Let m(k) be the first derivative of 0*k**2 + 0*k**3 - 3/20*k**4 - w*k**5 + 0*k + 1. Factor m(j).
-3*j**3*(j + 1)/5
Suppose m - 2*n + 4 = 0, 0*n + 8 = 4*n. Let o(u) be the second derivative of 1/90*u**6 + 1/30*u**5 - 1/9*u**3 - 1/6*u**2 - 2*u + m + 0*u**4. Factor o(w).
(w - 1)*(w + 1)**3/3
Let w(y) = y**2 + 8*y + 6. Let p be w(-7). Let c(h) = 4*h**2 + h - 4. Let o(z) = -z**2 + z + 1. Let s(a) = p*c(a) + o(a). Find i such that s(i) = 0.
-1, 1
Solve -2*w - 4*w**4 + 18*w**3 - 2*w - 62*w**3 + 32*w**3 - 12*w**2 = 0 for w.
-1, 0
Factor 8/5*d + 0 - 28*d**2.
-4*d*(35*d - 2)/5
Let m(r) be the third derivative of r**6/24 - 43*r**5/12 + 805*r**4/8 - 735*r**3/2 + 80*r**2 + 2*r. Suppose m(u) = 0. What is u?
1, 21
Let d(f) be the first derivative of -4 + 0*f + 1/900*f**6 - 4/3*f**3 - 1/75*f**5 + 1/15*f**4 + 0*f**2. Let g(v) be the third derivative of d(v). Factor g(l).
2*(l - 2)**2/5
Find n such that -1036*n - 292/5*n**2 + 5476/5 - 4/5*n**3 = 0.
-37, 1
Let v(q) be the third derivative of q**8/2856 - q**7/595 - q**6/68 - q**5/30 - q**4/34 + 145*q**2. Find f, given that v(f) = 0.
-1, 0, 6
Let l = 514 + -1027/2. Suppose -g - 3*g = 0. Factor 1/2*u**5 - 1/2*u**3 - 1/2*u**4 + l*u**2 + g + 0*u.
u**2*(u - 1)**2*(u + 1)/2
Let c(q) = -8*q**3 + 5*q**2 + 5*q - 5. Let d(y) = y**3 - y**2 + 1. Let n(t) = -5*c(t) - 15*d(t). Factor n(p).
5*(p - 1)*(p + 1)*(5*p - 2)
Let h = -1827 + 10963/6. Find a, given that -1/6*a**3 - h*a + 1/3*a**2 + 0 = 0.
0, 1
Let u = 8 + -257. Let x = u - -1249/5. Factor 4/5*k - 4/5*k**3 + 4/5*k**4 - x*k**2 + 0.
4*k*(k - 1)**2*(k + 1)/5
Let o be 0*(-2)/(-10) + 30. Let u = 1 - 6. Let h(m) = -m - 1. Let r(v) = -4*v**2 - 7*v - 6. Let x(l) = o*h(l) + u*r(l). Factor x(w).
5*w*(4*w + 1)
Let o be (-23290)/561 + 3 + (-93)/33. Let k = o - -251/6. Factor -3*v**3 - k*v**5 + 0 + 2*v**4 + 2*v**2 - 1/2*v.
-v*(v - 1)**4/2
Suppose 0 = 2*o - 4, o = -q + 6*o - 6. Factor 3*z**2 - q*z + 12 + 17*z - z.
3*(z + 2)**2
Let b be 278/(-168) + 9/3. Let f = b + -2/21. Solve f*o - 1/4*o**2 - 1/4*o**3 - 3/4 = 0.
-3, 1
Let u(l) = -l**3 - 4*l**2 - 32*l - 54. Let n be u(-2). Factor -4/9*h**3 - 8/9*h**n - 4/9*h + 0.
-4*h*(h + 1)**2/9
Suppose 45000 = -91*d + 187*d + 529*d. Factor 15/2*k**2 - d*k - 30.
3*(k - 10)*(5*k + 2)/2
Let r(q) = q**4 + 5*q**3 - 25*q**2 - 26*q + 51. Let x(z) = -4*z**4 - 16*z**3 + 76*z**2 + 80*z - 152. Let k(o) = -8*r(o) - 3*x(o). Determine b so that k(b) = 0.
-3, -2, 1, 2
Let p(w) be the third derivative of w**8/224 + 5*w**7/28 + 21*w**6/10 + 18*w**5/5 + 86*w**2. Suppose p(a) = 0. What is a?
-12, -1, 0
Let k(c) = 3*c**4 - 37*c**3 + 106*c**2 - 127*c + 41. Let d(j) = -j**4 + 12*j**3 - 35*j**2 + 42*j - 14. Let h(x) = 7*d(x) + 2*k(x). Factor h(n).
