) + 3*h(q). Let c(k) = 0. Calculate k.
-2, 2
Let r(z) be the first derivative of 3/4*z**5 + 0*z**2 + 5/6*z**3 + 33*z - 5/4*z**4 - 1/6*z**6 - 12. Let h(t) be the first derivative of r(t). Factor h(n).
-5*n*(n - 1)**3
Let g(i) be the second derivative of -i**4/30 + 143*i**3/15 + 58*i**2 + 301*i. Factor g(q).
-2*(q - 145)*(q + 2)/5
Let n(v) be the first derivative of 450*v**6 + 945*v**5 + 510*v**4 + 376*v**3/3 + 16*v**2 + 9*v + 29. Let h(z) be the first derivative of n(z). Factor h(d).
4*(d + 1)*(15*d + 2)**3
Suppose 0 = -5*f + 4*j - 1, -f - 3*j + 0*j = -15. Factor 14*h**2 + h**f - 2*h**4 - 10*h**2 - h**3 - 2*h**4.
-4*h**2*(h - 1)*(h + 1)
Let v(x) be the second derivative of -x**4/4 + 5*x**3/3 - 33*x**2/2 + 25*x. Let a(c) = 10*c**2 - 28*c + 99. Let w(k) = 6*a(k) + 21*v(k). Solve w(t) = 0 for t.
3, 11
Let c(o) be the second derivative of -o**5/60 + 7*o**4/36 + 17*o**3/18 + 3*o**2/2 + 3*o + 14. Suppose c(f) = 0. Calculate f.
-1, 9
Factor -3/7*w**2 + 480/7 - 36/7*w.
-3*(w - 8)*(w + 20)/7
Let j(m) be the first derivative of 49*m**6/9 + 266*m**5/3 - 53*m**4 - 680*m**3/9 - 56*m**2/3 + 277. Solve j(l) = 0.
-14, -2/7, 0, 1
Factor 35*r**4 - 206*r**3 + 132*r**3 - 37 + 82*r - 9*r + r**5 + 2*r**2.
(r - 1)**3*(r + 1)*(r + 37)
Let m(i) be the third derivative of 2*i**7/105 - 7*i**6/30 - 4*i**5/15 + 26*i**4/3 + 32*i**3 - 6488*i**2. Suppose m(n) = 0. What is n?
-2, -1, 4, 6
What is t in -88/7 - 38/7*t**2 + 128/7*t - 2/7*t**3 = 0?
-22, 1, 2
Let y(o) be the third derivative of o**8/224 - 89*o**7/28 + 9767*o**6/16 + 29837*o**5/8 + 9380*o**4 + 12544*o**3 - 7*o**2 + 17*o. Factor y(a).
3*(a - 224)**2*(a + 1)**3/2
Let k(n) be the first derivative of n**5/25 - 29*n**4/20 + 18*n**3/5 - 518. Factor k(a).
a**2*(a - 27)*(a - 2)/5
Let n(s) be the first derivative of -s**6/80 + 17*s**5/40 - 7*s**4/2 + 13*s**3 + 131*s**2/2 - 66. Let o(p) be the second derivative of n(p). Factor o(x).
-3*(x - 13)*(x - 2)**2/2
Let i = 14107 - 9718. Factor 24*x + 110*x + 130*x + i + 1843 - 424 + 3*x**2.
3*(x + 44)**2
Let 80/3*n**2 + 12*n**3 - 2/3*n**5 + 20 - 146/3*n - 28/3*n**4 = 0. Calculate n.
-15, -2, 1
Solve 44/5*z**2 + 2/5*z**3 + 0*z + 0 = 0.
-22, 0
Factor -66248*k**2 - 31004 + 15354 - 6552*k + 15488.
-2*(182*k + 9)**2
Let h(a) = -11*a - 77. Let g = -536 - -529. Let t be h(g). Find n, given that 0*n - 1/5*n**5 - n**3 + 4/5*n**4 + 2/5*n**2 + t = 0.
