t) = 0.
-2, 2
Let t be ((-2)/(-3))/((-2 - 1)/(-3)). Let a(v) be the first derivative of 2*v - 2 + 2*v**2 + t*v**3. Solve a(z) = 0.
-1
Let a(c) be the second derivative of c**4/15 - 2*c**3/15 - 4*c**2/5 + 2*c. Determine m, given that a(m) = 0.
-1, 2
Let q(d) = 14*d**2 - 8. Let f be 5 + 2 - 2/(-2). Let k(i) = -9*i**2 + 5. Let v(a) = f*k(a) + 5*q(a). Factor v(y).
-2*y**2
Let u be (-2)/(-3)*(1 - 7). Let c be (8 + -8)*(-2)/u. Factor 2/9*k**2 + 2/9*k + c - 2/9*k**4 - 2/9*k**3.
-2*k*(k - 1)*(k + 1)**2/9
Let y be 1 + 2 + 219/(-4). Let i = 52 + y. Factor 1/2*d**2 + 1/4*d - 1/2 - i*d**3.
-(d - 2)*(d - 1)*(d + 1)/4
Let m(g) be the first derivative of 10 - 1/4*g**4 + 1/3*g**3 + 3*g + 5/2*g**2. What is y in m(y) = 0?
-1, 3
Let t = -1 + -4. Let h(m) = 6*m**3 - m**2 - 6*m + 1. Let x(z) = -3*z**3 + 3*z. Let y(p) = t*x(p) - 2*h(p). Suppose y(r) = 0. Calculate r.
-1, -2/3, 1
Let x be 2 + 0*2/4. Suppose -t - 2*t**2 + 7 + 2*t - t**3 - 9 + 4*t**x = 0. Calculate t.
-1, 1, 2
Let j = -5/97 + 249/1067. Let r = j + 12/55. Factor -2/5*q**4 - r*q**5 + 4/5*q**3 - 2/5 + 4/5*q**2 - 2/5*q.
-2*(q - 1)**2*(q + 1)**3/5
Let n be (24/30)/(2/5). Let u(j) = -16*j**3 - 5*j**2 + 16*j + 16. Let d(h) = 3*h**3 + h**2 - 3*h - 3. Let q(m) = n*u(m) + 11*d(m). Factor q(y).
(y - 1)*(y + 1)**2
Let o(d) be the first derivative of -d**4/2 + 2*d**3 - 3*d**2 + 2*d + 30. Determine w so that o(w) = 0.
1
Let r(h) be the third derivative of -h**8/560 + 3*h**7/280 - h**5/10 + h**3/6 - 3*h**2. Let p(d) be the first derivative of r(d). Factor p(f).
-3*f*(f - 2)**2*(f + 1)
Let i(r) be the first derivative of 3*r**5/5 - r**3 - 4. Factor i(l).
3*l**2*(l - 1)*(l + 1)
Let p(r) be the first derivative of -r**3/21 - r**2/14 + 2*r/7 + 5. Suppose p(c) = 0. What is c?
-2, 1
Let n(l) = l**2 - 1. Let s(y) = -2*y + 2. Let q(g) = n(g) + s(g). Factor q(x).
(x - 1)**2
Suppose 3*l - 50 = 3*q + l, -3*l = q + 35. Let z be (6/5)/((-3)/q). Solve -8*k + 2*k**2 + z*k**3 - 2*k**2 - 6 + 2*k**2 + 4 = 0.
-1, -1/4, 1
Let i be -4 + ((-162)/(-24) - 2). Suppose 3*q**5 - 3*q**3 + i*q**2 + 0 + 0*q - 3/4*q**4 = 0. Calculate q.
-1, 0, 1/4, 1
Let g(f) be the second derivative of f**6/420 + 2*f**2 + 2*f. Let i(x) be the first derivative of g(x). Factor i(m).
2*m**3/7
Let o(t) be the third derivative of -t**8/1176 + t**7/735 + t**6/105 - 2*t**5/105 + 2*t**2 + 4*t. Determine s so that o(s) = 0.
-2, 0, 1, 2
Factor 9/5*l**3 - 3/5*l**5 - 6/5*l**4 + 12/5*l**2 - 12/5*l + 0.
-3*l*(l - 1)**2*(l + 2)**2/5
Suppose y = -4*r + 11, -4*r - 9*y + 14 = -7*y. Let 6/5*w**3 + 0*w**r - 3/5*w**5 + 0*w + 3/5*w**4 + 0 = 0. What is w?
-1, 0, 2
Let r(n) be the second derivative of 2*n - 1/7*n**3 + 1/35*n**5 + 1/21*n**4 + 1/7*n**2 - 1/35*n**6 + 1/147*n**7 + 0. Suppose r(p) = 0. What is p?
-1, 1
Let s(a) be the first derivative of -12/5*a**5 + 4 + 0*a + 27/4*a**4 - 6*a**3 + 3/2*a**2. Solve s(l) = 0.
