
19
Let q(r) be the first derivative of 3*r**5/20 + 3*r**4/4 - 9*r**3/2 + 15*r**2/2 - 20*r - 15. Let t(n) be the first derivative of q(n). Factor t(a).
3*(a - 1)**2*(a + 5)
Let r = -40/27 - -125/54. What is o in -5/3 + 5/6*o - r*o**3 + 5/3*o**2 = 0?
-1, 1, 2
Suppose 0*g + 20 = 5*g. Let m = -14 + 16. Suppose -q + 3*q + q**g + 3*q**m - 2*q**4 = 0. What is q?
-1, 0, 2
Suppose -5*t + l = -l - 35, 0 = 2*t + 2*l. Let i = t - -6. Suppose -4*u**4 - 21*u**3 - i*u**3 + u**2 - 33*u**2 + 108 - 40*u**2 = 0. What is u?
-3, 1
Factor 133*s**2 - 60*s - 264*s**2 + 134*s**2.
3*s*(s - 20)
Let l(d) = d**2 + 1. Let y(t) = -10*t**2 - 3*t + 5*t - 2*t. Let u(q) = -5*l(q) - y(q). Factor u(o).
5*(o - 1)*(o + 1)
Let s(i) be the third derivative of -22*i**5/15 + 67*i**4/6 - 2*i**3 - 67*i**2. Solve s(t) = 0.
1/22, 3
Let n be -6*(-1 - (-4)/8). Factor 6*d**2 - d - d - n*d**2 - 12 + 11*d.
3*(d - 1)*(d + 4)
Suppose 0 = h, 10*l - 11*l = 5*h - 5. Let u(g) be the first derivative of -1/3*g**2 - 1/3*g - 1/9*g**3 - l. Factor u(z).
-(z + 1)**2/3
Let y(p) be the third derivative of p**5/150 + 13*p**4/60 - 68*p**3/15 - 795*p**2. What is k in y(k) = 0?
-17, 4
Suppose -3*x - 30 = -2*x - 4*p, 4*p = 4*x + 60. Let n be (-6)/(-15)*1/(-8)*x. Let n*d**5 + 0 + 0*d**4 + 0*d**2 + 0*d**3 + 0*d = 0. What is d?
0
Factor 0 - 8/19*g**4 + 2/19*g**5 - 4/19*g**2 + 10/19*g**3 + 0*g.
2*g**2*(g - 2)*(g - 1)**2/19
Let v be (-9196)/(-3872) + 6/(-16). Determine l so that 1/3*l**v - 1/3 + 1/3*l**3 - 1/3*l = 0.
-1, 1
Let d(f) be the second derivative of -7*f**7/6 + 217*f**6/30 - 47*f**5/10 - 645*f**4/14 + 675*f**3/14 + 3375*f**2/14 + 10*f + 17. Find y, given that d(y) = 0.
-1, 15/7
Let z(t) be the first derivative of 7*t**6/9 - 416*t**5/15 + 1879*t**4/6 - 9812*t**3/9 + 3172*t**2/3 + 2704*t/3 + 482. Solve z(k) = 0.
-2/7, 2, 13
Let -4/9*z**2 - 2/3*z**3 + 0 + 2/9*z = 0. What is z?
-1, 0, 1/3
Let w(i) be the second derivative of -1/60*i**5 + 1/90*i**6 - 1/36*i**4 + 0*i**2 + 0 - 16*i + 1/18*i**3. Factor w(t).
t*(t - 1)**2*(t + 1)/3
Let f(s) = -140*s**2 + 1449*s - 409. Let j(a) = -35*a**2 + 362*a - 102. Let i(v) = -2*f(v) + 9*j(v). What is w in i(w) = 0?
2/7, 10
Let l(p) be the second derivative of 5/4*p**4 + 10*p + 5/2*p**3 + 1/4*p**5 + 5/2*p**2 + 0. Factor l(a).
5*(a + 1)**3
Factor 384/7*x - 608/7*x**2 + 0 - 72/7*x**4 + 4/7*x**5 + 48*x**3.
4*x*(x - 12)*(x - 2)**3/7
Suppose -3*l = -5*d + 10, 0 = -3*d - 2*d - 2*l + 35. Suppose -q - 8 = -3*u - 0*q, 5*u - d*q = 10. Factor -11*m**u - 3*m**2 + 8*m - m**2 + 7*m**3.
-4*m*(m - 1)*(m + 2)
Let l(m) be the first derivative of m**5/100 + 8*m**2 + 8. Let q(z) be the second derivative of l(z). Let q(n) = 0. What is n?
0
Suppose 0 = -0*a - 5*a + 1365. Let l = a + -3001/11. Let 6/11*m**2 - l*m + 0 = 0. Calculate m.