0, 1, 2
Let -3/7*a**3 + 90/7*a**2 - 90 + 543/7*a = 0. Calculate a.
-6, 1, 35
Let o(c) be the third derivative of -7*c**6/12 + 5*c**5/12 + 55*c**4/12 + 5*c**3/2 + 515*c**2. Factor o(x).
-5*(x + 1)*(2*x - 3)*(7*x + 1)
Let d(w) = -3*w**3 + 36*w**2 + 4*w - 46. Let b be d(12). Factor 1/5*j**b + 5*j + 0.
j*(j + 25)/5
Let n(y) be the third derivative of 0*y + 5/36*y**4 - 1/360*y**5 - 3*y**2 - 6 + 0*y**3. Factor n(b).
-b*(b - 20)/6
Let z(x) be the third derivative of x**5/12 - 365*x**4/12 - 245*x**3/2 - 2580*x**2. Factor z(i).
5*(i - 147)*(i + 1)
Let k = 7214 - 7190. Let w(y) be the first derivative of 1/21*y**3 - 3/14*y**2 - 10/7*y - k. Determine t so that w(t) = 0.
-2, 5
Suppose -1032/7*b - 120/7*b**3 + 634/7*b**2 + 520/7 - 2/7*b**4 = 0. What is b?
-65, 1, 2
Find f, given that -111 - 22 + 0*f**3 - 81*f**2 - 17 - f**4 - 15*f**3 - 185*f = 0.
-5, -3, -2
Let g = -14/1655 - -3436/14895. Solve g*d**2 + 10/9*d + 4/3 = 0.
-3, -2
Let y be 1 - (-2)/(1/1). Let i = 29/3056 - -9903/3056. Factor -11/2*s**2 + i*s - 1/2 + 2*s**y.
(s - 2)*(2*s - 1)*(4*s - 1)/4
Solve 5753 - 623*p**2 + 1755*p + 3*p**3 - 6629 - 259*p**2 = 0.
1, 292
Let n be (-3 - (-28)/4)*10/15. Let i(y) be the second derivative of 0 - n*y**3 - 13*y + 1/3*y**4 - 10*y**2. Determine r, given that i(r) = 0.
-1, 5
Let d(n) be the third derivative of -n**8/120960 - n**7/864 + n**6/120 - 23*n**5/20 - 2*n**2 + 17*n. Let h(u) be the third derivative of d(u). Solve h(x) = 0.
-36, 1
Let s be (-57)/15 + 23/(-115). Let z be (35/21)/(3*s/(-36)). Factor 0*o**2 + 4/9*o**4 + 0 + 2/9*o**3 + 2/9*o**z + 0*o.
2*o**3*(o + 1)**2/9
Let 699 + 649*g - 264*g - g**3 + 42*g**2 + 51 = 0. Calculate g.
-5, -3, 50
Let k = 20 - -394. Let m be k/(-69)*(-2)/6. Factor 1/2*f**3 + 3/2*f**m + 1/2 + 3/2*f.
(f + 1)**3/2
Suppose 4*f + 32 = 0, 5*p - f + 319 = 337. Factor -532*x - 164/3*x**p - 4/3*x**3 + 588.
-4*(x - 1)*(x + 21)**2/3
Suppose -5*l = -386 - 189. Factor -9*i**2 + 59 + 31*i - l*i + 1.
-3*(i + 10)*(3*i - 2)
Suppose -4*u**4 - 6*u**3 - 25*u + 2*u**2 + 3*u**2 + 23*u + 5*u**4 + 14*u = 0. Calculate u.
-1, 0, 3, 4
Let c = -1106 + 1103. Let d(p) = -46*p - 138. Let v be d(c). Suppose 8/7*s + 7*s**5 + 18/7*s**3 - 17*s**4 + 44/7*s**2 + v = 0. What is s?
-2/7, 0, 1, 2
Let n(a) be the first derivative of a**6/1800 - 17*a**5/600 + 2*a**4/15 + 190*a**3/3 + 6. Let c(b) be the third derivative of n(b). Factor c(u).
