
Let g(z) be the third derivative of 0*z + 0 + 5*z**2 + 11/30*z**5 + 1/18*z**6 + 16/9*z**3 + 1/315*z**7 + 10/9*z**4. Factor g(l).
2*(l + 1)**2*(l + 4)**2/3
Let t = -20830 + 20832. What is u in 6/7*u + 2/7*u**t + 4/7 = 0?
-2, -1
Let c = 11/73 + 113/219. Let -4/9*s - c*s**2 - 1/9*s**4 + 8/9 + 5/9*s**3 = 0. What is s?
-1, 2
Let m be (4 - -2)/((-39)/(-2)). Let w be (-1)/(5 + (-138)/12). Suppose m + w*l**3 - 4/13*l**2 - 2/13*l = 0. What is l?
-1, 1, 2
Let p(d) = -d**5 - d**3 + d**2 - d. Let g(b) = 12*b**5 + 5*b**4 + 2*b**3 - 2*b**2 + 2*b. Suppose -4 - 10 = 14*f. Let n(y) = f*g(y) - 2*p(y). Factor n(z).
-5*z**4*(2*z + 1)
Let j(i) be the first derivative of -i**4 - 2/5*i**5 + 0*i - 2/3*i**3 + 21 + 0*i**2. Let j(g) = 0. What is g?
-1, 0
Let b(a) be the third derivative of 0*a**7 - 1/112*a**8 + 1/10*a**5 - a**3 - 4 + 0*a - 3/8*a**4 + 1/10*a**6 - 2*a**2. Factor b(v).
-3*(v - 2)*(v - 1)*(v + 1)**3
Let g(l) be the first derivative of l**6/3 - 16*l**5/5 - 13*l**4 + 112*l**3 + 441*l**2 - 461. Factor g(n).
2*n*(n - 7)**2*(n + 3)**2
Let j(g) be the second derivative of 2*g + 0*g**2 + 0 - 1/15*g**4 - 8/15*g**3. Find w such that j(w) = 0.
-4, 0
Let m(l) be the third derivative of l**8/112 - l**7/35 + l**5/10 - l**4/8 - 39*l**2. Factor m(x).
3*x*(x - 1)**3*(x + 1)
Let i be (8/(-14))/((4/(-70))/((-12)/(-180))). Factor 1/3*l**3 - i*l**2 + 0 + 0*l.
l**2*(l - 2)/3
Let c(a) be the first derivative of a**8/560 + a**7/140 - a**5/20 - a**4/8 - 2*a**3 - 40. Let x(g) be the third derivative of c(g). Find q such that x(q) = 0.
-1, 1
Let s(y) be the second derivative of 0*y**5 + 1/28*y**7 + 0*y**2 - 23*y + 0 + 1/4*y**4 - 1/10*y**6 - 1/4*y**3. Factor s(p).
3*p*(p - 1)**3*(p + 1)/2
What is d in 13*d - 13*d + 61*d**2 - 52*d**2 - 3*d**3 = 0?
0, 3
Let u(s) be the second derivative of s**6/45 + 3*s**5/2 - s**4/18 - 5*s**3 - 3*s + 66. Factor u(l).
2*l*(l - 1)*(l + 1)*(l + 45)/3
Suppose -10 + 2*w**2 - 15 + w**3 + 15*w + 15*w**2 - 8*w**2 = 0. What is w?
-5, 1
Suppose 2*w + 3*w - l = 16, 2*l = -2. Let p(z) be the second derivative of 1/10*z**5 - 1/3*z**w + 0*z**4 + 0 + 0*z**2 - z. Let p(c) = 0. What is c?
-1, 0, 1
Suppose d - 14 = 4*w, 2*d + 5*w - 1 = 1. Let l(g) be the second derivative of 0*g**2 + 1/6*g**3 - d*g + 0 - 1/12*g**4. Let l(i) = 0. Calculate i.
0, 1
Let n be (1 - 5)/(-13 + 3). Let h be (13/(-5) - 3) + (-18 - -24). Factor -2/5*m**3 - n*m**2 + 2/5*m + h.
-2*(m - 1)*(m + 1)**2/5
Let b be (-18)/(-144)*(-1 + (-16)/(-10)). Let a(z) be the third derivative of 3/4*z**4 + b*z**6 - z**2 + z**3 + 0 + 1/140*z**7 + 0*z + 13/40*z**5. Factor a(n).
3*(n + 1)**2*(n + 2)**2/2
Let a(q) = 6*q**2 + 79*q - 80. Let p(j) = -5*j**2 - j + 1. Let l(b) = -a(b) - p(b). What is w in l(w) = 0?
-79, 1
Suppose -45 = -t - 8*t. Determine a so that -9*a + 4*a**2 - 8*a - 4*a**4 - 2*a**t + 19*a = 0.
