be the third derivative of 6/5*l**5 + 0*l + 1/105*l**7 + 0*l**4 + 0*l**3 + 0 + 1/5*l**6 - 25*l**2. Suppose d(a) = 0. What is a?
-6, 0
Suppose 335*r - 235*r = 800. Factor -40 - 2/5*i**2 - r*i.
-2*(i + 10)**2/5
Suppose 0 = -4*z + 5*q - 60, 0*z - 4*q - 15 = z. Let l(r) = 4*r**3 + r**2 + 5*r. Let x(i) = -i**3 - i. Let o(s) = z*x(s) - 3*l(s). Find y, given that o(y) = 0.
0, 1
Let u(o) be the second derivative of 0 + 11*o + 5/2*o**3 - 5/12*o**4 + 0*o**2. Factor u(c).
-5*c*(c - 3)
Let a(v) be the third derivative of v**8/1344 - 11*v**7/840 + 228*v**2. Find i, given that a(i) = 0.
0, 11
Let x be (113/(-21) + (-5)/(-1))/(64/(-96)). Determine q, given that -2/7*q - 2/7*q**3 + 0 - x*q**2 = 0.
-1, 0
Let o(a) = a**4 + a**3 + a**2 - 1. Let w(t) = 8*t**3 + 8*t**2 - 10*t - 10. Let y(q) = -2*o(q) - w(q). Let y(s) = 0. What is s?
-3, -2, -1, 1
Find i such that -3/5*i**3 + 1/5*i**4 + 0*i + 0 + 2/5*i**2 = 0.
0, 1, 2
Let f(z) be the third derivative of z**5/240 - 11*z**4/96 + 7*z**3/6 + 6*z**2 - 4*z. Factor f(l).
(l - 7)*(l - 4)/4
Solve 0 + 0*d - 6/7*d**5 + 0*d**2 - 8/7*d**3 + 26/7*d**4 = 0.
0, 1/3, 4
Let k(m) = -m**3 + m**2 + 4. Let j be k(0). Suppose -2*g + r = 5 - 3, -2*g = 2*r - j. Factor -2/11*p**3 + g - 4/11*p - 6/11*p**2.
-2*p*(p + 1)*(p + 2)/11
Let c be -1 - (-108)/21 - 5/35. Let j(s) be the third derivative of 0 + 5*s**2 + 1/6*s**c + 1/30*s**5 + 0*s - s**3. Factor j(h).
2*(h - 1)*(h + 3)
Let g = -16 - -16. Let x(k) be the second derivative of -2/15*k**3 + 2/15*k**4 - 2*k + 0*k**2 + g. Let x(c) = 0. What is c?
0, 1/2
Let m(c) = -151*c - 9511. Let k be m(-63). Let q(g) = g**3 + 3*g**2 + g - 2. Let t be q(-2). Factor 16/5*p**k - 32/5*p - 2/5*p**3 + t.
-2*p*(p - 4)**2/5
Let o(k) be the second derivative of -k**7/357 + k**6/85 + 3*k**5/170 - 7*k**4/102 - 2*k**3/17 - 214*k. Let o(h) = 0. Calculate h.
-1, 0, 2, 3
Let c = 461 + -456. Let s(g) be the second derivative of 1/160*g**5 + 0*g**2 - 1/48*g**3 + c*g + 0 + 0*g**4. Factor s(k).
k*(k - 1)*(k + 1)/8
Let z be (-2 - 279/12)*(-32)/(-36). Let x = -22 - z. Determine f so that 0*f**3 - 2/3*f**2 + 2/9*f**4 + 0 - x*f = 0.
-1, 0, 2
Let s = 1003/1348 - -2/337. Let o(l) be the second derivative of -3*l - s*l**4 + 0 + 0*l**3 + 3/20*l**5 + 6*l**2. Solve o(b) = 0.
-1, 2
Let x(d) = -d**3 + 9*d**2 - 10*d - 24. Let b be x(7). Let n(l) be the third derivative of -1/72*l**b - 6*l**2 - 1/60*l**5 + 0*l + 0 + 1/9*l**3. Factor n(g).
-(g + 1)*(3*g - 2)/3
Let d(u) be the second derivative of -u**7/504 - u**6/48 + u**4/6 - 5*u**2/2 - 30*u. Let m(q) be the third derivative of d(q). Factor m(a).
-5*a*(a + 3)
Let t(l) = -l**3 - 3*l**2 + 3*l + 3. Let d be t(-3). Let v(g) = g**3 + 7*g**2 + 4*g - 10. Let q be v(d). Factor 2/3*y**3 - q*y**2 + 2*y - 2/3.
2*(y - 1)**3/3
Let y(w) be the second derivative of -w**7/210 - 32*w**6/75 + 131*w**5/100 - 11*w**4/10 + 507*w. Factor y(l).
