rd derivative of r**8/6720 + r**7/1680 - 7*r**5/60 + 16*r**2. Let o(t) be the third derivative of i(t). Find a, given that o(a) = 0.
-1, 0
Let c(i) = i**3 - 2*i**2 - 2*i + 1. Let d(k) = 50*k**3 - 530*k**2 - 695*k - 115. Let f(j) = 5*c(j) + d(j). Determine t so that f(t) = 0.
-1, -2/11, 11
Let f(j) = -2*j**3 - 128*j**2 + 8. Let t(w) = -2*w**2 + 2. Let n(c) = -f(c) + 4*t(c). Factor n(b).
2*b**2*(b + 60)
Let q(b) be the first derivative of -b**4/6 + 5*b**3/3 - 4*b**2 + 46*b + 19. Let j(a) be the first derivative of q(a). Factor j(u).
-2*(u - 4)*(u - 1)
Factor 4/9*h**3 - 4/9*h + 0*h**2 - 2/9 + 2/9*h**4.
2*(h - 1)*(h + 1)**3/9
Let b be 10 - 9 - 3 - -6. Suppose 1/3*m**2 + 0 - 2/3*m + 4/3*m**3 - m**b = 0. What is m?
-2/3, 0, 1
Let h(t) be the second derivative of t**4/6 + 18*t**3 + 53*t**2 + 195*t + 1. Factor h(s).
2*(s + 1)*(s + 53)
Factor 4*v**4 + 4*v**2 + 14*v**2 - 2*v**4 - 160*v**3 + 138*v**2 + 2*v**4.
4*v**2*(v - 39)*(v - 1)
Let b(r) = 11*r**2 - 2144*r + 224717. Let t(a) = -24*a**2 + 4296*a - 449433. Let y(k) = 7*b(k) + 3*t(k). Factor y(m).
5*(m - 212)**2
Let n = 1516 + -1511. Solve -9/4*q**4 + 3/4*q**n - 3/4*q**2 + 0 + 0*q + 9/4*q**3 = 0 for q.
0, 1
Let x(l) be the first derivative of 4*l**3/21 - 32*l**2/7 + 60*l/7 + 135. Solve x(b) = 0.
1, 15
Let d = -5/2217 - -2227/4434. Solve -d*f - 1/8*f**2 - 1/2 = 0.
-2
Let a(l) = -11*l**2 - 53*l - 58. Let o be a(-2). Solve -2*c + 2*c**3 + 0 + 2/3*c**o - 2/3*c**2 = 0.
-3, -1, 0, 1
Let l be 3 + -2 + -3 + 9 + -4. Let -6*t + 4 - 7*t**l - t**3 + 21*t**3 - 11*t**3 = 0. Calculate t.
-2, 1
Factor -6*r**2 + 4*r**3 + 10*r**2 + 17*r**2 - 120*r - 137*r**2.
4*r*(r - 30)*(r + 1)
Let g(l) be the second derivative of l**7/1470 + l**6/630 - l**5/210 - l**4/42 - 5*l**3/3 - 10*l. Let q(s) be the second derivative of g(s). Solve q(a) = 0.
-1, 1
Suppose p**2 + 255 - 120 + 4*p - 118 - 22*p = 0. What is p?
1, 17
Let g(h) be the second derivative of 2*h**7/45 + 8*h**6/45 + 4*h**5/45 - 3*h**2/2 - 6*h. Let b(m) be the first derivative of g(m). Solve b(f) = 0 for f.
-2, -2/7, 0
Let k = -14083/5 - -2817. Suppose 0*s = 4*s + 8, -2*c + 3*s + 10 = 0. Factor -2/5*g**c + 4/5 - k*g.
-2*(g - 1)*(g + 2)/5
Let u be ((-24)/30)/((-2)/5). Find h such that -h**4 - 3*h**2 + 2*h**2 + 4*h**3 + u*h**3 - 4*h**3 = 0.
0, 1
Let z = -39 - -42. Let u(t) be the third derivative of 3*t**2 + 1/600*t**6 + 1/15*t**4 + 0*t + 0 + 2/15*t**z + 1/60*t**5. Determine o so that u(o) = 0.
-2, -1
Let l(f) be the first derivative of -16/5*f**3 + 21/10*f**4 - 19 - 18/25*f**5 - 6/5*f + 1/10*f**6 + 27/10*f**2. Solve l(g) = 0 for g.
1, 2
Let v(r) be the third derivative of -r**5/20 - 35*r**4/4 - 1225*r**3/2 - r**2 + 18*r. What is z in v(z) = 0?
