r(i).
2*(i - 14)*(i - 3)
Let c(d) be the second derivative of d**5/6 + 133*d**4/72 + 55*d**3/9 + 17*d**2/3 - 430*d. Factor c(z).
(z + 2)*(4*z + 17)*(5*z + 2)/6
Factor -272*c**2 + 327 - 216*c**2 - 4*c**3 - 54522*c + 4405 + 8957 - 447*c**2.
-(c + 117)**2*(4*c - 1)
Let j = 19 - 3. Factor 4*m**3 - 12*m**3 + 8*m**4 - 4*m + 3*m**3 + j*m**2 - 15*m**3.
4*m*(m - 1)**2*(2*m - 1)
Let z(f) be the second derivative of 3*f**5/20 + 5*f**4/4 + 3*f**3/2 - 27*f**2/2 - 2*f + 27. Factor z(w).
3*(w - 1)*(w + 3)**2
Let o be ((-24)/20)/((27/(-30))/3). Let z be 6/(-9)*-15*o/8. Determine a, given that -11/6*a**4 + 1/6*a - 3/2*a**3 - 2/3*a**z + 0 - 1/6*a**2 = 0.
-1, 0, 1/4
Factor 1/6*j**3 - 3*j**2 - 36 + 18*j.
(j - 6)**3/6
Let f(x) be the second derivative of -x**6/10 - 27*x**5/20 + x**4/4 + 9*x**3/2 - 2*x + 32. Let f(i) = 0. What is i?
-9, -1, 0, 1
Factor 758*a + 4*a**3 + 0*a**3 - 171 - 169 + a**3 - 73*a - 350*a**2.
5*(a - 68)*(a - 1)**2
Let t(c) be the first derivative of -3*c**6/16 + 21*c**5/8 - 39*c**4/8 + 5*c**3/2 - 232. Let t(r) = 0. Calculate r.
0, 2/3, 1, 10
Let l = 13127/2 + -6556. Solve -3*p + 0 + 3/2*p**4 + l*p**2 - 6*p**3 = 0 for p.
0, 1, 2
Let q = -87 - -88. Let s be (q/5)/(2 + -1). Find p, given that 0 + 3/5*p + s*p**2 = 0.
-3, 0
Let m = -185 + 188. Let v(u) be the first derivative of -1/3*u**2 - 5 - 1/6*u**4 - 4/9*u**m + 0*u. Factor v(l).
-2*l*(l + 1)**2/3
Let t(l) = 2*l**5 - 24*l**4 + 10*l**3 - 6*l - 6. Let m(z) = -2*z**5 + 23*z**4 - 11*z**3 + 5*z + 5. Let p(x) = 6*m(x) + 5*t(x). Let p(d) = 0. Calculate d.
0, 1, 8
Suppose -22/3 - 1/3*n**4 - 7*n + 23/3*n**2 + 7*n**3 = 0. Calculate n.
-1, 1, 22
Let t(v) be the third derivative of v**6/240 - 19*v**5/120 + 3*v**4/8 + 3*v**2 + 25. Determine f so that t(f) = 0.
0, 1, 18
Suppose 56 = c - 210. Let o = 2928/11 - c. Factor o*n**3 - 2/11 + 2/11*n**2 - 2/11*n.
2*(n - 1)*(n + 1)**2/11
Let i(v) be the second derivative of -v**4/24 + 17*v**3/12 - 4*v**2 - 59*v. Factor i(q).
-(q - 16)*(q - 1)/2
Let t(h) be the third derivative of 0 + 9*h**2 + 1/110*h**5 - 1/330*h**6 - 1/33*h**3 + 0*h + 0*h**4. Factor t(w).
-2*(w - 1)**2*(2*w + 1)/11
Let d be (-10)/15 + 14/20. Let z = 13/30 - d. Solve z*x + 6/5*x**3 + 0 - 2/5*x**4 - 6/5*x**2 = 0 for x.
0, 1
Find s such that 2/5*s**5 + 0 - 28/5*s**4 + 48/5*s**3 + 0*s + 0*s**2 = 0.
0, 2, 12
Let r(x) be the first derivative of x**6/30 + x**5/20 - x**4/12 - x**3/6 + 9*x - 3. Let a(v) be the first derivative of r(v). Suppose a(j) = 0. What is j?
-1, 0, 1
Let s(n) be the first derivative of -n**5/35 + 4*n**4/7 - 62*n**3/21 + 40*n**2/7 - 33*n/7 - 410. Factor s(o).
-(o - 11)*(o - 3)*(o - 1)**2/7
Factor -13/2*r**3 - 1 + 13/2*r + r**2.
-(r - 1)*(r + 1)*(13*r - 2)/2
Let m(y) be the second derivative of y**4/90 + y**3/3 - 3*y + 6. Factor m(u).
