 11)/6
Suppose 82*r + 45 = -153*r + 45. What is v in 0*v**2 + 1/3*v**3 + 0 + 2/3*v**4 + r*v + 1/3*v**5 = 0?
-1, 0
Suppose 0 = 511*g - 3689 + 623. Let 0 + g*x**2 + 44/3*x - 2/3*x**3 = 0. Calculate x.
-2, 0, 11
Let v = 3811/16 - 3803/16. Factor -v*t**2 + 54*t - 1458.
-(t - 54)**2/2
Let g(n) = 15*n**4 - 275*n**3 + 1200*n**2 + 11835*n - 12810. Let y(a) = -8*a**4 + 137*a**3 - 597*a**2 - 5917*a + 6406. Let t(l) = -3*g(l) - 5*y(l). Factor t(j).
-5*(j - 16)**2*(j - 1)*(j + 5)
Let n(f) be the second derivative of 5/2*f**4 - 2*f - 43/3*f**3 - 6*f**2 + 45. Factor n(m).
2*(m - 3)*(15*m + 2)
Let s(b) = -b**3 - 2*b**2 + 2*b + 165. Let f be s(0). Let t = 496/3 - f. Suppose 11/6*j + 23/6*j**3 + 23/6*j**2 + 1/3 + 11/6*j**4 + t*j**5 = 0. What is j?
-2, -1, -1/2
Suppose -202 + 67 + 99 - 6*k**2 - 26*k**2 + 292*k = 0. Calculate k.
1/8, 9
Let b(w) be the second derivative of 1/30*w**5 - 2 + 0*w**2 + 4*w - 7/9*w**4 + 13/9*w**3. Find m such that b(m) = 0.
0, 1, 13
Let h be (-78)/(-108) - (0 - 25/((-450)/4)). What is y in 0 - 3/2*y**2 - h*y**3 - y = 0?
-2, -1, 0
Let f(d) be the second derivative of -d**4/18 - d**3/3 - 235*d. Factor f(z).
-2*z*(z + 3)/3
Suppose -27 + 7 = -5*o. Solve -81*b**3 - 228*b**2 + 6*b**4 + 117*b + 9*b**o + 303*b**2 - 54 = 0.
-1, 2/5, 3
Factor -489*u**2 - 477*u**2 + 3*u**3 - 96*u - 483*u**2 - 489*u**2 + 1926*u**2.
3*u*(u - 8)*(u + 4)
Suppose -2*j + 10 = a, -j - 62*a - 9 = -65*a. Factor -8 + 0*m + 12 - 4*m**2 + 10*m**3 - 4*m - 6*m**j.
4*(m - 1)**2*(m + 1)
Suppose -201 = 4*q + 35. Let n = 63 + q. Factor 1 - 3 - 8*a**2 + 4 + 4*a**n + 2.
4*(a - 1)**2*(a + 1)**2
Let s be 8/10 - (-65 + 64). Let i(l) be the second derivative of -1/30*l**4 - s*l**2 + 0 - 2/5*l**3 + 6*l. Factor i(b).
-2*(b + 3)**2/5
Let n(g) be the second derivative of -g**4/42 + 744*g**3/7 - 1245456*g**2/7 - 19*g - 68. Find p such that n(p) = 0.
1116
Suppose 0 = -38*v + 40*v - 44. Let p = 25 - v. Factor 2*d - 3*d + 2*d**4 - p*d + 9*d**2 - 15*d**2.
2*d*(d - 2)*(d + 1)**2
Let m(b) be the second derivative of 400*b**6/9 + 2030*b**5/3 + 335*b**4/2 + 601*b**3/36 + 5*b**2/6 - 3*b - 423. Find r, given that m(r) = 0.
-10, -1/20
Let d be (-1372)/(-245)*(-595)/2. Let x = d + 1668. Find q, given that 0*q - 5/4*q**4 + 15/4*q**3 + 0 - 5/2*q**x = 0.
0, 1, 2
Let o(d) be the first derivative of -13 - 10*d**2 - 1/15*d**4 - 4/3*d**3 + 14*d. Let j(t) be the first derivative of o(t). Factor j(f).
-4*(f + 5)**2/5
Let v(r) = 5*r**4 - 72*r**3 + 207*r**2 + 451*r - 579. Let g(y) = -44*y**4 + 650*y**3 - 1862*y**2 - 4058*y + 5210. Let l(u) = -6*g(u) - 52*v(u). Solve l(o) = 0.
-2, 1, 4, 36
Let d(o) = o + 2. Let v be d(-1). Let a be (-7)/(-5) + (12/20)/v. Factor 12 + 4 + 12*c - 4 + 3*c**a.
3*(c + 2)**2
Factor -200/7*o + 344 + 2/7*o**2.