(u - 16)*(u - 1)/5
Let n(h) be the second derivative of -h**6/3 + 11*h**5/4 + 5*h**4/4 - 110*h**3/3 + 50*h**2 + 2103*h. Let n(p) = 0. What is p?
-2, 1/2, 2, 5
Let a(k) be the third derivative of -1/6*k**6 - 2/3*k**4 + 0 + 69*k**2 + 0*k - 8/3*k**3 + 13/15*k**5. Let a(p) = 0. Calculate p.
-2/5, 1, 2
Let q(a) be the second derivative of -a**4/24 + 1319*a**3/3 - 1739761*a**2 - 5919*a. Suppose q(k) = 0. Calculate k.
2638
Suppose -n - 352 = 5*c - 312, 3*c + 24 = n. Factor -5*g**2 + 15/4*g + 5/2*g**3 - 1 + n*g**4 - 1/4*g**5.
-(g - 1)**4*(g + 4)/4
Let r(v) be the third derivative of v**5/45 + 37*v**4/36 - 20*v**3/3 + v**2 + 2309. Suppose r(i) = 0. Calculate i.
-20, 3/2
Let m(w) = -20*w**2 + 96*w - 124. Let p(u) = 4*u**2 - 19*u + 25. Let o(s) = 2*s - 21. Let a be o(13). Let h(l) = a*m(l) + 24*p(l). Determine k so that h(k) = 0.
1, 5
Let k = 136550 - 136548. Suppose 1/2*x**4 + k + 1/2*x**5 + 2*x - 5/2*x**2 - 5/2*x**3 = 0. What is x?
-2, -1, 1, 2
Suppose 4108729/4 + 4104675/4*i + 1/4*i**3 - 4053/4*i**2 = 0. What is i?
-1, 2027
Let k(m) = m**3 - 3*m**2 + m + 1. Let i(n) = 3*n**3 - 8*n**2 - 17*n + 22. Let z(b) = i(b) - 2*k(b). Factor z(p).
(p - 5)*(p - 1)*(p + 4)
Let h = 963284/3 - 321094. Factor -3920/3*a**2 - 9604/3 - 3430*a - 700/3*a**3 - h*a**5 - 20*a**4.
-2*(a + 2)*(a + 7)**4/3
Find h such that -810 + 1635/2*h**3 + 1195/2*h**2 + 425/2*h**4 - 820*h + 5/2*h**5 = 0.
-81, -2, -1, 1
Let v = -8387 - -8387. Let j(c) be the third derivative of 0 + v*c + 3/4*c**4 + 11*c**2 - 1/20*c**5 + 7/2*c**3. Factor j(m).
-3*(m - 7)*(m + 1)
Let c(q) be the second derivative of -1/90*q**6 - 11/36*q**4 - 3/20*q**5 - 2/9*q**3 - 77*q + 0 + 1/126*q**7 + 0*q**2. Factor c(o).
o*(o - 4)*(o + 1)**3/3
Determine a, given that -5*a + 47*a**3 - 19*a**3 + 3*a - 6*a - 8*a + 108*a**2 = 0.
-4, 0, 1/7
Let m(q) = -5*q**2 - 62*q + 949. Let z(p) = -p**3 + 12*p**2 - 31*p - 14. Let j be z(8). Let i(f) = -f**2 - 2. Let n(l) = j*i(l) + m(l). Factor n(o).
(o - 31)**2
Let v = 9207 + -9202. Let x(z) be the second derivative of 2*z**2 + 0 - z**4 - 4/15*z**6 - 2/3*z**3 - 9*z + z**v. Factor x(b).
-4*(b - 1)**3*(2*b + 1)
Let x = -187234 - -187236. Determine d, given that -2/13*d**3 - 6/13*d - 20/13 + 12/13*d**x = 0.
-1, 2, 5
Let -3/2*k + 2 - 1/2*k**2 = 0. Calculat