ven that y(s) = 0.
0, 2/7
Factor 2/5*n**4 + 54/5*n**3 + 486/5*n**2 + 1458/5*n + 0.
2*n*(n + 9)**3/5
Let b(l) be the first derivative of 10/3*l**3 - 40*l - 10*l**2 + 5/4*l**4 + 27. Factor b(r).
5*(r - 2)*(r + 2)**2
Suppose 15 = -3*n + 36, u + n = 9. Factor 20/9*s + 0 - 4/9*s**u.
-4*s*(s - 5)/9
Let k(c) be the first derivative of -98*c**5/15 + 343*c**4/30 - 52*c**3/15 - 28*c**2/15 + 16*c/15 + 210. Determine r, given that k(r) = 0.
-2/7, 2/7, 2/5, 1
Let h(q) be the second derivative of -20*q**2 + 10*q**3 + 1/4*q**5 + 0 - 11*q - 5/2*q**4. Let h(y) = 0. What is y?
2
Suppose 370 = 44*h - 49*h. Let z = -73 - h. Find g such that -z - 7/4*g**4 + 15/2*g**3 + 6*g - 43/4*g**2 = 0.
2/7, 1, 2
Determine w so that -13/2*w - 6*w**2 + 0 + 1/2*w**3 = 0.
-1, 0, 13
Let a(m) = -2*m**2 - m - 1. Let h(k) = -5*k**2 - 455*k + 10120. Let g(d) = -5*a(d) + h(d). Determine j so that g(j) = 0.
45
Let i(l) = -l**2 + 6*l + 135. Let w be i(15). Let m(t) be the second derivative of 4*t**2 - 1/2*t**4 + 0*t**3 - 6*t + 1/10*t**5 + w. Factor m(p).
2*(p - 2)**2*(p + 1)
Suppose -19*t = -15*t + 664. Let w = t + 1333/8. Factor 1/8 + 5/8*o + 5/4*o**3 + w*o**4 + 5/4*o**2 + 1/8*o**5.
(o + 1)**5/8
Suppose -4084 = 9*h - 4102. What is q in 3/2*q**h + 1/2 - 3/2*q - 1/2*q**3 = 0?
1
Let u(p) be the first derivative of -4/3*p + 1/6*p**4 - 1/3*p**2 - 2/15*p**5 + 4 + 2/3*p**3. Find n such that u(n) = 0.
-1, 1, 2
Let m(i) = -3*i**2 + 71*i + 79. Let a(y) = -2*y**2 + 35*y + 40. Let j(o) = 5*a(o) - 3*m(o). Factor j(k).
-(k + 1)*(k + 37)
Let j = -3 + 8. Suppose -2*c + 20 = 3*c. Suppose 4*t**j + 9*t**3 + c*t**2 - t**2 + 5*t**5 - 6*t - 3*t**4 - 12*t**5 = 0. Calculate t.
-2, -1, 0, 1
Let v = 299/7160 + -3/179. Let o(n) be the third derivative of 0*n - 1/600*n**6 + 0 + v*n**4 - 4*n**2 + 1/15*n**3 + 0*n**5. Suppose o(p) = 0. What is p?
-1, 2
Let k = 24567 - 171966/7. Factor -k*x**3 + 6/7*x + x**2 + 0.
-x*(x - 3)*(3*x + 2)/7
Let z(u) be the second derivative of -1/18*u**4 + 17*u + 1/9*u**3 + 0*u**2 + 0. Find v, given that z(v) = 0.
0, 1
Suppose 0 = -3*i - x - 4*x - 85, -4*x = 4*i + 124. Let w = i + 41. Let 6*a - w*a**3 - 9/2*a**2 - 3/2*a**4 + 6 = 0. Calculate a.
-2, -1, 1
Let u = -26 + 28. Let 4*i**u - 2*i**3 - 4*i**4 - 6*i + 8*i - 3*i**3 + 3*i**3 = 0. Calculate i.
-1, -1/2, 0, 1
Let l(h) be the second derivative of -3/20*h**5 - 12*h**3 + 0 - 24*h**2 - 9/4*h**4 - h. Suppose l(g) = 0. What is g?
-4, -1
Factor -184 + 58 - 5*b**2 + b**2 + 54 - 76*b.
-4*(b + 1)*(b + 18)
Factor 12/7*z**3 + 0*z - 1/7*z**4 + 0 - 20/7*z**2.
-z**2*(z - 10)*(z - 2)/7
Let q(n) be the first derivative of 2/3*n**3 + 0*n**2 + 30 - 1/6*n**4 - 8/3*n. Factor q(p).
-2*(p - 2)**2*(p + 1)/3
Find v, given that -1/4*v**4 + 0*v + 9/4*v**2 + 0 - 2*v**3 = 0.
