et q(u) be the third derivative of 0 + 2/33*u**3 - 1/385*u**7 - 7/660*u**6 - z*u**5 + 5*u**2 + 1/44*u**4 + 0*u. Factor q(a).
-2*(a + 1)**3*(3*a - 2)/11
Let r(g) = 67*g + 80. Let c be r(-5). Let u = c + 258. Determine x, given that 0 - 13/2*x**u - 11/2*x**2 + x = 0.
-1, 0, 2/13
Let q(u) be the second derivative of 1/21*u**3 - 1/70*u**5 - 1/21*u**4 + 0 - 3*u + 2/7*u**2. Solve q(b) = 0.
-2, -1, 1
Let o(r) be the second derivative of -r**9/5040 - r**8/1120 + 11*r**4/12 - 15*r. Let f(d) be the third derivative of o(d). Let f(y) = 0. Calculate y.
-2, 0
Let u(d) be the first derivative of -2*d**2 + 0*d - 4/3*d**3 + 4. What is c in u(c) = 0?
-1, 0
Let y(n) be the third derivative of n**5/20 + 5*n**4/8 + 2*n**3 - 34*n**2. Factor y(c).
3*(c + 1)*(c + 4)
Let j be (135/(-28))/(-9) - 2/8. Let h(x) be the first derivative of 8/7*x + 4/7*x**2 - j*x**3 + 3. Factor h(m).
-2*(m - 2)*(3*m + 2)/7
Let o be (3/2)/(-5*3/(-30)). Suppose -5*c + 1 = o*r, -21*c - r = -19*c - 1. Factor -5/2*d + 1/2*d**2 + c.
(d - 4)*(d - 1)/2
Suppose z = -x + 4*z - 3, x + 4*z + 3 = 0. Let q(p) = p**2 + p + 1. Let h be q(x). Factor 0*j - 3*j**2 - h*j + 3*j + j.
-3*j*(j + 1)
Let l(c) be the first derivative of 5*c**4/24 - 5*c**2 - 31*c - 17. Let o(n) be the first derivative of l(n). Factor o(v).
5*(v - 2)*(v + 2)/2
Let b be (18/72)/((-1)/(-4)). Suppose 76 = 5*w + b. Factor 180*u**2 + 375*u**4 - 24*u - w + 15 - 450*u**3.
3*u*(5*u - 2)**3
Suppose 4*g - 8*g = -12. Factor 5*y - 2*y + 12 - y**g - 14 + 3*y**2 - 2*y - y**4.
-(y - 1)**2*(y + 1)*(y + 2)
Let d = -10832/3 + 3611. Factor d*l**4 - 1/3*l**2 + 0 + 0*l**3 + 0*l.
l**2*(l - 1)*(l + 1)/3
Let v(a) = a**3 - 15*a**2 - 8*a - 4. Let j(g) = 2*g**3 - 45*g**2 - 22*g - 11. Let w(t) = -4*j(t) + 11*v(t). Factor w(q).
3*q**2*(q + 5)
Let x = 3093 + -3090. What is d in 0*d - 1/6*d**2 + 7/6*d**4 + 1/3*d**x + 2/3*d**5 + 0 = 0?
-1, 0, 1/4
Suppose 4*i = 7*i - 201. Factor -150*d**3 + 125*d**4 - 55*d**2 + i*d + 5*d - 12*d + 20.
5*(d - 1)**2*(5*d + 2)**2
What is b in 6960*b - 105*b**3 + 4071 + 4*b**4 + 3832*b**2 + 345*b**3 - 707 = 0?
-29, -1
Let m be ((-2)/(-17))/(68/(-867)*-3). Factor 1/2*r**5 + 5*r**2 + m*r**3 - 2*r - 4 - 2*r**4.
(r - 2)**3*(r + 1)**2/2
Let m(g) = -5*g**2 - 4*g - 4. Let l be m(-2). Let z be (-66)/(-24) - 20/l. Find i, given that 1/7 + 2/7*i**3 - 2/7*i + 0*i**2 - 1/7*i**z = 0.
-1, 1
Let f = 1753/869 + 13/79. Factor 2/11*d**4 - 16/11*d - 12/11*d**3 + f*d**2 + 0.
2*d*(d - 2)**3/11
Let y(r) = 24*r + 3. Let l be y(3). Determine i, given that 37 - 252*i - 8 + 90 - 11 - 6*i**3 + l*i**2 = 0.
1/2, 6
Let s(j) be the first derivative of -2*j**3/3 - 8*j**2 - 32*j + 58. Factor s(n).
-2*(n + 4)**2
Let j(p) be the second derivative of -2*p**6/15 + 21*p**5/5 - 20*p**4/3 + 2*p - 1. Solve j(a) = 0 for a.
