*q**2 + 410*q. Suppose i(p) = 0. Calculate p.
204
Suppose 0 = 3*y + 12, 0 = -3*s - y - y - 2. Let h(w) be the first derivative of 4/5*w + 6/5*w**3 + 1 + 1/2*w**4 + 7/5*w**s + 2/25*w**5. Factor h(l).
2*(l + 1)**3*(l + 2)/5
Let g = 31 - 43. Let q(j) = -32*j**3 - 48*j**2 - 28*j + 12. Let i(n) = 13*n**3 + 19*n**2 + 11*n - 5. Let t(h) = g*i(h) - 5*q(h). Factor t(u).
4*u*(u + 1)*(u + 2)
Let y(v) be the second derivative of -v**6/120 - v**5/80 + 3*v**4/16 + 3*v**3/8 - 92*v. Factor y(l).
-l*(l - 3)*(l + 1)*(l + 3)/4
Factor -5*s**3 + 88*s**2 + 20*s - 53*s**2 - 50*s**2.
-5*s*(s - 1)*(s + 4)
Suppose 0 = 17*b - 51 - 0. Solve 6*k**2 + 2*k**4 - 8*k**b + 3668 - 3668 = 0 for k.
0, 1, 3
Let v(k) = 15*k + 423. Let b be v(-28). Factor -6/11 - 2/11*r**2 - 10/11*r + 2/11*r**b.
2*(r - 3)*(r + 1)**2/11
Let u(y) be the second derivative of 0*y**2 + 0*y**4 + 0 - 2/5*y**5 - 3*y + 2/15*y**6 + 0*y**3. Factor u(a).
4*a**3*(a - 2)
Let u(o) be the second derivative of 3*o**5/20 - 2*o**3 - o - 81. Factor u(z).
3*z*(z - 2)*(z + 2)
Solve -28/5*p + 2/5*p**3 + 0 - 26/5*p**2 = 0 for p.
-1, 0, 14
Let h(x) = x**4 + 5*x**3 - 2*x - 4. Let n = -32 + 29. Let c(y) = -y**3 + 1. Let g(w) = n*c(w) - h(w). Determine q, given that g(q) = 0.
-1, 1
Let m be -2 + ((-519)/(-692))/(3/10). Solve 2*n - m*n**2 - 1/2*n**3 + 2 = 0 for n.
-2, -1, 2
Let q(f) = 14*f + 112. Let r be q(-8). Let u(z) be the first derivative of -1 + r*z + 1/16*z**4 + 1/8*z**2 - 1/6*z**3. Factor u(s).
s*(s - 1)**2/4
Find a, given that -2*a**2 + 4*a**4 - 13*a + a + 12*a**3 - a**2 - a**2 = 0.
-3, -1, 0, 1
Let q(v) be the third derivative of -2*v**7/105 + v**6/6 - v**5/3 - 5*v**4/6 + 4*v**3 - 352*v**2. Suppose q(o) = 0. Calculate o.
-1, 1, 2, 3
Let g(m) be the third derivative of 2/315*m**7 + 0*m**4 + 0 + 2*m**2 + 1/180*m**6 + 1/504*m**8 + 0*m**5 + 0*m**3 + 0*m. Factor g(y).
2*y**3*(y + 1)**2/3
Let n be (2/(-3))/((-13)/78). Factor n*g - 3*g**2 + 0*g - 6 - 10*g - 3*g.
-3*(g + 1)*(g + 2)
Suppose 0 = l + j - 3, -7*l + 6*l - 3*j = -9. Let h be (-2)/13 + ((-357)/(-78))/7. Factor -1/2*o**2 + 0 + l*o**3 + 0*o + h*o**4.
o**2*(o - 1)*(o + 1)/2
Let c(q) be the first derivative of -35 - 1/10*q**5 + 0*q**2 + 0*q + 0*q**4 + 2/3*q**3. Determine i so that c(i) = 0.
-2, 0, 2
Let u be (-2)/10 + 8/40. Let c(h) be the second derivative of h + 1/4*h**4 + h**3 + 0*h**2 + u. Determine l so that c(l) = 0.
-2, 0
Let x(k) be the first derivative of -k**4/20 + 4*k**3/15 - 3*k**2/10 - 4. Solve x(m) = 0.
0, 1, 3
Suppose -17 = -6*s + 19. Let b(t) = -2*t**2 + 7*t - 3. Let z(a) = a - 1. Let y(f) = s*z(f) - 2*b(f). What is n in y(n) = 0?
0, 2
Let f(g) = -g**2 + 8*g - 8. Let w be f(6). Suppose w*r = 5*r. What is h in 3*h + 3*h + 3*h**2 + r*h - 9*h = 0?