-35
Let u = 17 - 14. Factor -184*z - 2*z**2 + z**u + 184*z.
z**2*(z - 2)
Let l(i) be the first derivative of i**7/399 + 2*i**6/285 - i**4/57 - i**3/57 - 19*i + 32. Let r(h) be the first derivative of l(h). Let r(p) = 0. What is p?
-1, 0, 1
Let a(h) be the first derivative of -125*h**4/4 - 75*h**3 - 135*h**2/2 - 27*h - 113. Solve a(q) = 0.
-3/5
Let k = 213/148 - -9/148. Factor 3/2*n**4 + 9/2*n**2 - k*n - 9/2*n**3 + 0.
3*n*(n - 1)**3/2
Solve 1/3*l**2 + 24025/3 + 310/3*l = 0 for l.
-155
Let j(a) be the first derivative of -2/3*a**4 + 4/15*a**5 + 0*a**2 - 10 + 0*a + 4/9*a**3. Factor j(x).
4*x**2*(x - 1)**2/3
Suppose -6*s = -10*s - 104. Let g be (-2 + s/(-10))*(-4)/(-6). Factor -7/5*d**4 + 4/5*d**5 - 1/5 - 2/5*d + 8/5*d**2 - g*d**3.
(d - 1)**3*(d + 1)*(4*d + 1)/5
Let l(a) be the second derivative of -a**7/63 + 2*a**6/9 - 19*a**5/15 + 34*a**4/9 - 19*a**3/3 + 6*a**2 + 84*a. Let l(c) = 0. What is c?
1, 2, 3
Let y(c) be the second derivative of -7*c**5/200 - 71*c**4/60 - 173*c**3/60 - 19*c**2/10 + 402*c. Factor y(a).
-(a + 1)*(a + 19)*(7*a + 2)/10
Let z(u) = -4*u**3 + u. Let p(l) = l**3 + l**2 - l. Let w(v) = -3*p(v) - z(v). Factor w(g).
g*(g - 2)*(g - 1)
Factor -23/4*c**2 - 3/4*c**3 - 1/2 + 9/4*c**4 - 13/4*c.
(c - 2)*(c + 1)*(3*c + 1)**2/4
Let t(c) be the second derivative of c**5/20 + c**4/8 - 7*c**2 + 18*c. Let g(u) be the first derivative of t(u). Factor g(a).
3*a*(a + 1)
Let a be ((-19 - -3)/(-4))/(-198 + 200). Factor 0*d - 2*d**4 + 16/7*d**a + 0 + 52/7*d**3.
-2*d**2*(d - 4)*(7*d + 2)/7
Suppose -157*o**2 - 12 - 155*o**2 - 153*o**2 + 463*o**2 - 10*o = 0. What is o?
-3, -2
Determine d so that -15*d**3 + 20*d**2 - 13*d**2 + 5*d**5 + 3*d**2 = 0.
-2, 0, 1
Let u(l) = 8*l**2 - 40*l + 50. Let q(z) = 14*z**2 - 80*z + 99. Let g(f) = -6*q(f) + 11*u(f). Let g(v) = 0. What is v?
-11, 1
Suppose 24/7*j**4 - 36/7*j**3 - 24/7*j**2 + 0 + 6/7*j**5 + 30/7*j = 0. Calculate j.
-5, -1, 0, 1
Let a = -380 - -1142/3. Let k(l) be the second derivative of 5/6*l**4 - 8*l + 0 - a*l**3 + 0*l**2. Let k(y) = 0. Calculate y.
0, 2/5
Let w(h) = 2*h**2 - h + 2. Let r be w(2). What is m in -r + 3*m**2 + 10 - 4 - 5*m = 0?
-1/3, 2
Let q(d) be the second derivative of -2197*d**5/50 + 169*d**4/10 - 13*d**3/5 + d**2/5 + 2*d + 45. Factor q(g).
-2*(13*g - 1)**3/5
Let q(f) be the second derivative of 0*f**3 + 0*f**4 + 1/15*f**6 - 1/20*f**5 - 1/42*f**7 - 2*f + 6 + 0*f**2. Let q(a) = 0. Calculate a.
0, 1
Let u(i) be the third derivative of -2*i**7/105 + 2*i**6/15 + 37*i**5/15 + 34*i**4/3 + 24*i**3 + 519*i**2. Factor u(g).
-4*(g - 9)*(g + 1)*(g + 2)**2
Let f(a) be the first derivative of 21*a**5/5 + 15*a**4/4 - 44*a**3 + 18*a**2 + 150. Determine h so that f(h) = 0.
-3, 0, 2/7, 2
Let w(h) be the third derivative of h**7/525 - h**6/50 + 11*h**5/150 - h**4/10 + 2*h**2 - 2. What is i in w(i) = 0?
