v(j) be the second derivative of 1/8*j**3 + 0 + 1/80*j**6 - 1/32*j**4 - 15*j + 0*j**2 - 3/80*j**5. Factor v(t).
3*t*(t - 2)*(t - 1)*(t + 1)/8
Let y = -144323 + 144326. Find h, given that -2/9*h**4 - 8/3*h**2 - 4/3*h**y - 2/3 - 20/9*h = 0.
-3, -1
Let f(k) = -939*k. Let t be f(0). Let b(v) be the first derivative of -2/9*v**5 + t*v**2 + 1 + 0*v + 1/3*v**4 - 2/27*v**3. Let b(l) = 0. Calculate l.
0, 1/5, 1
Let h = 118114 - 118111. Suppose -20/3 + 5/3*s**5 - 12*s + 31/3*s**h + 53/3*s**2 - 11*s**4 = 0. What is s?
-1, -2/5, 1, 2, 5
Suppose -133*o + 1164 = 93*o + 260. Let p(q) be the second derivative of -15*q + 0*q**2 + 1/100*q**5 - 1/60*q**o + 0*q**3 + 0. Factor p(m).
m**2*(m - 1)/5
What is d in 760/11*d + 304/11*d**2 - 2*d**3 + 128/11 = 0?
-2, -2/11, 16
Let z(t) = -2*t**3 + 14 - 12473*t - 9*t**2 + 12472*t - 5. Let n(g) = -2*g**3 - 8*g**2 + 8. Let q(w) = -3*n(w) + 2*z(w). Factor q(x).
2*(x - 1)*(x + 1)*(x + 3)
Determine a so that 9/7*a**3 + 0 - 9/7*a - 3/7*a**4 + 3/7*a**2 = 0.
-1, 0, 1, 3
Factor 2652/5*n + 879138/5 + 2/5*n**2.
2*(n + 663)**2/5
Let p = 630 + 116. Let o = -2983/4 + p. Factor o*i**2 - 1/4*i + 0 + 1/4*i**3 - 1/4*i**4.
-i*(i - 1)**2*(i + 1)/4
Let h(v) be the second derivative of -v**7/540 - 2*v**6/135 - v**5/45 + v**4/6 - 7*v**3/3 - 7*v + 1. Let d(f) be the third derivative of h(f). Factor d(q).
-2*(q + 2)*(7*q + 2)/3
Let k(p) = -88*p**2 + 1031*p + 192. Let l(b) = -22*b**2 + 48 + 135*b + 43*b + 80*b. Let r(j) = -4*k(j) + 18*l(j). Factor r(g).
-4*(g - 12)*(11*g + 2)
Let y(g) be the third derivative of -g**5/150 + 81*g**4/20 - 48*g**3 - 1020*g**2. Find b such that y(b) = 0.
3, 240
Let t(z) be the second derivative of -z**6/6 + 11*z**5/4 - 65*z**4/4 + 245*z**3/6 - 50*z**2 + 120*z + 19. Factor t(g).
-5*(g - 5)*(g - 4)*(g - 1)**2
Suppose -368/17*w - 2/17*w**2 - 366/17 = 0. What is w?
-183, -1
Suppose -6359*o + 1353 = -5908*o. Find k such that 0*k + 0 - 8/7*k**2 - 4/7*k**5 - 16/7*k**4 - 20/7*k**o = 0.
-2, -1, 0
Factor 1/3*g**3 + 283024*g - 150568768/3 - 532*g**2.
(g - 532)**3/3
Let c be 7/7 + -6 - (2 + 183/(-15)). Factor 12/5 + 4/5*d**2 + c*d.
2*(d + 6)*(2*d + 1)/5
Let u(o) be the second derivative of 2/45*o**6 - 1/10*o**5 + 1/3*o**3 - 2/9*o**4 + 2/3*o**2 + 0 + 21*o. Determine k so that u(k) = 0.
-1, -1/2, 1, 2
Let r(o) be the third derivative of -o**6/900 + 2359*o**5/150 - 5564881*o**4/60 + 13127554279*o**3/45 + 13449*o**2. Factor r(l).
-2*(l - 2359)**3/15
Let z = 570 + 367. Let v be (z/45 - 1) + 14/(-63). Factor -v - 2/5*o**2 - 28/5*o.
-2*(o + 7)**2/5
Suppose 22*d - 28 = 8*d. What is o in 59*o**3 + d*o**5 - 32 + 33*o**3 - 4*o**3 - 22*o**4 + 112*o - 146*o**2 - 2*o**3 = 0?
1, 4
Let l(p) be the second derivative of p**5/80 - 17*p**4/48 + 71*p**3/24 - 55*p**2/8 - 7933*p. Factor l(j).