0, 1
Suppose 3*i - 4*i + 19 = 4*p, 5*p = -3*i + 29. Let -2*o**4 + o**p + 2*o**2 + 14 - 15 = 0. Calculate o.
-1, 1
Let m(f) = -9*f**2 + 48*f - 85. Let u(t) = 4*t**2 - 24*t + 42. Let k(o) = -2*m(o) - 5*u(o). Let k(q) = 0. Calculate q.
2, 10
Determine q so that 80*q - 4*q**4 + 48*q**2 - 7633 - 36*q**3 + 7633 = 0.
-10, -1, 0, 2
Factor 5*h - 16*h + 3*h**3 + 54*h + 33*h**2 - 13*h.
3*h*(h + 1)*(h + 10)
Factor 4*b**4 + 4*b**5 - 12688*b**2 + 12688*b**2.
4*b**4*(b + 1)
Let n(u) = -7*u**2 + 3*u - 8. Let k(p) = 12*p**2 - 7*p + 15. Let z(b) = -3*k(b) - 5*n(b). Factor z(j).
-(j - 5)*(j - 1)
Let t(m) be the first derivative of -m**6/36 - 11*m**5/30 - 11*m**4/6 - 38*m**3/9 - 4*m**2 - 279. Find d, given that t(d) = 0.
-4, -3, -2, 0
Suppose 2*h - 38 = -2*l - h, 4*l - 4*h - 36 = 0. Determine g, given that 4*g**2 - 6 - 42 + 0*g + l*g + 3*g = 0.
-6, 2
Let r(g) be the third derivative of g**8/110880 - g**7/6930 + g**6/1320 - 2*g**5/5 + 15*g**2. Let z(v) be the third derivative of r(v). Factor z(y).
2*(y - 3)*(y - 1)/11
Let l = -174/13 - -1244/91. Let m be 2/(-10) + (-1)/(-5). Let m + l*x**2 + 4/7*x - 2/7*x**3 = 0. Calculate x.
-1, 0, 2
Let n(r) be the first derivative of -r**5/100 + r**4/30 + r**3/10 - 30*r - 6. Let t(u) be the first derivative of n(u). Let t(d) = 0. What is d?
-1, 0, 3
Factor -2/5*a**2 + 0 - 2*a.
-2*a*(a + 5)/5
Let g(x) be the third derivative of x**8/196 + 13*x**7/490 + 3*x**6/56 + x**5/20 + x**4/56 + x**2 + 51*x. Factor g(a).
3*a*(a + 1)**3*(4*a + 1)/7
Let i = 424 - 422. Let h(w) be the first derivative of 1/12*w**3 + 1/4*w + 1/4*w**i - 3. Suppose h(r) = 0. What is r?
-1
Solve -34/3*x**4 + 10/3*x**5 + 0 + 0*x**2 + 4*x**3 + 0*x = 0.
0, 2/5, 3
Let x(d) be the first derivative of d**3 + 0*d + 0*d**2 - 3/5*d**5 - 1/2*d**6 + 3/4*d**4 - 3. Factor x(v).
-3*v**2*(v - 1)*(v + 1)**2
Determine t, given that 24*t**4 + 4*t**2 + t**5 - 99*t**3 - 23*t**4 + 87*t**3 + 16*t = 0.
-4, -1, 0, 2
Let v(b) = 8*b**2 + 32*b + 32. Let y(p) = -23*p**2 - 95*p - 98. Let q(i) = -11*v(i) - 4*y(i). Factor q(a).
4*(a + 2)*(a + 5)
Suppose t - 3*s - 6 = 2*s, 3*s = 5*t + 36. Let d be ((-8)/42)/(6/t). Solve -4/7*l**4 - d*l + 4/7*l**2 + 0*l**3 + 0 + 2/7*l**5 = 0 for l.
-1, 0, 1
Let n(y) be the first derivative of -1/12*y**5 + 0*y + 0*y**4 + 0*y**2 - 2 + 1/8*y**6 - 3*y**3. Let z(v) be the third derivative of n(v). Factor z(l).
5*l*(9*l - 2)
Let t(c) be the second derivative of 7*c**4/15 - 11*c**3/15 - 3*c**2/5 + 3*c - 51. Factor t(h).
2*(h - 1)*(14*h + 3)/5
Suppose -8 = -f - 3. Factor -17*z**2 + 18*z**3 + 9*z**4 + 18 + 77*z**2 + 57*z - 13*z**5 - 15*z**4 + 10*z**f.
-3*(z - 3)*(z + 1)**3*(z + 2)
Let q(d) be the third derivative of d**5/60 - 11*d**4/24 - 7*d**3 - d**2 - 16*d. Factor q(v).
(v - 14)*(v + 3)
Find y such that 2/19*y**2 - 2/19*y**5 - 6/19*y**3 + 0 + 0*y + 6/19*y**4 = 0.