-(n - 4)**2*(n - 1)**2
Suppose 0 = 35*q - 84 - 21. Let g(j) be the first derivative of 2/3*j**4 - 2/9*j**q + 0*j + 3 - 2/3*j**2 + 2/5*j**5. Let g(x) = 0. What is x?
-1, 0, 2/3
Let l = -7 - 8. Let o be -3 + -2 + 2 - (10 + l). Suppose -2/7*v + 2/7*v**o + 0 = 0. Calculate v.
0, 1
Let -4*q**4 + q**4 - 140*q**3 + 137*q**3 + 3*q + 3*q**2 = 0. What is q?
-1, 0, 1
Let f(c) be the second derivative of -c**5/60 - 29*c**4/36 - 65*c**3/6 + 75*c**2/2 + 6*c - 7. Solve f(v) = 0.
-15, 1
Let n(t) be the first derivative of -t**6/10 + 3*t**5/10 - t**3 + 3*t**2/2 + 10*t - 41. Let r(p) be the first derivative of n(p). Factor r(j).
-3*(j - 1)**3*(j + 1)
Suppose u - 4*u - a = -194, -5*u - 4*a + 321 = 0. Factor -40 - 5*b**3 + 45*b - 30*b**2 - 40*b - u*b.
-5*(b + 2)**3
Let f = -10439/30 + 348. Let c(h) be the second derivative of -2/5*h**2 - f*h**4 + 0 - 1/5*h**3 - 4*h. Factor c(i).
-2*(i + 1)*(i + 2)/5
Let d(r) be the second derivative of -2/3*r**3 - 28*r + 0 - 1/12*r**4 - 2*r**2. Factor d(p).
-(p + 2)**2
Let s(m) be the first derivative of m**6/780 + 2*m**5/65 + 4*m**4/13 + 64*m**3/39 + 5*m**2/2 - 2. Let t(n) be the second derivative of s(n). Factor t(f).
2*(f + 4)**3/13
Let l = 4 + -2. Let u = 55 + -53. Suppose l*c - c**2 + c**2 - c**u = 0. What is c?
0, 2
Determine g so that -8/5*g**2 + 12/5 + 2/5*g**3 + 2/5*g = 0.
-1, 2, 3
Let g be 40/(-50)*(-10)/4. Solve -7*w**4 + 20*w**3 - 13*w**2 + 3*w**2 - 5*w**g + 2*w**4 = 0 for w.
0, 1, 3
Let r(t) be the second derivative of -t**4/4 - 14*t**3 - 294*t**2 - 100*t. Let r(d) = 0. Calculate d.
-14
Let d(f) = 4*f**5 - 17*f**4 - 7*f**3 + 18*f**2 + 3*f - 11. Let x(v) = -v**5 + 2*v**4 + v**2 + v - 1. Let m(i) = d(i) + 5*x(i). Factor m(g).
-(g - 1)**2*(g + 1)*(g + 4)**2
Solve 2/9*b**2 + 4 + 22/9*b = 0 for b.
-9, -2
Let c(q) be the second derivative of q**7/168 + q**6/96 - 5*q**2/2 - 2*q. Let n(j) be the first derivative of c(j). Factor n(x).
5*x**3*(x + 1)/4
Let t be (-284)/(-64) + 4/(-1). Let p = t - -1/16. Factor -p*i**3 + i**2 + 0 - 1/2*i.
-i*(i - 1)**2/2
Determine p so that 8/5*p**2 + 0 - 2/5*p**3 + 2*p = 0.
-1, 0, 5
Determine u so that 0*u - 5/4*u**4 + 0*u**2 + 3/2*u**3 + 0 + 1/4*u**5 = 0.
0, 2, 3
Suppose 140*f**2 + 1690 - 7*f**3 + 18*f**3 - 12*f**3 - 1105*f - 4*f**3 = 0. What is f?
2, 13
Let y(z) = -2*z**2 + 2. Let k(f) = f**2 - 1. Let p(a) = -8*k(a) - 5*y(a). Factor p(r).
2*(r - 1)*(r + 1)
Let c(z) = z**3 - 4*z**2 - 4*z. Let t be c(5). Suppose -18 = 290*x - 296*x. Factor -m**x + 1/2*m**2 + 5/4*m - m**4 - 1/4*m**t + 1/2.
-(m - 1)*(m + 1)**3*(m + 2)/4
Let d = -849/5 - -170. Let n(j) be the second derivative of 0 + 2/3*j**4 - 2/3*j**3 - 9*j + 0*j**2 - d*j**5. Solve n(w) = 0.
0, 1
Suppose -27/2 - 3/2*g**3 - 21/2*g**2 - 45/2*g = 0. What is g?
-3, -1
Let -15*g**3 + 5*g + 27/2*g**2 + 0 - 7/2*g**4 = 0. What is g?
