01*g**2 = 0. Calculate g.
-2, -5/4
Factor 13*r**2 - 9 - 48*r - 22*r**2 - 6*r**2.
-3*(r + 3)*(5*r + 1)
Let n(z) be the first derivative of z**6/6 - 9*z**5/5 - 11*z**4/2 - 2*z**3/3 + 21*z**2/2 + 11*z + 66. Find m such that n(m) = 0.
-1, 1, 11
Let z be (11 + (-3 - 8))*(2 - 1). Let c(u) be the second derivative of 1/15*u**4 + 1/5*u**2 - 1/6*u**3 + z - 7*u - 1/100*u**5. Factor c(j).
-(j - 2)*(j - 1)**2/5
Suppose 3 = -4*j - 5*c, 5*c + 105 = 2*j + 84. Determine y, given that 1/3*y**4 - 5/3*y**j + 4/3*y + 2*y**2 - 8/3 = 0.
-1, 2
Let f(b) = 3*b**2 + 63*b + 153. Let p(g) = 5*g**2 + 61*g + 154. Let w(d) = -4*f(d) + 3*p(d). Let w(m) = 0. Calculate m.
-2, 25
Suppose -4*p + 5*b + 33 = 0, 5*p + 6*b - 3*b = -5. Determine j, given that -4*j**3 - 79*j**2 + 37*j**p + 16 + 38*j**2 + 16*j = 0.
-2, -1, 2
Let a = 15/107 - -888/535. Factor 1/5*p**4 + p**3 + 7/5*p + a*p**2 + 2/5.
(p + 1)**3*(p + 2)/5
Let j = -249/2 + 126. Let m(i) be the first derivative of -4 + 3/2*i + j*i**2 + 1/2*i**3. Factor m(t).
3*(t + 1)**2/2
Factor 1/2*c**3 - 6 - 4*c + 1/2*c**2.
(c - 3)*(c + 2)**2/2
Let x be 76/(-24)*3 - -2. Let v = x + 8. Determine r so that -1/2*r**4 + 0*r + v*r**2 - 2*r**5 + 2*r**3 + 0 = 0.
-1, -1/4, 0, 1
Let p(m) = 5*m**3 - 19*m**2 - m - 3. Let k(w) = 5*w**3 - 22*w**2 - 3*w - 4. Let l(i) = -3*k(i) + 4*p(i). Suppose l(o) = 0. What is o?
0, 1
Let v = 25 - 36. Let u = v - -13. Solve 0*l**3 - l + u - 6*l**2 + l**3 + 4*l**2 = 0 for l.
-1, 1, 2
Let d(v) be the second derivative of -5*v**4/6 - 94*v**3 - 112*v**2 + 233*v. Find l, given that d(l) = 0.
-56, -2/5
Let x = 17712 + -159404/9. Solve x*p**3 - 4/9*p**2 + 0 - 8/9*p = 0 for p.
-1, 0, 2
Let v(d) be the first derivative of 2/15*d**2 - 20 + 2/45*d**3 + 0*d. Let v(a) = 0. Calculate a.
-2, 0
Let -5408*h - 80*h**4 - 69*h**3 + 76*h**4 - 3120*h**2 - 147*h**3 = 0. Calculate h.
-26, -2, 0
Let a(x) be the second derivative of -x**5/110 - 2*x**4/11 - 35*x**3/33 - 37*x + 9. Factor a(p).
-2*p*(p + 5)*(p + 7)/11
Suppose 14*t - 48 = 22. Suppose -5*p + 6 = 3*f, -t*f + 10 = -2*p - 2*p. Factor 2/7*j + 2/7*j**f + 0.
2*j*(j + 1)/7
Let x = -78640/9 - -8738. Let x*u**2 - 2/3*u + 4/9 = 0. Calculate u.
1, 2
Let q(z) be the first derivative of z**5/50 + 19*z**4/10 + 361*z**3/5 + 6859*z**2/5 + 130321*z/10 - 844. Factor q(t).
(t + 19)**4/10
Let r be (-3)/13 + (-5576)/(-1066). Factor -4/11*s + 0 - 2/11*s**r - 18/11*s**3 - 10/11*s**4 - 14/11*s**2.
-2*s*(s + 1)**3*(s + 2)/11
Let n be (-35)/(-11) - 14/77. Suppose -c = d - 2, 0*d - 8 = -4*c + 5*d. Determine w, given that -3*w**n + w**c + 4*w**3 - 2*w**3 = 0.
0, 1
Let g(y) be the third derivative of -y**6/24 + 9*y**5/4 - 405*y**4/8 + 1215*y**3/2 + 85*y**2. Find l such that g(l) = 0.
9
Let f = -393 + 395. Let q(r) be the second derivative of 3*r**f - 3/2*r**3 + 3*r + 0 + 1/4*r**4. What is w in q(w) = 0?