-9, 0, 1
Solve -10*u + 2*u**3 - 16/3*u**2 - 8/3 = 0 for u.
-1, -1/3, 4
Suppose 5*k - 10 = 0, 3*f - 4*k + 22 - 2 = 0. Let b be ((-6)/f)/(26/4 - 6). Factor -1 + 7/3*p - 5/3*p**2 + 1/3*p**b.
(p - 3)*(p - 1)**2/3
Let b(j) = j**3 + j**2 - 1. Let r(d) = 8*d**2 + 16*d - 20. Let f(y) = 4*b(y) - r(y). Determine z, given that f(z) = 0.
-2, 1, 2
Suppose -4*q - 1541 + 1608 = -u, -q + u = -19. Suppose q + 1/4*g**2 - 4*g = 0. What is g?
8
Suppose 10*c - 11*c = -1. Let n be 5/c + 924/(-196). Factor -n*d**3 + 2/7*d**5 - 2/7*d**4 + 2/7*d**2 + 0*d + 0.
2*d**2*(d - 1)**2*(d + 1)/7
Let n(g) be the second derivative of g**9/113400 + g**8/25200 - g**7/18900 - g**6/2700 - 7*g**4/12 - g. Let s(u) be the third derivative of n(u). Factor s(d).
2*d*(d - 1)*(d + 1)*(d + 2)/15
Let y = 46179 + -46179. Suppose y*p + 0*p**3 + 1/4*p**4 - p**2 + 0 = 0. What is p?
-2, 0, 2
Let r(m) be the first derivative of 10/9*m**3 - 2/3*m**2 + 0*m + 2/15*m**5 + 1 - 2/3*m**4. Let r(y) = 0. Calculate y.
0, 1, 2
Let q(i) = -9*i**2 - 15*i - 12. Let b(z) be the third derivative of 19*z**5/60 + 31*z**4/24 + 25*z**3/6 + 5*z**2 - z. Let o(u) = 6*b(u) + 13*q(u). Factor o(v).
-3*(v + 1)*(v + 2)
Let s be -7 + -3 + 126/8. What is g in 7/4*g**4 + 13/4*g + s*g**3 + 1/2 + 27/4*g**2 = 0?
-1, -2/7
Let p be 4 + -3 + 4/(-8) - 267/(-54). What is r in -1/9*r**2 - p + 14/9*r = 0?
7
Let r(k) be the first derivative of -k**6/10 + 39*k**5/25 - 36*k**4/5 + 36*k**3/5 + 63. Solve r(s) = 0 for s.
0, 1, 6
Factor 25*o + 54*o + 62*o + o**2 + 21*o + 6561.
(o + 81)**2
Let n = 935/8 + -925/8. What is c in 5/2*c**4 - 5/2*c**2 + n*c**5 + 0 + 0*c**3 - 5/4*c = 0?
-1, 0, 1
Let n(h) be the second derivative of h**3 + 0*h**2 + 0 + 38*h + 1/4*h**4. Factor n(p).
3*p*(p + 2)
Suppose 0*i - 8 = -4*h + i, 8 = 4*h + 3*i. Let o(d) = 2*d**3 + 77*d**2 - 36*d + 119. Let u be o(-39). Factor h*z**2 + 7*z + 2*z**u + z.
4*z*(z + 2)
Let t = 2 + 1. Suppose 3*p + 3*u + 3 = 0, -t*u - u = -5*p - 14. Let l(w) = w + 1. Let v(d) = d**3 + 7*d**2 + 13*d + 7. Let y(s) = p*l(s) - v(s). Factor y(g).
-(g + 1)*(g + 3)**2
Let i(n) be the first derivative of -n**5/105 + n**4/42 + 4*n**3/7 - 7*n**2/2 - 42. Let d(m) be the second derivative of i(m). Solve d(h) = 0 for h.
-2, 3
Let l(j) = j**3 - 24*j**2 - 52*j + 10. Let b be l(26). Let g be 3/2 + 2 + (-15)/b. Let 2/3*d**g - 2/3*d - 4/3 = 0. Calculate d.
-1, 2
Factor 2/13*p**5 + 10/13*p**4 - 50/13*p**2 - 10/13*p**3 - 32/13 + 80/13*p.
2*(p - 1)**3*(p + 4)**2/13
Let 968/9*o + 2/9*o**3 + 0 + 88/9*o**2 = 0. Calculate o.
-22, 0
Let 363/4 - 33/2*f + 3/4*f**2 = 0. Calculate f.
11
Let x(r) be the second derivative of -7*r**4/60 - 11*r**3/15 + 12*r**2/5 - 606*r. Suppose x(w) = 0. Calculate w.
-4, 6/7
Let l(i) be the third derivative of -i**7/630 + i**6/108 + 11*i**5/540 - 5*i**4/108 - 4*i**3/27 + 2*i**2 + 81. What is v in l(v) = 0?