0, 1
Let m(y) be the second derivative of -y**6/180 - y**5/45 + y**4/36 + 2*y**3/9 + y**2/2 + 3*y. Let k(n) be the first derivative of m(n). Solve k(h) = 0 for h.
-2, -1, 1
Let l = -533/5 - -107. Find g, given that -3/5*g**2 + 1/5*g + 1/5 - g**3 - l*g**4 = 0.
-1, 1/2
Let j(v) be the second derivative of -v**7/168 + v**6/120 + v**5/80 - v**4/48 - v + 125. Factor j(w).
-w**2*(w - 1)**2*(w + 1)/4
Let i(b) be the third derivative of b**8/336 + b**7/210 - b**6/12 - b**5/15 + b**4 - 197*b**2. Factor i(h).
h*(h - 2)**2*(h + 2)*(h + 3)
Let w(a) = 5*a**4 - a**3 + 6*a**2 + 8*a - 4. Let u(j) = 6*j**4 + 7*j**2 + 8*j - 5. Let q(p) = 4*u(p) - 5*w(p). Solve q(x) = 0 for x.
-1, 0, 2, 4
Let u be ((-8)/(-20) - 298/(-80)) + (-176)/1408. Factor -3/2*m**3 + 3/4*m**u - 9/4*m**2 + 0 + 0*m.
3*m**2*(m - 3)*(m + 1)/4
Let i(m) = -m**3 + 1. Suppose -5*c + 5 = -3*s, -3*c + 5*s - 5 = -8*c. Let t(g) = -110*g**3 - 826*g**2 + 496*g - 60. Let p(l) = c*t(l) - 12*i(l). Factor p(n).
-2*(n + 9)*(7*n - 2)**2
Let z(y) be the first derivative of 4 + 0*y + 0*y**3 - 1/3*y**4 + 0*y**2 + 2/15*y**5. Find k, given that z(k) = 0.
0, 2
Let d(l) be the first derivative of l**6/21 - 24*l**5/35 + 10*l**4/7 + 220*l**3/21 - 3*l**2 - 28*l + 510. Suppose d(n) = 0. Calculate n.
-2, -1, 1, 7
Let j = -9/2 - 14. Let h = -109/6 - j. Factor -2/3*y - h - 1/3*y**2.
-(y + 1)**2/3
Let x = -20 + 26. Let l(t) = -6*t**2 + 7*t - 7. Let k(v) = -5*v**2 + 6*v - 6. Let y(f) = x*l(f) - 7*k(f). Let y(h) = 0. What is h?
0
Let x(l) = l**3 - 10*l**2 + 8*l + 11. Let z be x(9). Factor 52*a + 13*a**2 + 20 - 2*a**2 - 6*a**z.
(a + 10)*(5*a + 2)
Factor 12 - 120 - 57 - u + 4*u**2 - 9*u**2 - 169*u.
-5*(u + 1)*(u + 33)
Let r(x) be the first derivative of -2*x**6/45 - x**5/30 + x**4/18 + 3*x - 13. Let n(k) be the first derivative of r(k). Factor n(z).
-2*z**2*(z + 1)*(2*z - 1)/3
Suppose 0 = -47*r - 137*r - 39 + 591. Let y = 82 - 491/6. Factor y*p**4 + 1/6*p**r + 0 - 2/3*p - 2/3*p**2.
p*(p - 2)*(p + 1)*(p + 2)/6
Let v(h) be the second derivative of h**5/4 + 5*h**4/6 - 80*h**3/3 - 240*h**2 - 7*h + 4. Let v(c) = 0. Calculate c.
-4, 6
Suppose -10*t**4 + 0 + 20*t + 42*t**2 + 6/5*t**5 + 54/5*t**3 = 0. Calculate t.
-1, -2/3, 0, 5
Let z be (72/(-30) + 4)*2/8. Let o = -272/5 - -279/5. Factor 0 + z*y + o*y**2.
y*(7*y + 2)/5
Let z(s) be the first derivative of s**3/3 - 10*s**2 + 19*s + 11. Let q(m) = m**2 - 40*m + 39. Let c(u) = -4*q(u) + 9*z(u). Factor c(t).
5*(t - 3)*(t - 1)
Let j(q) = -2*q**3 - 12*q**2 - 18*q + 10. Let o(f) = 2*f**3 + 12*f**2 + 18*f - 8. Let s(r) = -4*j(r) - 5*o(r). Determine h, given that s(h) = 0.
-3, 0
Let t be ((-20)/360)/(10/(-3)). Let y(v) be the third derivative of -4*v**2 - 1/4*v**4 + 0 + 0*v**5 + 0*v + t*v**6 - 2/3*v**3. Find j, given that y(j)