2*(o - 86)*(o - 14)/7
Let n be 2 + 196/(-156) + 10/270*9. Factor 0*a + 8/13*a**2 + 0 - 4/13*a**4 + n*a**3.
-2*a**2*(a - 4)*(2*a + 1)/13
Let b(c) be the third derivative of c**8/168 - c**7/70 - c**6/10 + c**5/30 + 3*c**4/4 + 3*c**3/2 - 1052*c**2. Factor b(f).
(f - 3)*(f + 1)**3*(2*f - 3)
Let w(h) = 4*h**2 - 9*h - 9. Let j be (0 - 0 - 2) + 4. Let i(k) = 7 - 3 + j*k - 2 - k**2. Let z(u) = 9*i(u) + 2*w(u). Factor z(m).
-m**2
Let m(p) be the first derivative of p**7/168 - 19*p**3 - 122. Let r(d) be the third derivative of m(d). Solve r(n) = 0 for n.
0
Let t = -1728 - -1644. Let k be -8*(t/80)/21. Factor -24/5 + k*n**2 + 22/5*n.
2*(n - 1)*(n + 12)/5
Let t(q) be the first derivative of 2/3*q**3 - 3/2*q**2 - 1/6*q**6 + q**4 + 15 - 2*q + 0*q**5. Factor t(m).
-(m - 2)*(m - 1)*(m + 1)**3
Suppose -5*u = 5*p + 115, -5*u + 4*p = -7*u - 46. Let b(a) = 15*a + 349. Let m be b(u). Solve -84*n**m - 24*n**2 + 8/3*n + 218/3*n**3 + 98/3*n**5 + 0 = 0 for n.
0, 2/7, 1
Let m(a) be the first derivative of a**6/6 + 11*a**5/5 + 15*a**4/4 - 9*a**3 + 637. What is z in m(z) = 0?
-9, -3, 0, 1
Let j(r) be the first derivative of -36*r**2 + 1/3*r**3 + 1296*r - 143. Factor j(n).
(n - 36)**2
Let f(h) be the first derivative of 35*h**4/2 - 65*h**3/3 - 425*h**2/2 - 30*h - 7303. Factor f(a).
5*(a - 3)*(a + 2)*(14*a + 1)
Let b(j) = -j**3 + 10*j**2 + 16. Let f = 26 - 16. Let s be b(f). Factor 25*z**2 - s*z**2 - 3*z**3 + 3 - 10*z + z.
-3*(z - 1)**3
Let r = 1031571/5 + -206304. Factor r*v - 12/5*v**4 - 14/5 + 44/5*v**3 + 1/5*v**5 - 14*v**2.
(v - 7)*(v - 2)*(v - 1)**3/5
Solve 8272/7*f + 4/7*f**2 + 4276624/7 = 0.
-1034
Let z be (-64)/(-104) - (-168)/572. Factor -12/11*n + 2/11*n**2 + z.
2*(n - 5)*(n - 1)/11
Let f = -12194783/1008 + 12098. Let n(s) be the third derivative of 0*s**3 + 0*s + 0 - 1/315*s**7 + 2*s**2 + 0*s**4 - 1/360*s**6 + 0*s**5 - f*s**8. Factor n(u).
-u**3*(u + 1)**2/3
Let m be -2 + 5 + (0/(-12))/(-1). Suppose -16*u + 39 + 12 - 27*u - 11*u + m*u**2 = 0. What is u?
1, 17
Let a = 2226 + -1682. Suppose 99 = -511*v + a*v. Solve 27/2*m**v + 117/2*m + 27 + 3/2*m**4 + 87/2*m**2 = 0 for m.
-3, -2, -1
Let h(c) be the first derivative of -c**4/2 + 2*c**3/3 + 4. Let o(l) = -l**3. Let g = -1951 + 1947. Let t(m) = g*h(m) + 12*o(m). What is s in t(s) = 0?
-2, 0
Let o be (-3)/(-18)*10 - 6/18. Let w(a) = 3*a**2 - 66*a + 123. Let f be w(20). Suppose -4/3*k + 1/3*k**f - 1/3*k**2 + o = 0. Calculate k.
-2, 1, 2
Factor 705*h + 456 - 979*h - 2*h**2 + 100.
-2*(h - 2)*(h + 139)
Factor -7/8*r + 0 + 27/8*r**2 + 1/2*r**3.
r*(r + 7)*(4*r - 1)/8
Suppose -13*a + 11 = x - 12*a, 4*a = 4*x + 12. Factor 2/9*p**x + 16/3*p**2 + 0 - 22/9*p**3 + 8*p.
2*p*(p - 6)**2*(p + 1)/9
Suppose -z = 3*n - 63, 691*n + 4*z + 48 = 694*n. Let d(a) be the first derivative of 25 + n*a + 5/3*a**3 + 10*a**2. Factor d(p).