0, 1, 2, 3
Let r(n) be the first derivative of 2*n**6/9 - 4*n**5/3 + 5*n**4/3 + 20*n**3/9 - 4*n**2 + 99. What is u in r(u) = 0?
-1, 0, 1, 2, 3
Let c be 150/252 - 8/14. Let s(v) be the second derivative of -1/7*v**2 + 0 - c*v**4 + 2/21*v**3 + 5*v. Factor s(n).
-2*(n - 1)**2/7
Let x(y) = y**2 + 11*y + 12. Let n be x(-10). Let i be n + 0 + 3 + -5. Find j such that 0*j**4 - 3/2*j**3 + i*j**2 + 0 + 3/4*j**5 + 3/4*j = 0.
-1, 0, 1
Suppose 0 = -14*m + 34 + 8. Let w = 339 - 4403/13. Factor 0*k + 0 + 2/13*k**m - w*k**2.
2*k**2*(k - 2)/13
Suppose -5*o - g = -14, -3*o - 7*g = -3*g - 22. Factor -2*d**2 - 2*d - 3*d + 3*d**o + 2*d.
d*(d - 3)
Let g(s) be the third derivative of 5*s**9/3024 + s**8/126 + s**7/84 - s**5/72 + 4*s**3/3 + 18*s**2. Let k(n) be the first derivative of g(n). Factor k(r).
5*r*(r + 1)**3*(3*r - 1)/3
Determine c, given that 10*c**3 + 6*c**3 + 186*c + 22 - 65*c**4 + 122 + 66*c**4 + 85*c**2 = 0.
-8, -3, -2
Let r(s) = 2*s**2 - 947*s + 4688. Let k be r(5). Factor 2/13*m**4 - 6/13*m**2 + 0 + 4/13*m + 0*m**k.
2*m*(m - 1)**2*(m + 2)/13
Let j = 7 + -3. Let k be (2 - j - 2)/(-6). Suppose 0 + k*u + 2*u**3 - 2*u**2 - 2/3*u**4 = 0. Calculate u.
0, 1
Factor 0 - 15/2*g**4 + 0*g - 99/4*g**3 - 3/4*g**5 - 27*g**2.
-3*g**2*(g + 3)**2*(g + 4)/4
Let j(a) be the second derivative of -a**8/2240 - a**7/840 + 3*a**4/4 + 10*a. Let k(l) be the third derivative of j(l). Find c, given that k(c) = 0.
-1, 0
Let s(u) be the second derivative of u**5/30 - u**3/3 + u**2 + 10*u. Let w(o) be the first derivative of s(o). Factor w(l).
2*(l - 1)*(l + 1)
Let d(f) = 7*f - 1. Let r be d(-1). Let b be (-1)/2*r + -1. Factor -a + 7*a + 3 - 2*a**b + 3 - 2.
-2*(a - 2)*(a + 1)**2
Let q(b) = -9*b**3 + 4*b - 5. Let z be q(1). Let m be 12/21 + (z - -10). Factor 8/7*s - 12/7 + m*s**2.
4*(s - 1)*(s + 3)/7
Let w(j) = -j**3 + 13*j**2 + 15*j - 12. Let p be w(14). Factor -3*f + 0*f - 21*f**2 + 24*f**p.
3*f*(f - 1)
Factor 0 + 3/2*g**2 + 9/2*g - 9/2*g**3 - 3/2*g**4.
-3*g*(g - 1)*(g + 1)*(g + 3)/2
Let x(a) be the second derivative of 0*a**2 - 5/12*a**4 - 6*a + 0*a**3 + 0. Find o, given that x(o) = 0.
0
Let h(f) = f**2 - f - 5. Let g be h(-4). Let t be (4/5)/(6/g). Factor t - y**4 + 2*y + 2*y**3 + y**3 - 5*y - y**2.
-(y - 2)*(y - 1)**2*(y + 1)
Suppose 2*h - 19 = -7. Let l be (h/(-5) + (15 - 13))/2. Suppose 0*x + 4/5*x**2 - 2/5*x**4 - l + 0*x**3 = 0. What is x?
-1, 1
Suppose -10*y = -7*y + 18. Let h(m) = 11*m**3 - 21*m**2 + 10*m. Let n(j) = 12*j**3 - 22*j**2 + 10*j. Let k(r) = y*n(r) + 7*h(r). Let k(u) = 0. Calculate u.
0, 1, 2
Let z(v) be the third derivative of 0*v + 1/180*v**6 - 1/36*v**4 - 7/90*v**5 + 7/9*v**3 + 0 + 17*v**2. Suppose z(q) = 0. What is q?
-1, 1, 7
Let x(m) = -m**4 + 20*m**3 - 28*m**2 + 15*m - 3. Let l(q) = -6*q**4 + 100*q**3 - 