-l**2*(l - 1)**2*(l + 66)/5
Let 54/11 - 18/11*q - 6/11*q**2 + 2/11*q**3 = 0. Calculate q.
-3, 3
Let p = -12 + 22. Let x be (15/p)/((-3)/(-4)). Factor -6*j**x + j**2 + 9*j**2 - 16 + 12*j.
4*(j - 1)*(j + 4)
Find f, given that 123*f - 93*f**2 + 74*f**2 - 30 - 101*f**2 = 0.
2/5, 5/8
Let i(f) be the first derivative of -f**5/2 - 15*f**4 - 295*f**3/3 + 390*f**2 - 845*f/2 - 250. Solve i(o) = 0.
-13, 1
Let w(a) = 17*a**2 - a - 33. Let c(t) = 63*t**2 - 5*t - 131. Let p(v) = 6*c(v) - 22*w(v). Determine j so that p(j) = 0.
-3, 5
Solve 0 + 3/7*g**3 - 90/7*g**2 + 0*g = 0.
0, 30
Factor 25*g**2 - 6*g**2 + 57*g + 102 - g**2 - 15*g**2.
3*(g + 2)*(g + 17)
Factor 4523*c**2 - 8*c - 3 - 4535*c**2 + 7.
-4*(c + 1)*(3*c - 1)
Let r = 4 - 0. Let y = 13 - r. Factor -3*h + 4*h**4 - 2*h**3 + y*h**2 - h**4 - 4*h**3 - 3*h**3.
3*h*(h - 1)**3
Let u(c) be the third derivative of -1/6*c**4 - 12*c**2 + 1/30*c**6 + 0*c + 1/35*c**7 - 1/10*c**5 + 0*c**3 + 0. Factor u(i).
2*i*(i - 1)*(i + 1)*(3*i + 2)
Factor -2/3*k**2 + 0*k + 0 - 2/3*k**4 - 4/3*k**3.
-2*k**2*(k + 1)**2/3
Let y be (3 - 20/6)*-18. Suppose 3*z = -0*q + 3*q + 6, 4*q = -3*z + y. Factor q*a - a**3 + 2*a**4 - 2*a + 6*a**2 - 6*a**3 + a**3.
2*a*(a - 1)**3
Let k(z) be the first derivative of -z**4/16 + z**3/3 + z**2/8 - z - 23. Suppose k(d) = 0. What is d?
-1, 1, 4
Let v(g) be the first derivative of -4*g**3/9 + 44*g**2/3 - 484*g/3 + 91. Determine k so that v(k) = 0.
11
Let y(v) be the second derivative of 0*v**4 + 19*v + 0 + 1/10*v**6 + 0*v**2 + 1/4*v**3 - 9/40*v**5. Factor y(l).
3*l*(l - 1)**2*(2*l + 1)/2
Let c = 3 + 1. Suppose -c*i + 17 = 5*z, -2*i + 5 + 6 = 3*z. Find h such that -10*h + h**2 - h**4 + 3*h**3 + 3*h + z*h - h**5 = 0.
-2, -1, 0, 1
Factor 29015*d**3 + 13*d**2 - 29013*d**3 + 32*d + 3*d**2.
2*d*(d + 4)**2
Let p(m) = 5*m**5 + 7*m**4 + m**3 + m**2 - 2*m. Let q(r) = -11*r**5 - 16*r**4 - 3*r**3 - r**2 + 4*r. Let w(h) = 9*p(h) + 4*q(h). Determine n so that w(n) = 0.
-2, 0, 1
Let h(d) be the third derivative of d**6/60 - 2*d**5/15 + d**4/3 + 2*d**2 + 13*d. Let h(k) = 0. Calculate k.
0, 2
What is l in 3/7*l**4 - 9/7*l**3 + 9/7*l + 3/7*l**2 - 6/7 = 0?
-1, 1, 2
Suppose -3 = 3*b - 12. Let j be 11/b - 16/24. Factor -g**5 + 3 - 3 + 2*g**5 - g**j.
g**3*(g - 1)*(g + 1)
Let r be (((-180)/(-42) + -4)/(-10))/(-2). Let t(h) be the second derivative of 0*h**2 + 0*h**3 + 0 + 1/21*h**4 - 4*h - r*h**5. Suppose t(v) = 0. What is v?
0, 2
Let n(y) be the first derivative of -y**3/3 + y**2 - y + 443. Factor n(u).
-(u - 1)**2
Let o = 2022 + -2018. Find u such that -3/7*u**3 - 4/7*u + 1/7*u**5 + 0 - 8/7*u**2 + 2/7*u**o = 0.