5*(p + 2)**2
Suppose 2548 = 29*y + 608*y. Factor 9/4*n - 1/8*n**2 - y.
-(n - 16)*(n - 2)/8
Let s be (-5 - -3) + ((-54)/(-1))/3. Suppose -s*v = -11*v - 35. Solve 3*w + 10*w**5 - v*w - 16*w**2 + 16*w**4 - 8*w + 8*w**3 - 6*w**5 = 0 for w.
-3, -1, 0, 1
Let 0*s + 0 + 7*s**5 - 6/7*s**2 + 37/7*s**3 + 92/7*s**4 = 0. What is s?
-1, 0, 6/49
Let n(k) be the second derivative of -46*k**6/15 - 104*k**5/5 - 140*k**4/3 - 32*k**3 + 5787*k - 1. Find z such that n(z) = 0.
-2, -12/23, 0
Let q(u) be the third derivative of -37/4*u**4 - 3*u**2 - 303/20*u**6 - 877/140*u**7 - 3*u**3 + 0 - 2*u - 651/40*u**5 - 45/56*u**8. Solve q(s) = 0 for s.
-3, -1, -2/5, -1/4, -2/9
Suppose 301 + 254 = 5*k. Suppose 80*j - 328*j = -496. Factor -k*i + 105*i + i**2 + 2*i**2 + 0*i**j.
3*i*(i - 2)
Let u be (12/10)/(-30 + 30 - (-14)/5). Find s such that 3*s - 18/7 - u*s**2 = 0.
1, 6
Suppose 23*j - 47 + 1 = 0. Let b(f) be the first derivative of 7*f**5 + 0*f**j + 0*f + 19 + 10/3*f**3 + 45/4*f**4. Factor b(t).
5*t**2*(t + 1)*(7*t + 2)
Let v(j) be the third derivative of 2/15*j**6 + 0*j**3 + 0*j**4 + 0 + 3/10*j**5 + 0*j - 1/105*j**7 - 137*j**2. Factor v(l).
-2*l**2*(l - 9)*(l + 1)
Let i(t) = -10*t**4 + 5*t**3 - 38*t**2 + 51*t + 69. Let w(a) = 5*a**4 - 5*a**3 + 18*a**2 - 26*a - 34. Let u(n) = 6*i(n) + 11*w(n). Factor u(v).
-5*(v - 1)*(v + 2)**3
Let s(c) be the first derivative of 2*c**5/5 + 463*c**4/4 - 1869*c**3/8 - 3497*c**2/16 - 233*c/4 + 711. Let s(v) = 0. Calculate v.
-233, -1/4, 2
Let a(x) be the second derivative of -1/6*x**3 - 66*x + 1/2*x**2 - 1/48*x**4 + 0 + 1/80*x**5. Factor a(o).
(o - 2)*(o - 1)*(o + 2)/4
Let j = -234/193 - -2410/1351. What is i in -j*i**3 - 2/7*i**4 - 72/7 + 22/7*i**2 + 24/7*i = 0?
-3, 2
Let d = 750 + -693. Suppose d*s = 84*s - 54. Factor -6/5*u**4 + 0*u - s*u**3 + 0 + 4/5*u**2.
-2*u**2*(u + 2)*(3*u - 1)/5
Let g be (((-1)/(-4))/((-87)/348) - 13) + 15. Factor l**2 + 1/6*l**3 + g + 11/6*l.
(l + 1)*(l + 2)*(l + 3)/6
Let g be (-2 + 19/3)*(186 + -183). Suppose -16*s - g*s + 58 = 0. Suppose -21/2*x**5 + 57/2*x**s - 57/2*x**4 + 0 + 39/2*x**3 - 9*x = 0. What is x?
-3, -1, 0, 2/7, 1
Suppose 0 = -16*f + 13*f + 4*o + 62, 5*f = -o + 65. Factor 0*p**4 - 5*p**3 + 4*p**5 - 7*p**4 - 8*p**2 + 16 - f*p**3 - p**4 - 13*p**3 + 28*p.
4*(p - 4)*(p - 1)*(p + 1)**3
Let b(q) = 3*q**2 + 9*q + 5. Let n be b(-3). Suppose -45 = -4*u - 5*i - 0*i, 2*i - n = u. Find k, given that u*k + 332 - 119 + 4*k**2 + 363 + 91*k = 0.
-12
Let y(c) = 55*c**2 + 11*c + 10. Let t(z) = 28*z**2 + 6*z + 4. Let g be ((-35)/21)/(4/((-60)/5)). Let k(d) = g*t(d) - 2*y(d). Suppose k(f) = 0. What is f?
-4/15, 0
Suppose -564*n + 9 = 4*r - 563*n, 2*r = -n + 5. Let o(w) be the first derivative of 32 - 4/11*w - 7/11*w**r - 4/33*w*