2 - 2480*a**4 + 1236*a**4 + 40*a**3 + 198*a**2 + 1246*a**4.
2*a**2*(a + 10)**2
Solve -7*g**5 + 220*g + 68*g**4 - 20*g**2 + 13*g**5 + 2*g**4 - 165*g**3 - 6*g**5 - 5*g**5 = 0.
-1, 0, 2, 11
Let f(p) be the first derivative of p**7/105 - p**5/30 - 3*p**2 - 26. Let k(z) be the second derivative of f(z). Factor k(u).
2*u**2*(u - 1)*(u + 1)
Factor 2/5*q**4 + 0*q - 8/5*q**3 + 0 + 0*q**2.
2*q**3*(q - 4)/5
Let u(c) be the first derivative of 12 + 0*c**2 + 1/5*c**5 - 1/12*c**3 - 3/16*c**4 + 0*c. Factor u(v).
v**2*(v - 1)*(4*v + 1)/4
Let h(g) = 2*g**2 - 42*g - 1077. Let u be h(-15). What is r in -6/7*r**2 + 0*r - 4/7*r**u + 2/7*r**4 + 0 = 0?
-1, 0, 3
Let i(l) be the first derivative of -l**4/2 + 2*l**3/3 + 2*l**2 + 66. What is u in i(u) = 0?
-1, 0, 2
Let g(f) be the first derivative of 5*f**3/3 - 10*f**2 + 15*f + 124. Determine t, given that g(t) = 0.
1, 3
Suppose -3*n - 36 = -0*n. Let g be (-4)/n + ((-26)/30)/(-1). Suppose -18/5*t + 2*t**3 + 0 + 2/5*t**4 + g*t**2 = 0. Calculate t.
-3, 0, 1
Let m(z) be the first derivative of -z**5/20 + 7*z**4/16 - 7*z**3/6 + z**2 - 59. Factor m(c).
-c*(c - 4)*(c - 2)*(c - 1)/4
Let o be (-2)/4*3*294/1764*-8. Find k such that 0 + 8/9*k**4 + 4/9*k**3 - 4/9*k**5 - 8/9*k**o + 0*k = 0.
-1, 0, 1, 2
Let w(v) be the first derivative of -v**6/30 - 2*v**5/5 - 6*v**4/5 - 22*v**3/15 - 7*v**2/10 - 20. Let w(i) = 0. What is i?
-7, -1, 0
Let w be ((-22)/(-8))/((-2)/8). Let i = -5 - w. Factor 4*x - i*x + 4*x**3 + 6*x - 6*x**2 - 2*x**2.
4*x*(x - 1)**2
Let v(q) = -q**3 - q**2 + q - 3. Let l(p) = 15 - 6 - p**3 - 11. Let n(a) = 4*l(a) - 3*v(a). Factor n(r).
-(r - 1)**3
Let a(c) = 3*c**2 + 20*c - 19. Let z(d) = -8*d**2 - 39*d + 37. Let i(s) = 10*a(s) + 4*z(s). Factor i(j).
-2*(j - 21)*(j - 1)
Let j(i) = -i**3 + 10*i**2 - 8*i + 9. Suppose 19 - 64 = -5*z. Let l be j(z). Let -18*p - 3*p**4 - 24*p**2 - 12 - l*p**3 - 18*p - 15*p**2 = 0. Calculate p.
-2, -1
Let r(i) = -i**3 + 1. Let u be r(1). Suppose -4*v - 4 = -4*g, -4*v + 2*g = -3 - 3. Factor 2/7*b**v + 0*b**3 - 4/7*b**2 + 2/7 + u*b.
2*(b - 1)**2*(b + 1)**2/7
Let d = 984 + -981. Let j(q) be the second derivative of 1/20*q**4 + 3*q + 24/5*q**2 + 4/5*q**d + 0. Suppose j(t) = 0. Calculate t.
-4
Let i be 5*(-1 + -1) + 4. Let u(r) = -3*r**3 - r - 2. Let v(c) = 4*c**3 + c**2 + 2*c + 2. Let q(g) = i*u(g) - 4*v(g). Let q(k) = 0. What is k?
-1, 1, 2
Let j(o) = o**3 - 2*o**2 - o - 2. Let r be j(3). Let l be (-160)/(-88) - (-4)/22. Factor -3*a**2 + l*a**2 + 7*a**2 - r*a**2 - 2*a.
2*a*(a - 1)
Factor -v**2 + 5*v**2 + 5*v**4 - v**4 + 0*v**2 - 4723*v**3 + 4715*v**3.
4*v**2*(v - 1)**2
Let b(s) be the second derivative of 14*s + 16*s**2 - 8/15*s**6 + 2/7*s**7 + 0 + 40/3*s**3 - 13/5*s**5 + 2*s**4. Solve b(m) = 0 for m.