0, 1/3
Find u such that -8/7*u**3 - 12/7*u**4 + 10/7*u - 2/7*u**5 - 24/7 + 36/7*u**2 = 0.
-4, -3, -1, 1
Let i(j) = -11*j**3 + 49*j**2 + 15*j - 36. Let a(l) = -21*l**3 + 97*l**2 + 31*l - 72. Let d(f) = -3*a(f) + 5*i(f). Let d(g) = 0. Calculate g.
-1, 3/4, 6
Let u = 73 + -69. Suppose -w = 4*x + 14, u*w - 3*x = -w + 22. Factor -2/5*l**w + 4/5 + 2/5*l.
-2*(l - 2)*(l + 1)/5
Factor -1/5*l**3 - 19/5*l**2 - 32/5 - 10*l.
-(l + 1)*(l + 2)*(l + 16)/5
Let m(q) be the second derivative of -7*q + 1/14*q**7 + 9/2*q**3 + 21/10*q**5 + 3*q**2 + 4*q**4 + 0 + 3/5*q**6. Solve m(h) = 0 for h.
-2, -1
Let g be 10/8 + ((-45)/20)/(-3). Factor -6*p**3 - 3/2*p**4 - 3*p - 15/2*p**g + 0.
-3*p*(p + 1)**2*(p + 2)/2
Let a(s) be the first derivative of -4*s**3/27 - s**2 + 10*s/9 + 22. Factor a(x).
-2*(x + 5)*(2*x - 1)/9
Let d(n) = n**2 + 13*n + 55. Let r be d(-11). Let s be r/44*(-16)/(-18). Factor 1/3*f**2 + s - f.
(f - 2)*(f - 1)/3
Let i(z) be the second derivative of -7*z**6/10 - 111*z**5/20 - 59*z**4/4 - 35*z**3/2 - 9*z**2 + 10*z + 1. Solve i(l) = 0.
-3, -1, -2/7
Let n(g) be the first derivative of -g**7/5040 - g**6/360 - g**5/80 - g**4/36 + 31*g**3/3 + 7. Let r(m) be the third derivative of n(m). Factor r(d).
-(d + 1)**2*(d + 4)/6
Let i be (30/(-25))/((-3)/(-10)). Let q = i - -4. Solve -3*m + 2*m + 2 + m**3 + q*m**2 - 2*m**2 = 0.
-1, 1, 2
Factor 3*u**3 + 2*u**3 + 24 - u**3 - 44*u - 4*u**2 + 20*u**2.
4*(u - 1)**2*(u + 6)
Let p(d) be the first derivative of -3*d**4/4 + 27*d**3 - 209. Factor p(y).
-3*y**2*(y - 27)
Let 0*x - 16/13*x**4 + 0 + 0*x**2 + 2/13*x**5 + 32/13*x**3 = 0. What is x?
0, 4
Let n(u) be the first derivative of 3*u**5/10 + 39*u**4/8 + 33*u**3/2 + 93*u**2/4 + 15*u - 35. Factor n(p).
3*(p + 1)**3*(p + 10)/2
Factor 2 + 3 + 3386*a**2 + 4*a - 3387*a**2.
-(a - 5)*(a + 1)
Let u(t) be the second derivative of t**7/42 - t**6/30 - 3*t**5/10 + t**4/3 + 4*t**3/3 - 2*t - 8. Factor u(v).
v*(v - 2)**2*(v + 1)*(v + 2)
Let l(z) be the second derivative of z**7/210 - z**6/50 - z**5/20 + 9*z**4/20 - 16*z**3/15 + 6*z**2/5 + z - 9. Determine m, given that l(m) = 0.
-3, 1, 2
Let s(n) = n**5 - n**3 - n + 1. Let m(a) = -4*a**5 - 32*a**4 + 26*a**3 + 124*a**2 - 140*a + 26. Let f(y) = -m(y) - 10*s(y). Solve f(b) = 0 for b.
-2, 1/3, 1, 3
Suppose -3*d + 6 = 5*t - d, 2*t = 5*d + 14. Let a be (-1)/2 - (-49)/t. Let -2*b**4 + 0*b**2 - a*b**2 - 12*b**3 - b - 15*b + 0*b**4 = 0. What is b?
-2, 0
Factor -2/5 - 1/5*j**4 + 1/5*j - 1/5*j**3 + 3/5*j**2.
-(j - 1)**2*(j + 1)*(j + 2)/5
Let i(r) be the second derivative of -r**4/36 - 22*r**3/3 - 726*r**2 + 470*r. Let i(v) = 0. Calculate v.
-66
Let m be ((-39)/52)/(1/8). Let z be (-1)/m - 2/12. Let z*r + 2/5*r**2 - 2/5*r**4 + 0 + 0*r**3 = 0. Calculate r.