0, 1, 20
Let x be ((-2)/(-3))/(13/3). Let k(g) = -2*g**3 + 6*g**2 + 185*g - 555. Let b be k(3). Factor 2/13*h**3 + b - x*h**2 + 0*h.
2*h**2*(h - 1)/13
Let b(i) be the third derivative of -i**7/840 + i**6/240 - i**4/8 + 6*i**2. Let h(o) be the second derivative of b(o). Find a such that h(a) = 0.
0, 1
Let y be (-28)/(-84)*(0 - 0 - -18). Let w be (10/y + -3)/(12/(-27)). Factor -4/7*m - 2*m**w + 18/7*m**2 + 0.
-2*m*(m - 1)*(7*m - 2)/7
Let o(t) be the third derivative of t**5/140 + t**4/4 + 20*t**3/7 - 954*t**2. Factor o(h).
3*(h + 4)*(h + 10)/7
Let n(m) = 21*m**4 - 5*m**4 - 4 + 0*m**2 - 4*m**2 - 6*m**2 - 20*m + 16*m**3. Let x(h) = -h**4 + h**3 + h. Let t(f) = 2*n(f) + 4*x(f). What is o in t(o) = 0?
-1, -2/7, 1
Let p = 50 - -4. Let i = 166/3 - p. Suppose -4/3*k**2 - 2/3*k**3 + i + 2/3*k = 0. Calculate k.
-2, -1, 1
Let b = -373037/121 + 3083. Let a = 950/363 + b. What is g in a + 10/3*g + 2/3*g**2 = 0?
-4, -1
Determine q, given that -17*q**2 + 4*q**2 - 88*q + 4*q**4 + 36*q**3 + 4*q**3 - 39*q**2 = 0.
-11, -1, 0, 2
Let t be (-5)/25 - (-530)/150. Determine y so that t*y - 4/3 + 2/3*y**3 - 8/3*y**2 = 0.
1, 2
Let k(p) be the first derivative of 2*p**3/21 - 2*p**2/7 - 6*p/7 - 58. Factor k(u).
2*(u - 3)*(u + 1)/7
Let g(z) be the first derivative of -z**5/120 - z**4/12 - 11*z**2/2 + 9. Let o(a) be the second derivative of g(a). Factor o(h).
-h*(h + 4)/2
Let u(p) be the first derivative of -p**5/15 + 2*p**3/3 - 5*p**2 - 7. Let n(a) be the second derivative of u(a). Suppose n(b) = 0. What is b?
-1, 1
Let u(r) be the first derivative of -r**4/12 + 2*r**3/9 - r**2/6 + 214. Find i such that u(i) = 0.
0, 1
Let l be (-50)/(-6) + (-24)/18. Let a(r) be the third derivative of 0 + 0*r**6 + 0*r**3 + 0*r**4 - 1/15*r**5 + 9*r**2 + 0*r + 2/105*r**l. Factor a(o).
4*o**2*(o - 1)*(o + 1)
Let d(o) = o**3 - 3*o**2 + 3*o. Let u be d(2). Factor -h - 9*h - 9*h + 5*h**u + 9*h.
5*h*(h - 2)
Let x(q) be the third derivative of 0*q + 1/48*q**5 + 1/840*q**7 + 1/120*q**6 + 0 + 0*q**3 - 20*q**2 + 1/48*q**4. Solve x(i) = 0 for i.
-2, -1, 0
Let r(o) be the third derivative of 0*o**3 - 1/12*o**4 + 0 - 12*o**2 + 0*o + 1/120*o**5. Factor r(q).
q*(q - 4)/2
Let l be 6/5 - 4/20. Let s be 1 - l/((-2)/36). Find u such that 2*u**2 - 1 + 23*u + 3 - s*u = 0.
-1
Suppose 2*y = 5*a - 16, 2*y - y - 7 = -5*a. Suppose 4*h**3 - 2*h**3 + 646*h**a - 644*h**2 = 0. What is h?
-1, 0
Suppose 3*p - 4*i = 28, 2*p + 0*i + 3*i + 4 = 0. Determine h, given that -3*h**3 + 413*h**p - 3*h**3 - 411*h**4 - 2*h + 6*h**2 = 0.
0, 1
Let o(a) be the third derivative of a**8/2016 - a**7/180 - a**6/40 - a**5/180 + 17*a**4/144 + a**3/4 - 155*a**2. Factor o(j).
(j - 9)*(j - 1)*(j + 1)**3/6
Let r be (-2 - -4 - 0) + 16/12. Suppose -r*g**2 + 0 + 8*g**4 - 8/3*g**3 + 4/3*g = 0. What is g?
-2/3, 0, 1/2
Let x = -323 + 1624/5. Suppose 2*t = t + 2. Factor -6/5 - 3/5*a**t - x*a.