-1, -2/3, 2
Let p(k) be the second derivative of -k**7/147 - 3*k**6/35 - k**5/10 + 3*k**4/14 + 8*k**3/21 + 3*k - 1. Determine j so that p(j) = 0.
-8, -1, 0, 1
Suppose 4*h - 4*y - 11 = y, 2*y - 55 = -5*h. Let j = h - 7. Factor 0*f**2 + 3*f**2 - f**j.
2*f**2
Let w(y) be the second derivative of y**7/105 - 7*y**6/180 + y**5/18 - y**4/36 + 6*y**2 - 9*y. Let j(u) be the first derivative of w(u). Solve j(r) = 0.
0, 1/3, 1
Suppose 0*u + 14 = 4*u - 3*m, -5*u + 2*m + 21 = 0. Suppose -u*t + 45 = 4*t. Factor -2/3*s**3 + 2/3*s**4 + 0 - 2/3*s**2 + 2/3*s**t + 0*s.
2*s**2*(s - 1)*(s + 1)**2/3
Suppose -446 = 3*i - 431. Let j be 0/((3 - 13)/i). Factor 10/11*a**4 + 0 - 2/11*a**5 + j*a - 16/11*a**3 + 8/11*a**2.
-2*a**2*(a - 2)**2*(a - 1)/11
Let h(r) be the second derivative of -r**4/20 + 9*r**3/10 + 3*r**2 + 4*r. Factor h(p).
-3*(p - 10)*(p + 1)/5
Let u(l) be the second derivative of -l**5/4 - 5*l**4/3 + 25*l**3/2 + 45*l**2 + 262*l. Factor u(x).
-5*(x - 3)*(x + 1)*(x + 6)
Suppose 6*v + 70*v = 0. Suppose 0 - 3/7*k**3 + 3/7*k**4 + v*k - 1/7*k**5 + 1/7*k**2 = 0. Calculate k.
0, 1
Let w be (1/(-2))/(9/(-126)). Solve 16 - 16 + 2*z**5 + 2*z + 3*z**3 - w*z**3 = 0.
-1, 0, 1
Suppose -26*z + 30*z = 0. Let a = z + 3. Factor -3*h**2 + 9*h - 9 + 1/3*h**a.
(h - 3)**3/3
Let r(f) = -2*f**2 + f. Let c(u) = -3*u**4 + 576*u**3 - 26464*u**2 - 112900*u - 115248. Let d(z) = c(z) + 4*r(z). Factor d(b).
-3*(b - 98)**2*(b + 2)**2
Let o(n) = 2*n**2 - 8*n - 2. Let r(k) = -k + 13. Let d be r(7). Let i(b) = 24*b - 5 - d*b**2 + 7 + 3 + 2. Let m(t) = 2*i(t) + 7*o(t). Factor m(h).
2*h*(h - 4)
Let a = 3732/5 - 746. Let n(t) be the second derivative of -3*t - a*t**2 - 1/5*t**3 - 1/30*t**4 + 0. Solve n(s) = 0.
-2, -1
Let x = 21010 + -1995901/95. Let p = x + -6/19. Find o such that -4/5*o**3 + 0 - p*o - o**2 = 0.
-1, -1/4, 0
Let t(u) = 4*u**2 - 4*u + 2. Suppose 44 = 4*y - 8*y. Let b(p) = -21*p**2 + 20*p - 10. Let v(q) = y*t(q) - 2*b(q). Find g such that v(g) = 0.
1
Let z(o) be the third derivative of -o**7/840 - o**6/160 + o**5/60 + o**4/8 + 99*o**2 + 2. Factor z(k).
-k*(k - 2)*(k + 2)*(k + 3)/4
Suppose -1418*b**3 + 224*b**2 + 1106*b**3 - 4*b**5 + 648 - 72*b**4 + 476*b + 640*b = 0. Calculate b.
-9, -1, 2
Let x(i) = 7*i**2 + 21*i - 75. Let d(h) = 10*h**2 + 20*h - 76. Let f(w) = 3*d(w) - 4*x(w). Determine t so that f(t) = 0.
6
Solve 33*v**3 - 84*v - v**2 - 43*v**5 + 7*v**4 + 90*v**5 - v**4 - 50*v**5 - 11*v**2 - 48 = 0 for v.
-2, -1, 2, 4
Let f be 60/10*(-4)/(-8). Suppose 0 = f*s + 4*m + 14, 3*m = 7*m + 20. Factor -9/5*o + 0 + 3/5*o**s.
3*o*(o - 3)/5
Let c(x) = 4*x**2 - 8*x - 6. Suppose -5*n - 24 = w + 22, 5*w = -n + 10. Let j(h) = 1. Let m(k) = n*j(k) - c(k). Let m(i) = 0. What is i?
1
Let p be ((-16)/12)/(30/(-270)) + -10. Suppose 3/2*c - 6*c**3 - 15/4*c**4 + 0 - 3/4*c**p = 0. Calculate c.