2*u*(u + 15)/15
Let b = 289/8 - 71/2. Let o = b - -1/24. Factor x**4 - o*x + 0 + 1/3*x**5 - x**2 + 1/3*x**3.
x*(x - 1)*(x + 1)**2*(x + 2)/3
Let p(m) be the first derivative of -2*m**3/15 - 10*m**2 - 348. What is o in p(o) = 0?
-50, 0
Let j be 10/(-8) + 425/340. Let i(t) be the third derivative of -5*t**2 - 1/15*t**5 - 1/2*t**4 + j + 8/3*t**3 + 0*t. Factor i(x).
-4*(x - 1)*(x + 4)
Let u = 565/732 - 4/183. Let -u*s**3 - 6*s - 21/4*s**2 + 12 = 0. Calculate s.
-4, 1
Let j(s) = -3*s**5 - 21*s**3 + 24*s**2 + 12*s + 12. Let c(f) = f**4 - f**3 + f**2 + 1. Let h(v) = 12*c(v) - j(v). Factor h(n).
3*n*(n - 1)*(n + 1)*(n + 2)**2
Let x(y) = -y**3 + 5*y**2 - y + 3. Let k be x(4). Let p = 17 - k. Factor -4*z**3 + 3*z - z + p - 4 + 2*z**4 + 2*z.
2*(z - 1)**3*(z + 1)
Find q such that 6/11*q**2 + 6/11*q**3 - 2/11*q**4 + 12/11 - 2*q = 0.
-2, 1, 3
Let o(f) = 11*f**3 - 33*f**2 + 222*f - 435. Let u(s) = -3*s**3 - s**2 - 2*s + 1. Let c(t) = o(t) + 3*u(t). Let c(m) = 0. Calculate m.
6
Let u be 8/(-12)*15/(-30). Factor -1/3*s**3 + 2/3*s**4 + 0 - 2/3*s**2 + u*s.
s*(s - 1)*(s + 1)*(2*s - 1)/3
Let m(a) be the second derivative of 0 - 1/20*a**6 + 9/10*a**5 + 0*a**2 - 6*a**4 + 16*a + 16*a**3. Factor m(d).
-3*d*(d - 4)**3/2
Suppose 8*f + 2*r - 10 = 5*f, 0 = 3*f - 3*r + 15. Factor -1/3*w**4 + 0*w**2 + 0 + 0*w**3 + f*w.
-w**4/3
Let f be 9 - 12/3 - 23/5. Let v = 2 + 1. Determine q, given that -2/5*q**v - 2/5 + 2/5*q + f*q**2 = 0.
-1, 1
Let u = -4788/5 + 958. Factor u*f**3 + 4/5 + 0*f**2 - 6/5*f.
2*(f - 1)**2*(f + 2)/5
Let y be (-164)/(-2) + (-2 - (5 - 4)). Suppose -79*i - i**2 + y*i = 0. What is i?
0
Let z(k) = -26*k**3 - k**2 + 2*k - 2. Suppose -3*q + 3 = -0*q. Let i(u) = u**3 - u**2 - 1. Let a(c) = q*z(c) - 2*i(c). Factor a(h).
-h*(4*h + 1)*(7*h - 2)
Suppose y = -1 + 3. Factor 7 - 3*c**2 - 17 - 25*c - y*c**2 + 10*c.
-5*(c + 1)*(c + 2)
Let s = 63 + -43. Suppose s + 4 = 6*n. Factor 96/5*g**2 + 0 + 12/5*g + 147/5*g**n + 231/5*g**3.
3*g*(g + 1)*(7*g + 2)**2/5
Let j(y) be the second derivative of -y**7/21 - 2*y**6/5 - 7*y**5/5 - 8*y**4/3 - 3*y**3 - 2*y**2 - 195*y. Factor j(u).
-2*(u + 1)**4*(u + 2)
Let j(x) = 48*x**2 + 90*x - 57. Let c(d) be the third derivative of 7*d**5/60 + 13*d**4/24 - 4*d**3/3 + 13*d**2. Let s(q) = 27*c(q) - 4*j(q). Factor s(p).
-3*(p - 1)*(p + 4)
Solve -4/5*k + 6/5 - 2/5*k**2 = 0 for k.
-3, 1
Factor 4/5*u**3 - 8/5*u - 4/5*u**2 + 0.
4*u*(u - 2)*(u + 1)/5
Let 0*z + 0*z**2 + 5/2*z**3 + 5/2*z**5 - 5*z**4 + 0 = 0. What is z?
0, 1
Factor -27/5*s**2 + 324/5 - 3/5*s**3 + 0*s.
-3*(s - 3)*(s + 6)**2/5
Factor 2/3*t**2 + 96 - 16*t.
2*(t - 12)**2/3
Let m = 22 - 19. Let v = -7 + 11. Find u, given that 70*u**3 + 2 - 15*u**v - u**2 + 11*u**2 - 45*u**5 - 7*u + m - 18*u = 0.