-3*(a + 1)*(a + 2)/5
Factor -648*a - 18*a**4 + 1944 + 478/3*a**3 + 2/3*a**5 - 414*a**2.
2*(a - 9)**3*(a - 2)*(a + 2)/3
Suppose 0 = -135*l + 179*l - 156 - 20. Find q, given that -7/3*q**3 + 0 + q**2 + 5/3*q**5 - q**l + 2/3*q = 0.
-1, -2/5, 0, 1
Suppose -3*g - 5 = -23. Let t(x) be the second derivative of 4/3*x**3 + 4*x**2 + 4*x - 1/5*x**5 + 0 - 1/2*x**4 + 1/15*x**g. Let t(z) = 0. What is z?
-1, 2
Suppose -p = 4*p - 15. Determine s so that 13*s**3 - 27*s**2 - 2*s - s**p + 8*s = 0.
0, 1/4, 2
Suppose -2*d = 3*w - 11, -7*w + 12 = -4*w + 3*d. Suppose 16/7*n**2 + 2*n**4 + 0 - 38/7*n**w + 8/7*n = 0. Calculate n.
-2/7, 0, 1, 2
Let a(q) = 2*q**2 + 7*q + 10. Let g be a(-4). Factor -9*i - i - 7*i**2 - 25*i**3 - 14*i**2 - g*i**2.
-5*i*(i + 1)*(5*i + 2)
Let f(s) = -s**3 + 4*s**2 + 3. Let w be f(4). Suppose -3 = -w*y + 6. Factor 12/5 - y*c + 3/5*c**2.
3*(c - 4)*(c - 1)/5
Let j(c) be the third derivative of c**6/30 - c**5/3 + 4*c**4/3 - 8*c**3/3 + 143*c**2. Find h such that j(h) = 0.
1, 2
Let y be (-1)/1*(-49 + (-3)/3). Let p = y + -45. Factor 0*x**3 + 3/5*x - 6/5*x**4 + 0 - 3/5*x**p + 6/5*x**2.
-3*x*(x - 1)*(x + 1)**3/5
Suppose 33 - 23 = 5*a. Factor -9*b**2 + b**2 + 4*b**a + b**2 + b**3.
b**2*(b - 3)
Let y(v) be the second derivative of -3*v**5/20 - v**4/2 + 41*v**3/2 + 63*v**2 - 5*v - 5. Suppose y(o) = 0. What is o?
-7, -1, 6
Let q = -2/23817 - -47648/166719. Solve 8/7 + 16/7*s + q*s**3 + 10/7*s**2 = 0 for s.
-2, -1
Let k(i) = -i**3 + i**2 - i + 16. Let y be k(0). Suppose -4 = -5*x + y. Let 3*a**2 - 3*a**2 - 3*a**2 + x*a**2 = 0. What is a?
0
Let g = 1489/2 - 744. Let p(a) be the first derivative of 0*a**3 + g*a**2 - 1/12*a**4 + 9 - 2/3*a. Suppose p(m) = 0. What is m?
-2, 1
Let c be ((-2)/(-1))/(3/3). Let d be (400/(-25)*-2)/34. Factor -d*j - 32/17 - 2/17*j**c.
-2*(j + 4)**2/17
Let v = 103/832 + 1/832. Let c(i) be the third derivative of v*i**3 - 3*i**2 - 3/32*i**4 + 0*i + 0 + 3/80*i**5 - 1/160*i**6. Determine t so that c(t) = 0.
1
Let f(d) be the second derivative of -1/3*d**4 + 3/2*d**2 + 8*d + 0 + 1/6*d**3. Solve f(z) = 0.
-3/4, 1
Let n(h) be the third derivative of 5/24*h**4 + 0 + 0*h + 1/12*h**5 - 5/3*h**3 + h**2. Factor n(l).
5*(l - 1)*(l + 2)
Let o = -6634 + 6639. Suppose -2/7*y + 0 + 1/7*y**3 + 3/7*y**4 + 1/7*y**o - 3/7*y**2 = 0. What is y?
-2, -1, 0, 1
Let f be 6/(((-945)/10)/27)*114/(-2). Solve f*a**3 + 0*a + 0 - 146/7*a**4 - 162/7*a**2 + 8/7*a**5 = 0 for a.
0, 1/4, 9
Let c(s) be the second derivative of 9*s**4/4 + 77*s**3 + 51*s**2/2 - 13*s - 4. Factor c(i).
3*(i + 17)*(9*i + 1)
Factor 33/7*q**4 + 141/7*q**2 + 54/7*q + 120/7*q**3 + 0.
3*q*(q + 1)**2*(11*q + 18)/7
Let r(i) be the fir