-1, 0, 2/5
Let m(y) = 3*y**2 - 31*y + 10. Let k be m(10). Suppose 4*n + 2*g = 16, -3*n + g + 4*g - 14 = k. Suppose 0*i + 1/3*i**3 + 0*i**n + 0 - 1/3*i**4 = 0. Calculate i.
0, 1
Suppose 39*h - 33*h - 12 = 0. Let b be -3*10/54*(-18)/45. Determine i so that 4/9 - 2/3*i + b*i**h = 0.
1, 2
Let b(f) = -4*f**3 - 13*f**2 + 4*f + 13. Let s = 92 + -98. Let x(p) = 4*p**3 + 14*p**2 - 4*p - 14. Let k(l) = s*b(l) - 5*x(l). Solve k(w) = 0 for w.
-2, -1, 1
Let f(l) be the third derivative of -l**6/450 + l**5/30 - l**4/5 + 7*l**3/3 + 27*l**2. Let i(o) be the first derivative of f(o). Factor i(w).
-4*(w - 3)*(w - 2)/5
Let p(u) be the third derivative of -u**7/630 - u**6/80 - u**5/40 + 305*u**2 - 2. Find b, given that p(b) = 0.
-3, -3/2, 0
Factor -8*x**2 - 17440*x**4 - 17*x**3 + 17445*x**4 + 36*x**2 - 18*x**3 + 2*x**2.
5*x**2*(x - 6)*(x - 1)
Let b(o) be the second derivative of -10*o + 0*o**4 + 0*o**2 + 2/225*o**6 + 1/315*o**7 + 0*o**3 + 1/150*o**5 + 0. What is j in b(j) = 0?
-1, 0
Let t(z) be the second derivative of -1/200*z**5 + 18*z + 1/5*z**2 + 0 - 2/15*z**3 + 1/24*z**4. Factor t(q).
-(q - 2)**2*(q - 1)/10
Let m = -174 - -248. Find n, given that 9*n - m*n**4 + 28*n**4 + 180*n**3 - 54*n**4 - 96*n**2 + 7*n = 0.
0, 2/5, 1
Suppose 2*j - 104 = 4*j. Let c = j - -76. Factor 2*q**4 - 3*q**2 - 23*q + 4*q**2 + 3*q**2 + c*q + 5*q**3.
q*(q + 1)**2*(2*q + 1)
Let h(n) be the first derivative of -4*n**3/3 + 22*n**2 + 48*n + 88. Solve h(k) = 0 for k.
-1, 12
Let r(h) be the first derivative of h**5 - 20*h**4 + 105*h**3 + 40*h**2 - 320*h - 206. Factor r(l).
5*(l - 8)**2*(l - 1)*(l + 1)
Let d be (-1 + 3 - 24)/(-4 - -5). Let w be d/(-10) - (-6)/33*-11. Suppose w*h**2 + 1/5*h - 2/5 = 0. Calculate h.
-2, 1
Suppose 0*i + 5*i = 5*n + 5, -n = 3*i - 19. Let m be (27/24)/(2 - 2/n). Factor 0 - 2*c**2 - m*c**3 - c.
-c*(c + 2)*(3*c + 2)/4
Let h(u) = -u - 13. Let f be h(-16). Suppose f*v + 0 = 15. Factor -7/2*o**2 + 1/2*o**v + o + 0 + 9/2*o**3 - 5/2*o**4.
o*(o - 2)*(o - 1)**3/2
Let i = -7589 - -15181/2. Suppose 27/2*t + 6 + i*t**3 + 9*t**2 = 0. What is t?
-4, -1
Let a be (-4)/(-392)*443 + -4. Let c = a + -1/49. Let 1/4 + 1/4*f**2 + c*f = 0. Calculate f.
-1
Let j be (-6)/8 + 3451/3828. Let q(z) be the second derivative of 1/11*z**5 + 2*z + 1/11*z**2 + 0 + j*z**3 + 1/231*z**7 + 1/33*z**6 + 5/33*z**4. Factor q(r).
2*(r + 1)**5/11
Factor 3*g - 44*g**2 + 49*g**2 + 12*g - 20.
5*(g - 1)*(g + 4)
Let y(q) = -2*q - 3. Let a be y(6). Let u be a/5 + 3/(3/5). Suppose -9/7*v + 6/7 + 3/7*v**u = 0. What is v?
1, 2
Let a be 0 + 4/((-20)/(-15)). What is y in 23*y**3 + y + 41*y**a - 5*y = 0?
-1/4, 0, 1/4
Let s be 234/10 - (-24)/(-60). Suppose -5 + s = 6*p. Factor -2*w**3 + 0*w + 5*w**3 + 3*w**p - 3*w**5 - 3*w.
-3*w*(w - 1)**2