-2, -1, 0, 2
Let s(k) be the third derivative of -k**5/70 - 3*k**4/28 + 4*k**3/7 - 67*k**2. Find o, given that s(o) = 0.
-4, 1
Let i(m) = -m**3 - 7*m**2 - m - 2. Let a be i(-7). Suppose -4*l = a*r - 0*l + 10, -21 = 2*r + 5*l. Factor 2/7*v**3 - 2/7*v + 2/7*v**r - 2/7.
2*(v - 1)*(v + 1)**2/7
Let h(c) be the third derivative of -5*c**6/24 - c**5/30 + 15*c**2 - 13. Solve h(t) = 0 for t.
-2/25, 0
Suppose 47*x + 26*x = -5*x + 156. Factor -24/13*l + 2/13*l**x + 72/13.
2*(l - 6)**2/13
Factor 450*i**2 + 4*i**5 + 135 - 4*i - 401*i - 5*i**5 - 230*i**3 + i**5 - 5*i**5 + 55*i**4.
-5*(i - 3)**3*(i - 1)**2
Let v(p) be the first derivative of 14 + 1/3*p**3 + 3/2*p**2 - 4*p. Factor v(m).
(m - 1)*(m + 4)
Let k(b) = b**3 - 24*b**2 + 77*b + 63. Let n be k(20). Factor 4/7*x**2 + 2/7*x**5 + 0*x + 0 + 10/7*x**n + 8/7*x**4.
2*x**2*(x + 1)**2*(x + 2)/7
Suppose -21*w = 100*w - 242. Factor -3/5*y + 3/5*y**3 + 0 + 0*y**w.
3*y*(y - 1)*(y + 1)/5
Let s(a) be the first derivative of 5*a**6/12 + 9*a**5/4 + 25*a**4/8 + 5*a**3/4 - 488. Solve s(x) = 0 for x.
-3, -1, -1/2, 0
Let i(k) be the third derivative of -k**6/40 + 21*k**5/10 - 41*k**4/8 + 3*k**2 + 80. Suppose i(u) = 0. What is u?
0, 1, 41
Let m(u) be the third derivative of u**6/300 + 3*u**5/50 + u**4/4 + 7*u**3/15 + 4*u**2 - 25*u. Solve m(y) = 0 for y.
-7, -1
Let t = 11799/4 - 2943. Factor 0 - 27/4*d**5 + 0*d + 1/4*d**2 - 9/4*d**3 + t*d**4.
-d**2*(3*d - 1)**3/4
Let m be 2 + 0/(-1 + 3). Suppose -m*c = -6 - 0. Factor -g + g**2 - 1/4*g**5 - 1/2*g**4 + 0 + 3/4*g**c.
-g*(g - 1)**2*(g + 2)**2/4
Let h(w) = 5*w**4 - 20*w**3 + 67*w**2 - 86*w + 36. Let f(q) = 11*q**4 - 38*q**3 + 133*q**2 - 173*q + 72. Let z(j) = 2*f(j) - 5*h(j). Factor z(i).
-3*(i - 3)*(i - 2)**2*(i - 1)
Let r(s) be the first derivative of -s**4/18 + 70*s**3/27 - 34*s**2/9 - 63. Suppose r(t) = 0. What is t?
0, 1, 34
Determine y, given that 210*y**2 + 25/3*y**3 + 104/3 - 172*y = 0.
-26, 2/5
Let z(w) be the third derivative of -w**5/30 - 55*w**4/6 - 3025*w**3/3 + 3*w**2 + 21*w. Factor z(l).
-2*(l + 55)**2
Suppose -d + 6*d + 3 = -b, b = 2*d - 3. Let g(v) be the first derivative of d*v - 2 + 0*v**2 - 2/3*v**3. Factor g(j).
-2*j**2
Let f be ((-265)/30 - -10)*4/7. Let h = 2 - 0. What is z in 0 + f*z**h + 2/3*z = 0?
-1, 0
Let f(p) be the first derivative of -p**8/112 + 13*p**2/2 - 14. Let i(j) be the second derivative of f(j). Find t, given that i(t) = 0.
0
Let x(w) be the first derivative of 3/16*w**4 - 7/4*w**3 - 34 + 21/4*w - 3/8*w**2. Find u such that x(u) = 0.
-1, 1, 7
Let t be (80/(-14))/2*(-49)/7. Suppose 8*f = 12 + t. Factor -i**3 + 70/3*i**f + 4/3*i + 49/3*i**5 + 0 - 20/3*i**2.
i*(i + 1)**2*(7*i - 2)**2/3
Let x(m) be the second derivative of -m**4/4 - 30*m**3 - 1350*m**2 - 22*m. Determine f, given that x(f) = 0.
-30
Let b(z) be the second derivative of 12/5*z**