derivative of -9 - 1/3*s**2 + 0*s + 1/9*s**b. Determine p, given that x(p) = 0.
0, 2
Let l be 5/((-5)/3) + 5. Suppose -p = -l, -2*k = -0*k + 2*p - 12. Factor 4*b - 4*b**3 + k*b**5 - 5*b**3 + b**3.
4*b*(b - 1)**2*(b + 1)**2
Let m = 1044 + -1044. Let f(n) be the first derivative of -4 - n**3 + 3/5*n**5 + 3/4*n**4 + 0*n + m*n**2 - 1/2*n**6. What is k in f(k) = 0?
-1, 0, 1
Let o(q) = q**3 + 17*q**2 + 29*q - 180. Let h be o(-14). Suppose 0*p**h + 0 - 10/9*p**3 + 0*p - 2/9*p**4 = 0. What is p?
-5, 0
Let l(y) be the first derivative of y**3/33 + 10*y**2/11 + 36*y/11 - 676. Factor l(j).
(j + 2)*(j + 18)/11
Let w = 16001/100 - 3524/25. Let s = 104/5 - w. Factor -7/4*i**3 + 1/2*i**2 - 1/2 + s*i.
-(i - 1)*(i + 1)*(7*i - 2)/4
Let d(u) be the first derivative of u**5 - 115*u**4/4 - 125*u**3/3 + 115*u**2/2 + 120*u + 25. Factor d(v).
5*(v - 24)*(v - 1)*(v + 1)**2
Factor -16*o**2 + 0 + 14/5*o**3 + 40/3*o - 2/15*o**4.
-2*o*(o - 10)**2*(o - 1)/15
Let k(j) be the first derivative of j**5/5 - 7*j**4/2 + 13*j**3/3 + 798. Determine x so that k(x) = 0.
0, 1, 13
Let p(g) be the second derivative of -g**6/70 + 3*g**5/140 + 5*g**4/14 + 4*g**3/7 - 2*g - 7. Factor p(f).
-3*f*(f - 4)*(f + 1)*(f + 2)/7
Let k = 51 + -40. Suppose -3*s + 9*s**2 - 5*s**2 + k*s = 0. Calculate s.
-2, 0
Factor -3 + 6*n**2 + 10 - 105*n + 90*n + 2.
3*(n - 1)*(2*n - 3)
Solve -20/3*o + 14 + 2/3*o**2 = 0.
3, 7
Let o(i) be the second derivative of -i - 7/60*i**4 - 1/6*i**3 + 1/5*i**2 + 0. What is u in o(u) = 0?
-1, 2/7
Let j(g) be the third derivative of 4/15*g**6 - 1/5*g**5 - 2/35*g**7 + 0*g**3 + 0*g + 0 + 9*g**2 - 1/3*g**4. Suppose j(a) = 0. What is a?
-1/3, 0, 1, 2
Let m = -1748 - -6993/4. Let -m*n**4 + n**3 - 3/4*n**2 + 1 - n = 0. Calculate n.
-1, 1, 2
Let w(g) be the first derivative of -g**3/3 - 4*g**2 + 12*g + 5. Let x be w(-9). Find k such that 0 - 4/7*k - 6/7*k**2 + 2/7*k**4 + 0*k**x = 0.
-1, 0, 2
Let i(y) = 2*y**3 + 18*y**2 + 42*y - 38. Let l(t) = -t - 1. Let m(u) = -u**2 + 9*u - 15. Let o be m(7). Let x(w) = o*i(w) - 12*l(w). Factor x(n).
-2*(n - 1)*(n + 5)**2
Let t(r) be the second derivative of r**4/66 - 3*r**3/11 + 8*r**2/11 + 124*r. Solve t(k) = 0.
1, 8
Let u(s) be the third derivative of s**8/6720 + s**7/2520 - 11*s**4/24 + 4*s**2. Let k(g) be the second derivative of u(g). Factor k(m).
m**2*(m + 1)
Let k be (-14)/(-3)*(-17 - 4000/(-224)). Find y such that -3/7*y**5 + 0 + 0*y + 12/7*y**3 - 9/7*y**k + 0*y**2 = 0.
-4, 0, 1
Let z = 9179/403 - 687/31. Solve 8/13*r + 2/13*r**4 - 8/13*r**3 + 6/13*r**2 - z = 0 for r.
-1, 1, 2
Let v(q) be the first derivative of -q**6/15 - 2*q**5/5 - q**4/5 + 16*q**3/15 + 22. Solve v(c) = 0 for c.
-4, -2, 0, 1
Let f(h) be the first derivative of 2*h**3/45 - h**2/5 - 8*h/15 + 89. Let f(u) = 0. What is u?