0, 1/4, 1
Let x = -5 + 29. Determine y, given that 3/2 + 3*y**5 + 21*y**2 + 9*y + x*y**3 + 27/2*y**4 = 0.
-1, -1/2
Let n be (-2)/8 + (-27)/(-12). Solve 8*x**3 + 6*x**3 - 16*x - x**5 + 10*x**4 + 3*x**5 - 2*x**n - 8 = 0 for x.
-2, -1, 1
Let t be ((-3)/(-1))/(3/(-80)). Let i be 6/33 - t/44. Solve -2/3*d**i - 2/3*d**3 + 2/3 + 2/3*d = 0.
-1, 1
Suppose 2*n + 6 = 0, 5*z + 4*n - 48 = 5*n. Let y = -6 + z. Let -d - 1 - d**2 - 2*d**3 + 2 + y*d**3 + 0*d = 0. What is d?
-1, 1
Suppose 2*a**4 + 1/2*a**5 + 2*a**3 - 1 - a**2 - 5/2*a = 0. Calculate a.
-2, -1, 1
Solve 0 - 8/3*f - 12*f**2 = 0 for f.
-2/9, 0
Suppose -7*s = 11*s - 36. Find c such that -2/3*c**s + 2/3*c + 2/9*c**3 - 2/9 = 0.
1
Let w(s) be the second derivative of -s**5/50 + s**4/10 - 2*s**3/15 + s. Let w(g) = 0. What is g?
0, 1, 2
Factor -27*t**4 - 147*t**2 + 147*t**2 + 21*t**5 + 6*t**3.
3*t**3*(t - 1)*(7*t - 2)
Factor 3/7*g**2 + 6/7*g + 3/7.
3*(g + 1)**2/7
Let p = -51 + 54. Factor 1/2*l - 7/4*l**p + 0 - 5/4*l**2.
-l*(l + 1)*(7*l - 2)/4
Let j(s) be the third derivative of -s**8/1176 - s**7/735 + s**6/140 + s**5/210 - s**4/42 + 35*s**2. What is r in j(r) = 0?
-2, -1, 0, 1
Suppose -s = -3*s - 4*u + 4, 4 = 4*u. Let h(a) be the second derivative of 1/10*a**5 - 1/12*a**4 + s + 4*a + 0*a**2 + 0*a**3 - 1/30*a**6. What is w in h(w) = 0?
0, 1
Let g(d) be the third derivative of -4*d**7/1575 - d**6/75 - d**5/50 - d**4/90 + 10*d**2. Solve g(y) = 0 for y.
-2, -1/2, 0
Suppose -q - 2 = -2*q. Suppose -18 = -4*m - q. What is v in -4/3*v**2 + 2/3*v**3 + 0 + 0*v + 2/3*v**m = 0?
-2, 0, 1
Let u(w) be the first derivative of -w**6/30 - 2*w**5/25 - w**4/20 - 19. Let u(x) = 0. What is x?
-1, 0
Let g(r) = 4*r**2 + 14*r + 10. Suppose -4*v + 6*v = 4. Let z(c) = c + 1. Let q(p) = v*z(p) - g(p). Find o such that q(o) = 0.
-2, -1
Suppose 4*w - 2*h - 16 = 2*h, -5*h - 15 = -4*w. Factor -j**3 - 25*j**4 + 3*j + w*j**2 + 24*j**4 + 2*j**3.
-j*(j - 3)*(j + 1)**2
Let g(u) = -2*u**3 - u**2 + 5*u + 1. Let h(k) = 2*k**3 + 2*k**2 - 6*k - 2. Let s(c) = -4*g(c) - 3*h(c). What is n in s(n) = 0?
-1, 1
Let y = 73 - 73. Let z(h) be the first derivative of 2/15*h**5 - 1 - 1/3*h**6 + 0*h**3 + y*h**2 + 1/3*h**4 + 0*h. Find t, given that z(t) = 0.
-2/3, 0, 1
Factor 2/3*m**2 + 0*m - 8/3.
2*(m - 2)*(m + 2)/3
Find i such that -36*i**4 + 2*i**2 + 37*i**4 - i**2 + 2*i**3 = 0.
-1, 0
Let 0 - 1/3*v**4 + 1/6*v**5 - 1/2*v**3 + 2/3*v**2 + 2/3*v = 0. What is v?
-1, 0, 2
Factor 9/4*g**3 - 2 - 3/2*g**2 - 5*g.
(g - 2)*(3*g + 2)**2/4
Determine o, given that -1/2 - 7/4*o - 5/4*o**3 - 9/4*o**2 - 1/4*o**4 = 0.
-2, -1
Let q be (-4)/(-16)*-2 - -1. Let t = -9/14 + 25/28. Factor -t - 1/4*l**2 + q*l.