-1, 0, 1
Let j(o) = -4*o**2 - 4*o + 5. Let t(q) = -q**2 - q + 1. Let i(m) = 4*j(m) - 20*t(m). Factor i(p).
4*p*(p + 1)
Let n(j) = -3*j**2 + 156*j - 2181. Let t(b) = -9*b**2 + 469*b - 6544. Let v(i) = -17*n(i) + 6*t(i). Let v(z) = 0. Calculate z.
27
Let s be (2 - 15/10)/(28/112). Factor -3/2*o + 1/2*o**s - 2.
(o - 4)*(o + 1)/2
Let h(t) be the third derivative of -t**6/480 + 5*t**5/24 - 97*t**4/96 + 2*t**3 + 214*t**2. Determine z so that h(z) = 0.
1, 48
Let b(a) = -13*a**3 - 39*a**2 + 150*a - 168. Let m(l) = -8*l**3. Let w(g) = -b(g) + 2*m(g). Let w(z) = 0. Calculate z.
2, 4, 7
Let f = -333 + 2337/7. Let g be (-4)/(-10)*30*19/114. Factor -2/7*t**3 + 2/7 + f*t**g - 6/7*t.
-2*(t - 1)**3/7
Let q be (-6 + 1)*((-1906)/10 + 1). Let -2*p - 38*p - 5*p**3 - 20 - q*p**2 + 923*p**2 = 0. Calculate p.
-2, -1
Let r(c) be the first derivative of -c**9/13608 + c**7/3780 + 14*c**3/3 - 14. Let t(f) be the third derivative of r(f). Factor t(w).
-2*w**3*(w - 1)*(w + 1)/9
Suppose a - 21 = 4*i, -5*a - 24 = -4*a + 5*i. Let t be (-7 + 4)/((-1)/a). Factor -5/2*n + 3/4 + 1/4*n**4 - 3/2*n**t + 3*n**2.
(n - 3)*(n - 1)**3/4
Suppose 0 = o - 6*o + 50. Suppose o + 4 = 3*g - 4*h, -h = -5*g + 12. Factor -4 - 5*m**4 + 3*m**5 + 4 + g*m**3.
m**3*(m - 1)*(3*m - 2)
Suppose 386*y - 292*y - 470 = 0. Factor 25/2 + y*z + 1/2*z**2.
(z + 5)**2/2
Let v(x) be the third derivative of x**7/42 - x**6/2 + 90*x**4 - 1080*x**3 - 2*x**2 - 126. What is d in v(d) = 0?
-6, 6
Suppose 3*g - 30 = -4*q - 7, 6 = -2*g. Find b, given that -15*b**3 - 13*b**4 + 8*b**4 + 18*b**2 + 12*b + q*b**4 - 24 = 0.
-1, 2
Let b(u) be the second derivative of u**4/30 - 2*u**3/5 + 8*u**2/5 - 45*u. Factor b(t).
2*(t - 4)*(t - 2)/5
Let n be (3 + -7)*(37/(-37) - (-3)/6). Find j such that -3/7 + 4/7*j - 1/7*j**n = 0.
1, 3
Factor -10/3*t**2 - 22/3 + 112/3*t.
-2*(t - 11)*(5*t - 1)/3
Let x(o) be the third derivative of -1/15*o**4 + 0*o + 1/150*o**5 + 0 - 1/3*o**3 + 32*o**2. What is m in x(m) = 0?
-1, 5
Factor -47/2*t - 12 + 1/4*t**4 - 43/4*t**2 + t**3.
(t - 6)*(t + 1)**2*(t + 8)/4
Let q(d) = d**2 - 23. Let y be q(-5). Let p be (6 - (-264)/(-45))/(y/20). Factor 8/3*v + 4/3*v**2 + p.
4*(v + 1)**2/3
Let t be (-11*9/((-18)/(-4)))/(-1). Factor 2 + 121/2*s**2 - t*s.
(11*s - 2)**2/2
Let v be (83/(-216))/((-88)/12 - -8). Let q = v - -11/16. Factor -2/9*c + 0 - q*c**2.
-c*(c + 2)/9
Let o be 6 - (136/(-102))/(1/(-3)). Let w(q) be the first derivative of -1/4*q**3 + 3/4*q**o - 3/4*q - 4. Solve w(l) = 0 for l.
1
Factor -13*p**2 - 197*p - 1764 + 29*p + 13*p**2 - 4*p**2.
-4*(p + 21)**2
Suppose 16/3*c + 1/3*c**2 - 12 = 0. Calculate c.
-18, 2
Let t = 93 - 83. What is k in -t*k**2 - 4137*k + 5*k**4 + 5 + 4137*k = 0?
-1, 1
Let f(m) be the second derivative of -m**4/42 - 64*m**3/21 - 124*m**2/7 - 332*m. Solve f(d) = 0 for d.
-62, -2