-1, 4
Let c be (-5)/((-10)/(-68))*-1. Let f be (-1 - -9) + (c - 39). Factor -2/9*u**f + 0*u - 2/9*u**4 + 0*u**2 + 4/9*u**5 + 0.
2*u**3*(u - 1)*(2*u + 1)/9
Let h(r) be the third derivative of -r**6/540 + r**5/135 - r**4/108 - 320*r**2. Factor h(n).
-2*n*(n - 1)**2/9
Suppose 0 = 144*a - 146 - 142. Find y, given that 0 + 1/2*y**a - y - 1/2*y**4 + y**3 = 0.
-1, 0, 1, 2
Let n = 213028/11 - 19366. Factor -22 - 4*s - n*s**2.
-2*(s + 11)**2/11
Let j(v) be the third derivative of 1/72*v**5 - 35/36*v**3 + 16*v**2 + 5/24*v**4 + 0 + 0*v. Find o, given that j(o) = 0.
-7, 1
Let y = -4942 + 4947. Factor -10/3 - 65/6*v**2 + 10*v - 5/6*v**4 + y*v**3.
-5*(v - 2)**2*(v - 1)**2/6
Suppose 4*b = b. Let y be -4 - (-5 + -4 + b). Suppose 2 + 12*i**3 + 5*i - 11*i + 0 + 0 + 2*i**4 - 6*i**y - 4*i**2 = 0. What is i?
-1, 1/3, 1
Factor 17/7*m**2 - 1/7*m**3 + 1/7*m - 17/7.
-(m - 17)*(m - 1)*(m + 1)/7
Let k(r) be the second derivative of -2*r**5/65 + 47*r**4/78 - 73*r**3/39 + 30*r**2/13 + 7*r + 67. Let k(a) = 0. Calculate a.
3/4, 1, 10
Suppose 0 = 4*y + 5*y - 36. Suppose y = -4*g + 6*g. Find o, given that 0 - 3/4*o**3 - 1/4*o**5 + 3/4*o**4 + 1/4*o**g + 0*o = 0.
0, 1
Let q = -17 + 19. Let 5*t**3 - q*t**3 + 3*t**2 + 0*t**3 - 2*t**3 = 0. Calculate t.
-3, 0
Let n be (1/(-4))/(5/(-25)). Suppose -28*s = -17*s - 33. Solve -2*a - n*a**2 - 1/4*a**s - 1 = 0 for a.
-2, -1
Let f(a) be the second derivative of 5*a**4/3 - 44*a**3 + 26*a**2 - 8*a - 2. Factor f(p).
4*(p - 13)*(5*p - 1)
Let j(q) = q - 2. Let a(m) = 4*m**2 - 102*m - 124. Let o(z) = -a(z) + 6*j(z). Suppose o(x) = 0. Calculate x.
-1, 28
Let v(l) be the third derivative of l**8/1344 - l**7/504 - l**6/144 + l**5/24 - 5*l**4/24 - 8*l**2. Let z(t) be the second derivative of v(t). Factor z(x).
5*(x - 1)**2*(x + 1)
Let i be 28/98 - (-2012)/14. Suppose -5*m + 35 = 5*u, -5*u + 4*m = -52 - 19. Find r such that -24*r**2 + 83*r**3 + 8 - i*r + 36*r**4 + u + 13 + 17*r**3 = 0.
-2, 2/9, 1
Factor 361*j + 3 + 50*j**2 + 25*j**3 + 2*j**5 + 5 + 13*j**3 + 14*j**4 - 329*j.
2*(j + 1)**3*(j + 2)**2
Factor -18/7*t**3 + 8/7*t - 32/7*t**2 + 0.
-2*t*(t + 2)*(9*t - 2)/7
Let h = -7237 + 50660/7. Factor 22/7*i - h*i**2 - 121/7.
-(i - 11)**2/7
Let m(f) be the first derivative of -7/15*f**5 - 15 + 1/3*f + 2/3*f**3 - 5/6*f**2 + 1/6*f**6 + 1/6*f**4. Determine w so that m(w) = 0.
-1, 1/3, 1
Let a(v) be the first derivative of -2*v**5/5 - 7*v**4/2 + 82*v**3/3 - 33*v**2 + 223. Solve a(l) = 0 for l.
-11, 0, 1, 3
Let t(r) be the first derivative of r**9/4536 + r**8/1260 - 17*r**3/3 + 17. Let z(p) be the third derivative of t(p). Factor z(u).
2*u**4*(u + 2)/3
Suppose -20*c + 25 = 65. Let t be (-5)/c - 20/(-40). Suppose f**2 + 0 + 1/2*f**t + 1/2*f = 0. Calculate f.
-1, 0
Let t(k) be the first derivative of k**6/2 + 3*k**5/4 - 9*k**4/16 - 5*k**3/4 - 3*k**2/8 + 39. What is o in t(o) = 0?