-5, -2/7, 0, 1
Factor -4/3*i + 0 + 1/6*i**2.
i*(i - 8)/6
Let y = 153 + -149. Let b(q) be the first derivative of 0*q + 0*q**2 + 2 - 1/6*q**y + 0*q**3 - 1/15*q**5. Determine a so that b(a) = 0.
-2, 0
Let b(j) be the third derivative of -3*j**5/20 + 13*j**4/4 - 8*j**3 - j**2 + 706*j. Factor b(a).
-3*(a - 8)*(3*a - 2)
Let z(b) = 8*b**2 - 36*b + 28. Let s(i) = i**2 - 2*i + 1. Let p(h) = 4*s(h) - z(h). Factor p(n).
-4*(n - 6)*(n - 1)
Let o(u) = u**3 + 12*u**2 + 44*u + 36. Let r(b) = b**3 + 11*b**2 + 44*b + 34. Let v(l) = -3*o(l) + 2*r(l). Factor v(x).
-(x + 2)**2*(x + 10)
Let c = -74 - -74. Let t(x) be the third derivative of -1/60*x**5 + 5*x**2 + c + 1/18*x**3 + 0*x - 1/72*x**6 - 1/315*x**7 + 1/72*x**4. Factor t(w).
-(w + 1)**3*(2*w - 1)/3
Let u = 397/18 + -22. Let c(d) be the second derivative of 1/9*d**3 - 7*d - 1/30*d**5 - u*d**4 + 1/3*d**2 + 0. Factor c(f).
-2*(f - 1)*(f + 1)**2/3
Suppose -5*s = 5*f - 25, 5*s + 3*f - 25 = 2*f. Factor 5*y**s - 26*y**4 + 10*y**3 - 20*y + 6*y**4 + 5*y**3 + 20*y**2.
5*y*(y - 2)**2*(y - 1)*(y + 1)
Let j(s) be the second derivative of -s**5/40 - 73*s**4/24 + 149*s**3/12 - 75*s**2/4 - s + 18. Factor j(k).
-(k - 1)**2*(k + 75)/2
Let c(m) = -2*m + 5. Let w be c(1). Factor -1 + g**4 + 33*g**w - 39*g**2 + 7*g + 7 - 8*g**4.
-(g - 3)*(g - 1)**2*(7*g + 2)
Let n(p) be the third derivative of 0*p**3 + 10*p**2 - 1/48*p**6 + 0 - 5/48*p**4 + 0*p + 1/12*p**5. Suppose n(v) = 0. Calculate v.
0, 1
Suppose 0 = -22*u + 16*u + 24. Let c = 5 - 3. Factor 5*a**2 + 4*a**c - 6 + 4*a - u*a**2 - 3*a**2.
2*(a - 1)*(a + 3)
Suppose 44 - 68 = 11*z - 46. Determine r so that 2/11 - 12/11*r + 10/11*r**z = 0.
1/5, 1
Determine f, given that 5*f**4 - 10*f**3 + 1145 + 5*f - 4*f**2 - 1140 + 5*f**5 - 6*f**2 = 0.
-1, 1
Let v(s) be the third derivative of -s**7/630 + s**6/180 + s**5/60 - s**4/18 - 2*s**3/9 - 2*s**2 - 1. Determine t, given that v(t) = 0.
-1, 2
Let g(l) be the third derivative of 5/42*l**7 + 1/12*l**5 + 1/6*l**6 + 10*l**2 + 0*l**3 + 5/168*l**8 + 0 + 0*l + 0*l**4. What is o in g(o) = 0?
-1, -1/2, 0
Let m = 20 + -18. Suppose -m*d = 5*n - 148, -3*n + 2*d + 132 = 2*n. Suppose -5*x**4 - 4*x**2 + n*x**5 + x - 9*x + 60*x**3 - 71*x**4 = 0. Calculate x.
-2/7, 0, 1
Let c be 1/((-9)/3 - 28/(-8)). Factor 144*q + c*q**2 + 7 - 115 - 23*q**2 - 18*q**2 + 3*q**3.
3*(q - 6)**2*(q - 1)
Let r(n) = n - 8. Let q be r(12). Factor 2*o + 6*o - 8*o**4 + 4*o**q - 8*o**3 + 4*o**2.
-4*o*(o - 1)*(o + 1)*(o + 2)
Let o(w) be the third derivative of -w**7/420 + w**6/80 + w**5/120 - w**4/16 - 46*w**2 + 1. Let o(r) = 0. What is r?
-1, 0, 1, 3
Suppose 16 = -2*p + 36. Let s be (-6)/(-14) + (11 - p). Find n such that s*n + 2/7*n**3 + 8/7*n**2 + 4/7 = 0.
-2, -1
Let y(w) = w**3 - 17*w**2 - 19*w + 21. Let u be y(18). Factor 9*s**2 - 2*s**u - 