(j - 11)*(j - 5)*(j - 1)/4
Let b = -40 + 70. Let 22*h**2 + b*h + 20 - 64*h**2 - 5*h + 22*h**2 - 25*h**3 = 0. What is h?
-1, -4/5, 1
Let q be ((-4)/(-8))/((-6)/96). Let g be (2445/280 - 6) + (-1)/q. Factor -2/7*h**2 - g + 2*h.
-2*(h - 5)*(h - 2)/7
Let b(p) be the first derivative of p**6/390 - p**5/390 - p**4/12 - 2*p**3/13 + 3*p**2 + 4*p - 54. Let t(s) be the second derivative of b(s). Factor t(n).
2*(n - 3)*(n + 2)*(2*n + 1)/13
Let l(c) = -7*c**3 - 6*c**2 + 20*c - 5. Let j(n) = 3*n**3 + 3*n**2 - 10*n + 2. Suppose -18 = 11*h + 48. Let t(d) = h*l(d) - 15*j(d). Factor t(x).
-3*x*(x - 2)*(x + 5)
Let f be 90/(-7)*(-14)/2. Suppose 15*k - f = 10*k. Factor -9 + 6*v**2 - 4 - k*v - 4*v**2 - 7.
2*(v - 10)*(v + 1)
Suppose -1/5*k**3 - 332/5 - 419/5*k - 88/5*k**2 = 0. Calculate k.
-83, -4, -1
Let w(m) = 2*m**3 - 8*m**2 + 6*m + 6. Let h(f) = 2*f**3 - 416 - 2*f**2 - f**4 + f**2 + 417 + 2*f. Let k(c) = 2*h(c) - w(c). Solve k(x) = 0.
-1, 1, 2
Let r(n) be the second derivative of 4*n**5/15 + 11*n**4/6 - 2*n**3 - 155*n**2 - 5*n. Let q(v) be the first derivative of r(v). Determine s so that q(s) = 0.
-3, 1/4
Let b(s) be the second derivative of s**4/132 + 4*s**3/33 + 15*s**2/22 - 1220*s. Find f such that b(f) = 0.
-5, -3
Let r(m) = 1 - m**2 + m - 2*m - 2. Let y(b) = b**3 - b**2 - 6*b - 6. Let o be ((-3)/(-1))/(0 + 6/(-6) - 2). Let d(c) = o*y(c) + 2*r(c). Factor d(p).
-(p - 2)*(p + 1)*(p + 2)
Let d(h) = -2*h**3 - 6*h**2 + 6*h + 18. Let u(r) = -2*r**3 - 6*r**2 + 5*r + 15. Suppose -42 = -13*n - 3. Let o(q) = n*d(q) - 4*u(q). Factor o(k).
2*(k - 1)*(k + 1)*(k + 3)
Find w such that 64*w**4 - 13*w**3 - 87*w**5 + 70*w**5 + 32*w + 23*w**5 + 155*w**3 + 116*w**2 = 0.
-8, -1, -2/3, 0
Factor -2/13*k**2 + 12/13*k + 38.
-2*(k - 19)*(k + 13)/13
Let l = 10559/4 - 2639. Let r(f) be the second derivative of l*f**2 - 14*f + 1/16*f**4 - 3/8*f**3 + 0. Suppose r(s) = 0. Calculate s.
1, 2
Let w(u) be the second derivative of u**6/20 + 7*u**5/10 + 57*u**4/16 + 9*u**3 - 65*u**2 - 14*u. Let y(x) be the first derivative of w(x). Factor y(k).
3*(k + 4)*(2*k + 3)**2/2
Let r(n) be the third derivative of 117*n**5/16 - 4385*n**4/24 - 25*n**3/6 + 606*n**2 - 4*n. Factor r(w).
5*(w - 10)*(351*w + 2)/4
Let x(n) = -34*n - 57. Let p be x(-4). Suppose -p + 29 + 8*k**2 + 5*k - 16*k**3 + 17*k**3 = 0. Calculate k.
-5, 2
Let m be (-6)/30*5 - (-2 + -7). Let w be (-5)/(m/2 + -5). Factor 6/7 + 6/7*f**w - 12/7*f**2 + 6/7*f**4 + 6/7*f - 12/7*f**3.
6*(f - 1)**2*(f + 1)**3/7
Let w(n) = 10*n**3 + 152*n**2 - 308*n + 160. Let f(c) = -24*c**3 - 303*c**2 + 613*c - 321. Let h(j) = -2*f(j) - 5*w(j). What is i in h(i) = 0?
-79, 1
Suppose 0 = 2*s + 155 + 11. Let i = s - -88. Determine t so that t**2 - i - 1 + 0 - 4 - 3*t = 0.