-1, 1/3, 1
Let g = 2700 - 2697. Let q(k) be the first derivative of 0*k - 1/18*k**g - 6 + 5/12*k**2. Suppose q(v) = 0. What is v?
0, 5
Suppose -5*h = -2*h - 2*d + 8, -4 = -3*h - d. Factor -2/7*j - 1/7*j**2 + h + 1/7*j**3.
j*(j - 2)*(j + 1)/7
Factor 108*u - 13 + 37 + 71 + 3 + 6 + 4*u**2.
4*(u + 1)*(u + 26)
Factor -2*h**3 + 2086*h + 2*h**3 + 50410 - 10511*h - 5*h**3 - 700*h**2 - 15360*h.
-5*(h - 2)*(h + 71)**2
Let v(u) = 12*u**3 - 52*u**2 + 52*u + 20. Let p(o) = -12*o**3 + 51*o**2 - 52*o - 19. Let t(h) = 4*p(h) + 5*v(h). Let t(z) = 0. Calculate z.
-1/3, 2, 3
Suppose 8*f = 12*f. Suppose f = 32*w - 29*w. Factor -2*y**3 - y**3 + w*y**3 + 3*y.
-3*y*(y - 1)*(y + 1)
Let s = 34/21 - 20/21. Suppose -5 = -3*a + 1. Factor 0 + 2/3*w - s*w**a.
-2*w*(w - 1)/3
Let p(a) = -a**5 - 10*a**4 + 17*a**3 + 13*a**2 - 47*a + 13. Let z(b) = -10*b**4 + 16*b**3 + 12*b**2 - 50*b + 14. Let j(g) = 6*p(g) - 5*z(g). Solve j(h) = 0.
-2, 1/3, 1
Suppose -3*w - 4*y = -17, 0 = w - 2*w - 3*y + 9. Solve 14*a - 2*a + 3*a**4 + 7*a**w - 16*a**3 - 6*a**4 = 0 for a.
-2, 0, 1
Let s = -42 - -26. Let u be ((-3)/2)/(12/s). Factor 0*d - d**4 - 1/3*d**5 + 0*d**u - 2/3*d**3 + 0.
-d**3*(d + 1)*(d + 2)/3
Let z(g) be the first derivative of 3*g**5/5 + 27*g**4/4 + 21*g**3 + 57*g**2/2 + 18*g + 163. Find i such that z(i) = 0.
-6, -1
Let a(n) be the first derivative of 4*n**3/15 - 146*n**2/5 + 288*n/5 + 387. What is b in a(b) = 0?
1, 72
Let c be 16/9 - (-10)/45. Let i = 41/180 - -1/45. Factor -3/4*p**c + 1 + 0*p + i*p**3.
(p - 2)**2*(p + 1)/4
Let l(q) be the first derivative of -9*q**4/7 - 20*q**3/21 + 8*q**2/7 + 51. What is r in l(r) = 0?
-1, 0, 4/9
Suppose 26*w - 153 = -23. Let k(g) be the first derivative of -2*g + w - 2/3*g**2 - 2/27*g**3. Find u such that k(u) = 0.
-3
Let i(n) = -6*n - 40. Let p be i(-7). Factor 6*c**3 + 21*c**p + 6*c + 55*c**4 + 6*c - 28*c**4 - 30*c**4.
-3*c*(c - 4)*(c + 1)**2
Let j(s) = 4*s - 7 - 3*s + 0. Let h be j(9). Suppose -3 - 3*k**4 + 13*k**h + 3*k - 7*k**2 + 5*k**5 - 2*k**5 - 6*k**3 = 0. Calculate k.
-1, 1
Let g(h) be the third derivative of h**7/1960 + h**6/420 - h**5/40 + h**4/14 + 5*h**3/3 + 5*h**2. Let o(m) be the first derivative of g(m). Factor o(z).
3*(z - 1)**2*(z + 4)/7
Suppose 3*w - 4*w + 2 = 0. Suppose 4 + 1 - 12*s**w + 1 + 33*s - 12*s = 0. What is s?
-1/4, 2
Let j be (-20)/6*12/(-10). Suppose -9*p = -5*p + u - 97, -3*p + 69 = 2*u. Factor 0 + 3 - j - 20*f - 3 - p*f**2.
-(5*f + 2)**2
Suppose -2*v = -l + 4 - 16, 4*l + 48 = -4*v. Let g be (6/78)/(2/l*-3). Solve -g*q**5 + 4/13*q**3 - 2/13 - 2/13*q**4 - 2/13*q + 4/13*q**2 = 0 for q.
-1, 1
Suppose -1 = z - s, 58*z - 53*z - 31 = -4*s. Let d(c) be the first derivative of 0*c**2 - 3/10*c**4 + 5 + 0*c + 0*c**z - 9/25*c**5 - 1/10*c**6. Factor d(i).
-3*i**3*(i + 1)*(i + 2)/5
Let z = -25/2 + 13