-1, -2/3, 1, 4
Let v(g) = g**3 - g**2 + 1. Let j(x) = 6*x**3 - 6*x**2 - 8*x + 17. Let i(t) = 2*j(t) - 10*v(t). Factor i(q).
2*(q - 2)**2*(q + 3)
Suppose 4*l - l = -3*b - 60, -b = 2*l + 36. Let r be (-4)/3 + (-12 - l). Suppose 0*w + 2/3*w**2 - 14/3*w**4 - r*w**5 + 0 - 4/3*w**3 = 0. What is w?
-1, 0, 1/4
Let s = -2514 + 2519. Let x(k) be the second derivative of -1/2*k**s + 0*k**2 - 13*k + 0 + 0*k**3 + 5/6*k**4 + 1/12*k**6. Determine t so that x(t) = 0.
0, 2
Suppose 2*j - 28*d = -33*d + 19, -6 = 3*j - 4*d. Factor -4/5*n - 2/5*n**4 + 0*n**j + 4/5*n**3 + 2/5.
-2*(n - 1)**3*(n + 1)/5
Let l = 756 - 750. Let j(o) be the second derivative of 0 + l*o**2 + 7*o + 2*o**3 + 1/4*o**4. Factor j(x).
3*(x + 2)**2
Let a(b) be the second derivative of 3*b**5/20 - 25*b**4/16 + 21*b**3/4 - 27*b**2/8 + 2*b - 35. Suppose a(z) = 0. What is z?
1/4, 3
Let i be (3/50)/((-450)/(-375)). Let k(r) be the third derivative of 6*r**2 + 0 + 0*r - i*r**5 + 3/4*r**4 - 9/2*r**3. Let k(f) = 0. What is f?
3
Let s(i) be the first derivative of -5*i**4/4 + 20*i**3/3 - 15*i**2/2 - 281. Factor s(y).
-5*y*(y - 3)*(y - 1)
Let g be 4/24 + (-82)/(-12). Let f(b) = b**2 - 6*b - 4. Let q be f(g). Let -3*v**5 + 3*v**2 - 4*v**4 + 0*v**4 + v**4 + q*v**3 = 0. What is v?
-1, 0, 1
Let o(v) be the third derivative of -v**11/2162160 + v**9/196560 - v**7/32760 + 13*v**5/60 + 2*v**2. Let h(c) be the third derivative of o(c). Factor h(q).
-2*q*(q - 1)**2*(q + 1)**2/13
Let v = -14 - -25. Factor 9 + 18*n**3 + 13*n**2 + 16*n**2 + 3*n**4 + v*n**2 - 4*n**2 + 30*n.
3*(n + 1)**3*(n + 3)
Let d(j) = -19*j**2 + j + 9. Let z(h) = -6*h**2 - 2*h + 1. Let a(k) = -7*k**2 - k + 2. Let v(s) = 3*a(s) - 2*z(s). Let f(c) = 4*d(c) - 9*v(c). Factor f(r).
5*r*(r - 1)
Let n(i) be the third derivative of -i**6/40 - 11*i**5/35 - 17*i**4/14 - 8*i**3/7 - 71*i**2 - 2. Factor n(m).
-3*(m + 2)*(m + 4)*(7*m + 2)/7
Suppose 0 = -0*z + 3*z, 6 = 3*s - z. Let l(f) = -f**2 + f. Let m(b) = 3*b**2 - 8*b. Let y(c) = s*l(c) - m(c). Factor y(i).
-5*i*(i - 2)
Let n = 10/547 - 4312/56341. Let w = 91/206 - n. Factor -w - 1/6*l**2 + 2/3*l.
-(l - 3)*(l - 1)/6
Let p(i) be the first derivative of -4 - i**4 + 0*i**2 - 24/5*i**6 - 1/9*i**3 - 18/5*i**5 + 12*i. Let s(d) be the first derivative of p(d). Factor s(t).
-2*t*(6*t + 1)**3/3
Factor 4*g**3 + 58/3*g**2 + 40/3 + 88/3*g.
2*(g + 2)**2*(6*g + 5)/3
Let p be 24/4 - (-2 + 1). Suppose p*q - 80 = 2*q. Let 7 + 3*y**2 - 9*y + q - 17 = 0. Calculate y.
1, 2
Let t(f) be the second derivative of f**4/36 - 17*f**3/6 - 26*f**2/3 + 4*f - 15. What is g in t(g) = 0?
-1, 52
Let s(c) = -c. Let m be s(-7). Find w, given that 12*w**4 - 80*w**3 + 156*w**2 - m + 30 + 9 - 120*w = 0.
2/3, 1, 4
Suppose 0 = -x + 5*c - 32, -24 = 2*