-1, 0, 1
Suppose 3*b - 3*c = 3 + 15, c + 18 = 5*b. Let h = 5 - 2. Find m such that 8 - 4*m**2 + 3*m**2 + h*m + b*m**2 + 5*m = 0.
-2
Suppose a - 11 = -4*n, 4*a + 0*n = 3*n + 6. Factor 4 + 2 + 3*s**a + 0 - 9*s.
3*(s - 1)**2*(s + 2)
Let j be ((-148)/(-1998))/(2/468). Solve 0 - 4/3*h**5 - 4/3*h**4 + 28/3*h**3 + j*h**2 + 8*h = 0 for h.
-2, -1, 0, 3
Let x(a) = -3*a**2 - 1. Let y(s) = 2*s**2 - 8*s + 1. Let r(k) = x(k) + y(k). Let r(l) = 0. What is l?
-8, 0
Factor 6/7*d**2 + 0 - 2/7*d**3 + 8/7*d.
-2*d*(d - 4)*(d + 1)/7
Factor 16/5*k + 1/5*k**2 - 17/5.
(k - 1)*(k + 17)/5
What is q in 12/7 + 33/7*q**2 + 72/7*q = 0?
-2, -2/11
Let r(w) = 85*w**2 - 91*w + 6. Let c(y) = -86*y**2 + 92*y - 6. Suppose -11*m = -7*m + 20. Let g(v) = m*r(v) - 4*c(v). Solve g(k) = 0 for k.
2/27, 1
Let h(d) = -50*d - 1048. Let b be h(-21). Factor 0 - 2/3*q**3 + 1/3*q**4 + 0*q + 0*q**b + 1/3*q**5.
q**3*(q - 1)*(q + 2)/3
Let x(h) be the third derivative of -h**7/210 - 17*h**6/120 - 19*h**5/30 + 7*h**4/3 + 510*h**2. Factor x(k).
-k*(k - 1)*(k + 4)*(k + 14)
Let p(s) = -10*s + 6. Let y be p(2). Let x = 26 + y. Factor t**4 + x - t**4 + 6*t**3 - 9*t**2 - 10*t - 2*t + 3*t**4.
3*(t - 1)**2*(t + 2)**2
Let h(z) be the first derivative of -z**5/40 + 3*z**4/32 - z**3/24 - 3*z**2/16 + z/4 - 77. Let h(q) = 0. What is q?
-1, 1, 2
Let f(w) be the second derivative of 0 - 1/12*w**4 - 4*w + 3/2*w**2 + 1/3*w**3. Factor f(c).
-(c - 3)*(c + 1)
Let a be (-406)/(-116)*(-8)/(-14). Let y(f) be the second derivative of 1/3*f**3 + 0*f**a + 7*f + 0 - 1/6*f**4. Find c such that y(c) = 0.
0, 1
Solve 1062*l - 7*l**3 - 1046*l + 12*l**2 + 8*l**4 + 0*l**5 - 4*l**5 - 44*l**2 + 19*l**3 = 0.
-2, 0, 1, 2
Let p = 142 + -101. Determine z so that -3*z**4 - 6 - p*z**2 - 31*z**2 + 45*z**2 - 21*z - 15*z**3 = 0.
-2, -1
Let z(p) be the first derivative of -8*p**5/7 + 13*p**4/14 + 20*p**3/21 - 3*p**2/7 + 82. Determine t, given that z(t) = 0.
-3/5, 0, 1/4, 1
Let q(r) be the first derivative of -4*r**5/5 + 12*r**4 - 88*r**3/3 - 168*r**2 - 196*r + 142. Factor q(v).
-4*(v - 7)**2*(v + 1)**2
Factor 19/2*l - 23/2*l**2 - 2 + 5/2*l**3 + 3/2*l**4.
(l - 1)**2*(l + 4)*(3*l - 1)/2
Solve -8*l**2 + 12*l**2 - 60*l + 18 - 9*l**2 - 73 = 0 for l.
-11, -1
Let w(b) = 2*b**2 + 18*b - 18. Let u be w(-10). Let o(t) be the first derivative of 3/7*t**u + 4/7*t + 2/21*t**3 - 3. Solve o(d) = 0 for d.
-2, -1
Let s(k) = k**2 - 15*k + 17. Let q(x) = x**2 - 3*x - 1. Let h(z) = 3*q(z) - s(z). Let h(m) = 0. Calculate m.
-5, 2
Let w(a) be the first derivative of a**7/2100 - a**5/600 + 5*a**2/2 + 28. Let n(y) be the second derivative of w(y). Determine m, given that n(m) = 0.
-1, 0, 1
Let r(u) = -18*u. Let z be r(-1). Solve a**3 + 2*a**3 + 27*a + 31 - 43 - z*a**2 = 0.