1, 2
Suppose 3*f = 5*g + 3, f + 3*f = -2*g + 4. Let o = g - -2. Let 2*z - 21/2*z**4 + 8*z**o + 1/2*z**3 + 0 = 0. What is z?
-2/3, -2/7, 0, 1
Let m(t) be the first derivative of 4/5*t**5 + 0*t**4 + 0*t - 2/3*t**6 + 0*t**2 + 36 + 0*t**3. Factor m(z).
-4*z**4*(z - 1)
Suppose 11/4*b**2 + 1/4*b**4 + 3/2*b + 0 + 3/2*b**3 = 0. What is b?
-3, -2, -1, 0
Let x(b) = 4*b**2 + b + 5. Suppose 3*m = -0*m + 15. Let u(z) = 6*z**2 + z + 7. Let a(t) = m*u(t) - 7*x(t). Let a(v) = 0. What is v?
0, 1
Let k(q) be the first derivative of 5*q**4/4 - 50*q**3/3 - 7. What is f in k(f) = 0?
0, 10
Let j = -123/2 + 65. Let n = -11 - -15. Factor 0 + 13/2*r**2 - j*r**5 + 23/2*r**n - 27/2*r**3 - r.
-r*(r - 1)**3*(7*r - 2)/2
Let k(u) = -6*u**2 + 8*u + 10. Let l(d) be the third derivative of d**5/12 - 7*d**4/24 - 3*d**3/2 + 6*d**2. Let y(v) = 3*k(v) + 4*l(v). Solve y(b) = 0.
-1, 3
Let n = 244 + -485/2. Solve -n*w**3 - 3/8*w**4 + 0 - 3/2*w**2 + 0*w = 0.
-2, 0
Let j(z) = z**2 - 31*z + 62. Let f be j(29). Let m(k) be the third derivative of 0 + f*k**2 + 1/18*k**4 + 0*k + 0*k**3 - 1/180*k**6 + 1/90*k**5. Factor m(y).
-2*y*(y - 2)*(y + 1)/3
Suppose -3*z - 19 = -34. Let p(x) be the third derivative of 1/80*x**6 + 0*x - x**2 + 0 + 1/4*x**3 - 1/40*x**z - 1/16*x**4. Suppose p(m) = 0. What is m?
-1, 1
Let v(o) be the third derivative of o**5/180 + 3*o**4/4 + 81*o**3/2 - 91*o**2. Factor v(h).
(h + 27)**2/3
Let o(r) be the first derivative of -52/5*r**5 + 0*r**2 - 4*r**4 + 16/3*r**3 + 13 - 10/3*r**6 + 0*r. What is i in o(i) = 0?
-2, -1, 0, 2/5
Let y be (-3)/1*3/24*-2. Suppose y + 1/4*w**3 - 3/4*w**2 - 1/4*w = 0. Calculate w.
-1, 1, 3
Let p = -139550/9 - -15506. Factor 8/9*o**2 + 2/3*o**3 - p*o**4 + 0 - 8/9*o - 2/9*o**5.
-2*o*(o - 1)**2*(o + 2)**2/9
Let m(d) be the second derivative of 1/7*d**3 + 1/42*d**4 + 0 + d + 2/7*d**2. Factor m(a).
2*(a + 1)*(a + 2)/7
Let l be (-15)/35*(-68)/102. Suppose -12/7*x**3 + 12/7*x - l*x**4 - 16/7*x**2 + 18/7 = 0. What is x?
-3, -1, 1
Let h(j) be the second derivative of -j**9/37800 + j**8/8400 - j**6/900 + j**5/300 - j**4/2 - 4*j. Let b(s) be the third derivative of h(s). Factor b(k).
-2*(k - 1)**3*(k + 1)/5
Suppose 50*i**2 + 10 - 80*i**4 - 95*i**4 - 55*i**4 - 295*i**3 + 20*i**4 + 52*i + 93*i = 0. Calculate i.
-1, -1/14, 2/3
Let b(n) = -4*n**3 + n**2 - 1. Let i(c) = 13*c**3 + 8*c**2 + 26*c + 19. Let v(a) = -3*b(a) - i(a). Solve v(k) = 0.
-8, -2, -1
Suppose 0 = 4*b - 5*n - 23, 39*b - 37*b + 2*n = -2. Factor -2/5*u**b + 0 - 24/5*u.
-2*u*(u + 12)/5
Factor -1/3*h**3 + 0*h + 1/3*h**5 - h**2 + 0 + h**4.
h**2*(h - 1)*(h + 1)*(h + 3)/3
Let u be (-40)/(-72)*((-3)/5 + 1). Let g(q) be the third derivative of -6*q**2 - 1/180*q**5 + 0*q + 0 + 1/18*q**4 - u*q**3. Let g(z) = 0. What is z?