-(l - 1)**2/4
Let 5*l**2 - 3*l**2 + l - 3*l = 0. Calculate l.
0, 1
Let x(s) be the first derivative of -3/2*s**4 + s**3 + 0*s - 3/5*s**5 + 4 + 3*s**2. Factor x(r).
-3*r*(r - 1)*(r + 1)*(r + 2)
Factor 0 + 12/7*y**4 + 2/7*y**5 + 24/7*y**3 + 0*y + 16/7*y**2.
2*y**2*(y + 2)**3/7
Let j(s) be the first derivative of -s**6/2 + 3*s**5/5 + 3*s**4/2 - 2*s**3 - 3*s**2/2 + 3*s + 5. Let j(b) = 0. What is b?
-1, 1
Let k be (-17)/204*(-5 + (-6)/(-2)). Factor -1/3*m - 1/6 - k*m**2.
-(m + 1)**2/6
Let b(z) = z**3 + 13*z**2 - 15*z - 11. Let a be b(-14). Factor -3*k - a*k**4 - 10*k**3 + 4*k**3 + 12*k + 3 - 3*k.
-3*(k - 1)*(k + 1)**3
Let g(i) be the second derivative of -i**5/70 + i**4/14 - i**3/7 + i**2/7 - 7*i. Let g(p) = 0. What is p?
1
Let o(f) = 7*f**3 - 2*f**2. Let r = 5 + -3. Let p(l) = 8*l**3 - l**2 - r*l**2 + l**2. Let d(w) = -6*o(w) + 5*p(w). Factor d(t).
-2*t**2*(t - 1)
Let d(i) = i**3 - 3*i**2 + 2*i - 2. Let v be d(3). Find f, given that -3*f**3 + 5*f**4 + f**v - 2*f**5 - f**5 = 0.
0, 1
Suppose -5*k - 5 = 5*v, 4*v + k = -2*k - 9. Let o be (-3)/(-12)*v*-2. Factor -6*s**o - 13*s**2 + 9*s**2 - 8*s**4 - 6*s**3 - 6*s**3.
-2*s**2*(s + 2)*(4*s + 1)
Suppose 0 = 5*k - 8 - 7. Let c(h) be the first derivative of 2/3*h**k + 0*h - 2 - h**2. What is m in c(m) = 0?
0, 1
Let g be (8/20)/((-260)/(-175)). Let f = g - -187/78. Solve f*z**4 + 0 + 0*z + 8/3*z**3 + 2/3*z**2 = 0.
-1/2, 0
Let q(y) be the third derivative of y**7/70 - 11*y**6/80 + 19*y**5/40 - 13*y**4/16 + 3*y**3/4 + 6*y**2. What is p in q(p) = 0?
1/2, 1, 3
Factor -6*v**2 + 4*v**2 - 6*v + 0*v**2.
-2*v*(v + 3)
Let o be 4/6*9/2. Let u = 59 - 411/7. Factor -6/7*k - u*k**o - 6/7*k**2 - 2/7.
-2*(k + 1)**3/7
Let l(f) be the first derivative of 7*f**3/15 - f**2/2 - 2*f/5 - 4. Factor l(u).
(u - 1)*(7*u + 2)/5
Let s(j) be the second derivative of -j**5/20 - j**4/4 - j**3/3 - 3*j. Factor s(p).
-p*(p + 1)*(p + 2)
Factor -2*t - 3*t**2 - 3*t**2 + 3*t**3 - 4*t + 3*t**2.
3*t*(t - 2)*(t + 1)
Let u(z) = -z + 3. Let i be u(1). Suppose -i*g = 5*h - 11, 9 = 3*g - 2*h + 2. Factor 8*w + 2 + 17/2*w**2 + 5/2*w**g.
(w + 1)*(w + 2)*(5*w + 2)/2
Let i(h) be the second derivative of 4*h - 3/50*h**5 + 0 + 1/5*h**3 + 2/5*h**2 - 1/15*h**4. Factor i(o).
-2*(o - 1)*(o + 1)*(3*o + 2)/5
Suppose 3*s = 6*s - 3, -s = 2*p - 5. Factor 0 + 4*x - 13*x + 0 - 3*x**p.
-3*x*(x + 3)
Let y = 2/11 - 19/165. Let g(a) be the second derivative of 2/75*a**6 - 1/15*a**4 + y*a**3 - 1/105*a**7 + 0 + 0*a**2 + 0*a**5 - 2*a. Solve g(j) = 0 for j.
-1, 0, 1
Let x = -209/6 + 35. Let b(f) be the first derivative of 2 - x*f**2 + 2/3*f - 1/9*f**3. Factor b(a).
-(a - 1)*(a + 2)/3
Let a(u) = u. Let s be a(-2). Let l be (s/(-20))/(5/20). Factor 0 + 2/5*g**2 + 0*g + l*g**3.
2*g**2*(g + 1)/5
Let f(k) be the first derivative of 0*k - 1/1