1, 4
Let n(s) be the second derivative of -11*s - 8*s**2 + 16/3*s**3 - s**4 + 0. Factor n(d).
-4*(d - 2)*(3*d - 2)
Let c(y) be the first derivative of y**6/72 - y**5/6 + 5*y**4/6 - 5*y**3 + 2. Let m(r) be the third derivative of c(r). Factor m(j).
5*(j - 2)**2
Suppose -v - 4*v = -10. Solve -30*l + 48*l**3 - 27 - 15*l + 12*l**v + 12*l**2 = 0 for l.
-3/4, 1
Find m such that -8/3*m**5 - 2/3*m - 82/9*m**4 + 34/9*m**2 - 2*m**3 + 0 = 0.
-3, -1, 0, 1/4, 1/3
Let d = -7265 - -21803/3. Factor 2/3*h**3 + d*h**2 + 4/3 + 10/3*h.
2*(h + 1)**2*(h + 2)/3
Factor 20*o**3 - 12*o**2 + 5*o**4 - 6*o**2 + 10*o**2 - 17*o**2.
5*o**2*(o - 1)*(o + 5)
Let u(m) be the third derivative of -m**6/40 - 3*m**5/10 - 9*m**4/8 - m**2 - 45*m. Factor u(o).
-3*o*(o + 3)**2
Let t(v) be the second derivative of v**5/10 + v**4/3 + v - 16. Factor t(r).
2*r**2*(r + 2)
Let j(c) be the second derivative of -c**6/4 - 9*c**5/10 + 11*c**4/8 + 3*c**3/2 + 52*c. Let j(v) = 0. Calculate v.
-3, -2/5, 0, 1
Let o(g) be the first derivative of -g**7/840 - 7*g**6/360 - g**5/15 + 2*g**4/3 - 7*g**3/3 - 24. Let k(n) be the third derivative of o(n). Factor k(t).
-(t - 1)*(t + 4)**2
Let q(x) be the third derivative of 0*x - 9*x**3 - 1/105*x**7 - 6/5*x**5 + 4*x**2 + 0 + 1/6*x**6 + 9/2*x**4. Let q(s) = 0. What is s?
1, 3
Let k be 9/189*((-825)/4)/5. Let p = -12/7 - k. Find r, given that 0 + 1/2*r + p*r**2 = 0.
-2, 0
Suppose 4*h + 407 - 499 = 0. Let d(v) = v**3 - 24*v**2 + 24*v - 23. Let s be d(h). Factor 24/11*o**4 - 4/11*o**2 + 14/11*o**5 + 6/11*o**3 + s*o + 0.
2*o**2*(o + 1)**2*(7*o - 2)/11
Suppose 0 = -16*u + 6*u + 300. Let w be ((-1)/6)/(-2*3/u). Suppose -1/6*m**3 - 1/6*m**2 + w*m - 1/2 = 0. What is m?
-3, 1
Let g(o) be the second derivative of o**6/90 - o**5/20 + o**4/18 + o + 87. Factor g(h).
h**2*(h - 2)*(h - 1)/3
Suppose 30*w**3 - 45*w**2 + 30*w**3 - 55*w**3 - 50*w = 0. What is w?
-1, 0, 10
Let r be (-48)/(-12) + 3694*(-3)/2982. Let b = r + -10/71. Solve -1/7*u + b*u**2 + 0 = 0 for u.
0, 1
Suppose 2*s + 4*y + 14 = 0, -8*s + 86*y + 49 = 81*y. Suppose 1/7*u**4 - 1/7*u**2 + 0*u - 1/7*u**5 + 1/7*u**s + 0 = 0. Calculate u.
-1, 0, 1
Let l(v) be the second derivative of 0*v**5 + 0*v**2 - 1/1260*v**6 + 0 + 0*v**4 + 2*v - 1/6*v**3. Let r(h) be the second derivative of l(h). Factor r(a).
-2*a**2/7
Let y(x) be the second derivative of x**7/42 + x**6/8 - x**5/12 - 5*x**4/8 - 9*x**2/2 + 24*x. Let a(h) be the first derivative of y(h). Factor a(b).
5*b*(b - 1)*(b + 1)*(b + 3)
Let v(o) be the second derivative of 3*o**5/5 + 31*o**4/3 + 20*o**3/3 + 57*o - 1. Factor v(s).
4*s*(s + 10)*(3*s + 1)
Suppose 0 = 2*d - 4*k - 38, -4*k + 57 = d + 2*d. Factor -12*u + d*u - 10*u - 3*u**2.
-3*u*(u + 1)
Let 10/3 - 20*o**2 - 59/3*o**3 + 23/3*o + 14/3*o