2
Factor 0*t**4 - 12*t**4 + 12*t + 2*t**5 - 24 + t**5 - 6*t**5 + 15*t**3 - 18*t**3 + 30*t**2.
-3*(t - 1)**2*(t + 2)**3
Suppose -337*d - 5*d**3 + 62*d**2 + 2*d + 15*d + 18*d**2 = 0. Calculate d.
0, 8
Let n(f) = 6*f**3 + 579*f**2 + 286*f - 192. Let j be n(-96). Suppose j + 6*d - 2/3*d**2 = 0. Calculate d.
0, 9
Find n, given that 0*n - 17/6*n**2 + 0 - 1/6*n**3 = 0.
-17, 0
Let b(h) be the first derivative of 2*h**3/39 - 14*h**2/13 - 30*h/13 + 10. Factor b(d).
2*(d - 15)*(d + 1)/13
Let q be (-2)/(10/1) - 9917/2585. Let h = -40/11 - q. Factor -h*z**2 - 8/5*z - 6/5.
-2*(z + 1)*(z + 3)/5
Suppose 5*g + 0*b - 10 = 2*b, -2*b = 0. Suppose 6 = i + g. Determine f, given that 12*f**i + 10*f**3 + 3*f**3 - 4 - 8*f**2 + 3*f**3 - 16*f = 0.
-1, -1/3, 1
Suppose -5*o = 0, -4*w + o - 4*o = -16. Let 12*g**2 + 16*g**3 - 3*g**3 + g**5 + 3*g + g + 6*g**w = 0. Calculate g.
-2, -1, 0
Let o(l) be the third derivative of l**8/84 - 4*l**7/15 + 61*l**6/30 - 28*l**5/5 + 6*l**4 + 4*l**2 - 66*l. Factor o(d).
4*d*(d - 6)**2*(d - 1)**2
Find h, given that -28*h**3 - 964 + 112*h + 996 - 6*h**2 - 2*h**2 = 0.
-2, -2/7, 2
Let w = -46 + 50. Suppose 15 - n - w*n**2 - 5*n**3 + 5 + 21*n - n**2 = 0. Calculate n.
-2, -1, 2
Let w(q) be the second derivative of 5*q**7/42 - 11*q**6/3 + 169*q**5/4 - 220*q**4 + 480*q**3 + 4*q - 2. Factor w(s).
5*s*(s - 8)**2*(s - 3)**2
Let c(y) = -12*y + 123. Let s be c(10). Let g be (s/(-9))/(6/(-9)). Factor 1/2*p - g*p**3 + 0*p**2 + 0.
-p*(p - 1)*(p + 1)/2
Let h(v) be the third derivative of -v**6/420 + v**5/2 - 175*v**4/4 + 6125*v**3/3 + 22*v**2. Let h(x) = 0. What is x?
35
Let j be 11/((-847)/(-525)) - 7 - (-14)/77. Factor 0 - 3/7*a**3 + 12/7*a**2 + j*a.
-3*a**2*(a - 4)/7
Suppose 0*l = 2*l - 8. Suppose h - 5*j = 25, l*h + 14 - 4 = -2*j. Suppose 0*w + 4/3*w**2 + 2*w**4 + 10/3*w**3 + h = 0. What is w?
-1, -2/3, 0
Let n = 12554 + -12549. Determine m, given that 0*m - 8/3*m**4 + 7/6*m**n - 1/3*m**2 + 11/6*m**3 + 0 = 0.
0, 2/7, 1
Let p be (-3)/4 + 42/24. Let s be -1 - (-6 - (p - 3)). Let -t - 19*t**s - 18*t**2 - 5*t**3 + 2*t - 5*t - 10*t**4 = 0. What is t?
-1, -2/5, 0
Let h(i) be the second derivative of i**4/4 - 3*i**2/2 - 2*i + 14. Solve h(y) = 0.
-1, 1
Let i(c) be the third derivative of -c**6/15 + c**5/3 + 2*c**4/3 - 2*c**3 - 99*c**2. Let i(q) = 0. What is q?
-1, 1/2, 3
Let l(o) = -7*o - 61. Let m = -31 - -22. Let u be l(m). Let 2/3*d**5 + 2/3*d + 0 + 4*d**3 + 8/3*d**4 + 8/3*d**u = 0. Calculate d.
-1, 0
Let y(m) be the first derivative of m**7/210 - 3*m**5/20 - m**4/6 + 2*m**3 + 17*m**2 + 28. Let k(p) be the second derivative of y(p). Factor k(s).
(s - 3)*(s - 1)*(s + 2)**2
Let r(t) be the first derivative of -4/3*t**3 + 0*t + 2/3*t**2 - 13 + 4/5*t**5 - 1/3*t**4. Let