-1, -1/4, 0, 1
Let h = 3 - -3. Let n = h - 6. Factor -i + 2*i**3 - i + 2 - 4 + 2*i**2 + n.
2*(i - 1)*(i + 1)**2
Factor 15 - 1/3*s**2 - 44/3*s.
-(s - 1)*(s + 45)/3
Let f(l) be the third derivative of l**8/1008 + l**7/90 - 7*l**6/120 - 23*l**5/180 + 5*l**4/9 + 2*l**3 + 2*l**2 - 198*l. Suppose f(b) = 0. Calculate b.
-9, -1, 2
Suppose -20*h - 6*h - 6652 = -6652. Factor -8/3*m**2 + 0*m**4 + h + 0*m - 4*m**3 + 4/3*m**5.
4*m**2*(m - 2)*(m + 1)**2/3
Let g(n) be the first derivative of -3*n**2/2 + 45*n + 52. Let h be g(15). Factor h - 1/6*t**2 + 1/3*t - 1/6*t**3.
-t*(t - 1)*(t + 2)/6
Suppose -42*f**3 + 426/7*f**2 - 279/7*f - 3/7*f**5 + 81/7*f**4 + 69/7 = 0. What is f?
1, 23
Let a be (-5 + 7)*(2 + (-1)/2). Let j(h) be the third derivative of 8/3*h**3 + 0 - 1/3*h**4 + 0*h + 1/60*h**5 + a*h**2. Let j(q) = 0. Calculate q.
4
Factor -2/7*m**4 + 4/7*m**3 + 26/7*m**2 + 0 + 20/7*m.
-2*m*(m - 5)*(m + 1)*(m + 2)/7
Let i(u) = 2*u**5 + 20*u**4 - 24*u**3 + 28*u**2 - 26*u. Let z(c) = -c**4 - c**3 + c**2 + c. Let r(s) = i(s) + 12*z(s). What is v in r(v) = 0?
-7, 0, 1
Let s(q) = -q**2 + 2*q - 2. Let f be s(3). Let h = f + 5. Solve m**3 + h*m**3 + 3*m**3 + 0*m**3 - 8*m + 4*m**2 = 0 for m.
-2, 0, 1
Factor -70*y**2 - 28*y**2 - 56*y + 4*y**4 + 62*y**2 + 24*y**3.
4*y*(y - 2)*(y + 1)*(y + 7)
Let l(r) be the first derivative of -5*r**6/18 + 5*r**4/2 + 40*r**3/9 + 5*r**2/2 + 80. Let l(m) = 0. What is m?
-1, 0, 3
Let s(b) = b**2 + 9*b - 5. Let x be s(-10). Factor m**2 + 0 + x*m + 0 + 4.
(m + 1)*(m + 4)
Factor -882/11 - 2/11*v**2 - 84/11*v.
-2*(v + 21)**2/11
Let b(i) = -29*i**2 + 75*i + 63*i**2 + 2*i**4 + 30 - 4*i**3 - 17*i**4. Let d(t) = -3*t**4 - t**3 + 7*t**2 + 15*t + 6. Let s(r) = -2*b(r) + 11*d(r). Factor s(j).
-3*(j - 2)*(j + 1)**3
Let v be ((-4)/((-540)/501) - 2) + 37/(-333). Let i = 78 - 388/5. Suppose i*p**2 + 8/5 + v*p = 0. Calculate p.
-2
Let x(o) = o**2 - 20*o + 3. Let s(b) = 6*b**2 - 104*b + 16. Let t(c) = -3*s(c) + 16*x(c). Factor t(y).
-2*y*(y + 4)
Let s(h) = -6*h**2 - 94*h - 578. Let a(i) = 7*i**2 + 93*i + 579. Let v(z) = -2*a(z) - 3*s(z). Factor v(j).
4*(j + 12)**2
Find a such that 22 - 85*a**3 - 6 + 148*a + 15*a**4 + 14 - 263*a + 155*a**2 = 0.
2/3, 1, 3
Determine i so that -2/5*i**2 - 32/5 + 16/5*i = 0.
4
Let f = 2/27691 - -443042/193837. Suppose -4/7*a**4 + f*a**3 - 16/7*a + 4/7*a**2 + 0 = 0. What is a?
-1, 0, 1, 4
Let m = 3 - 7. Let t be m/(-6) - (-16)/(-24). Solve t*v**3 + 0*v**3 + 0*v + 2*v - 2*v**3 = 0 for v.
-1, 0, 1
Suppose 5*t = -3*s + 19, 2 = 5*t - 8. Let p be (1 + 0)*(s + 1). Let 8/3*u + 98/3*u**5 + 0 + 140/3*u**p - 2*u**3 - 40/3*u**2 = 0. Calculate u.
-1, 0, 2/7
Suppose -2*i = -16 + 12. Suppose -3*p = -4*y +