-2, 5
Let n = 1/4830 - -53/3220. Let a(l) be the third derivative of -1/15*l**3 + 0 + 0*l - 1/2100*l**7 - 1/600*l**6 + 13*l**2 + n*l**4 + 1/200*l**5. Factor a(r).
-(r - 1)**2*(r + 2)**2/10
Let n = -65 - -61. Let q be 12/16*n + (3 - -2). Factor 8/15 + 2/15*b**q - 2/3*b.
2*(b - 4)*(b - 1)/15
Let z = 64265/3 + -21420. Let w(l) be the second derivative of 0*l**2 + 0 + 19*l + 5/12*l**4 + z*l**3. Factor w(c).
5*c*(c + 2)
Let n(p) be the third derivative of p**8/756 + 23*p**7/945 - 49*p**6/270 + 103*p**5/270 - 5*p**4/18 - 675*p**2. Solve n(d) = 0 for d.
-15, 0, 1/2, 1, 2
Let c(b) be the second derivative of -6 - b**3 + 6*b + 0*b**2 + 3/20*b**5 + 1/4*b**4. What is y in c(y) = 0?
-2, 0, 1
What is u in -220 - 235*u**3 - 427*u**2 - 5*u**4 + 102*u - 541*u - 226*u - 248*u**2 = 0?
-44, -1
Let n(p) be the third derivative of 2/3*p**3 - 2/105*p**7 + 0 - 1/168*p**8 + 4/15*p**5 - 38*p**2 + 1/30*p**6 + 0*p + 7/12*p**4. Find s, given that n(s) = 0.
-1, 2
Let z(v) = 2*v**2 - 24*v - 20. Let u be z(12). Let l(i) = -4*i**2 - 36*i + 60. Let y(a) = a - 2. Let t(k) = u*y(k) - l(k). Suppose t(r) = 0. Calculate r.
-5, 1
Solve -97/11*i**2 - 1/11*i**3 - 14175/11 - 2655/11*i = 0 for i.
-45, -7
Let n(h) be the first derivative of -2*h**5/55 - 2*h**4 - 50*h**3/3 - 604*h**2/11 - 888*h/11 + 5495. Find r such that n(r) = 0.
-37, -3, -2
Let u(f) be the first derivative of -10/13*f**2 - 16/13*f + 22 + 2/13*f**3 - 2/65*f**5 + 2/13*f**4. Find i such that u(i) = 0.
-1, 2, 4
Let n = -836 - -839. Let r(a) be the second derivative of -40/9*a**n - 2/135*a**6 - 14*a - 8*a**2 + 0 - 2/9*a**5 - 37/27*a**4. Find v such that r(v) = 0.
-3, -2
Let b(d) be the third derivative of -d**6/40 + 2*d**5/5 + 539*d**4/8 + 1815*d**3 - 3334*d**2. Factor b(x).
-3*(x - 30)*(x + 11)**2
Let n(x) = x + 4. Let f be n(0). Suppose 0 = -s - s, -380 = -f*w + s. Suppose w*a**2 + 54 - 170*a - 14*a**3 - 14 + 49*a**3 = 0. What is a?
-4, 2/7, 1
Let c(j) be the third derivative of j**5/40 - 1919*j**4/8 + 3682561*j**3/4 + 2*j**2 + 4*j + 79. Factor c(z).
3*(z - 1919)**2/2
Suppose -o + 4 = 0, -2*g + 0*o = 3*o - 26. Suppose -9*x = -g*x - 6. Factor 432*y + 2*y**3 + 192 + 99*y**2 + 8*y**x - 10*y**3 + 6*y**3.
3*(y + 8)**2*(2*y + 1)
Suppose -2*i + 2*a + 12 = 5*a, 0 = -5*a + 10. Suppose -q**4 - 28*q**2 + 6*q**4 + i*q**2 + 60*q - 20*q**3 + 15*q**2 + 45 = 0. Calculate q.
-1, 3
Let x(c) be the second derivative of 3*c**5/50 + 31*c**4/10 + 191*c**3/5 + 483*c**2/5 + c - 163. Determine u so that x(u) = 0.
-23, -7, -1
Factor -17/7*a**3 + 17/7*a + 1/7*a**4 - 16/7 + 15/7*a**2.
(a - 16)*(a - 1)**2*(a + 1)/7
Let s be (-2)/10*-87 + 18/(-45). Suppose 23*q - s*q = 54. Factor -243 - 77 + q*l**4 - 60*l**3 - 406*l - 14*l**4 - 74*l - 260*l**2.
-5*(l + 2)**2*(l + 4)**2
Suppose 7*t + 88 - 102 = 0. Determine g so that 2*g**2