. Let r(n) be the third derivative of t(n). Factor r(h).
3*(h - 1)*(h + 5)
Let p(i) be the first derivative of 1/15*i**3 + 0*i**2 + 0*i - 1/30*i**6 + 1/20*i**4 - 1/25*i**5 - 4. Find r such that p(r) = 0.
-1, 0, 1
Let k(d) be the first derivative of -1/9*d**4 - 20 - 4/9*d**3 + 2*d**2 + 39*d. Let h(b) be the first derivative of k(b). Factor h(a).
-4*(a - 1)*(a + 3)/3
Let o(a) = 3*a**2 - a. Let w(d) = 13*d**2 + 1200*d - 301. Let z(h) = -3*o(h) + w(h). Let z(j) = 0. What is j?
-301, 1/4
What is o in 0*o**3 - 2*o**3 + 1985*o**2 - 238*o + 30*o - 2195*o**2 = 0?
-104, -1, 0
Let w be 27060/450 - (-2)/(-15). Let c be 2 - (1 + 0)*-3. Find q, given that -w*q - c*q**2 + 5083 - 5083 = 0.
-12, 0
Suppose -31*d + 28*d + 639 = 0. Suppose -2*g + d = g. Factor -4*m**2 - g - 78 + 145 + 8*m.
-4*(m - 1)**2
Let t = 10550 - 10535. Let d(w) be the third derivative of -1/48*w**4 + 0 + 1/240*w**5 - 1/8*w**3 + t*w**2 + 0*w. Factor d(h).
(h - 3)*(h + 1)/4
Let c(v) be the first derivative of v**5/4 + 5*v**4/4 - 45*v**3/4 - 175*v**2/4 + 250*v - 10511. Factor c(p).
5*(p - 4)*(p - 2)*(p + 5)**2/4
Let w(x) = x**2 - x - 1. Let t(z) = 8*z**2 - 116*z - 5. Let k(a) = t(a) - 5*w(a). Let k(u) = 0. Calculate u.
0, 37
Find y, given that 75*y**2 - 480*y - 572 + 1784 + 5*y**3 - 812 = 0.
-20, 1, 4
Let y(h) be the first derivative of 3*h**4/4 - 16*h**3 + 39*h**2/2 + 90*h + 818. Find w such that y(w) = 0.
-1, 2, 15
Let m(x) be the second derivative of -x**6/660 - 7*x**5/165 + 5*x**4/33 + 31*x**3/3 + 39*x. Let k(a) be the second derivative of m(a). What is o in k(o) = 0?
-10, 2/3
Determine t so that 81*t**2 + 90*t**2 - 169*t**2 + 83232 + 137*t + 679*t = 0.
-204
Let t be (-3)/(-1621*(-2)/540 + -6). Let l = -807 - t. What is v in -8/3*v**2 + 4 + 16/3*v - 4/3*v**4 - 16/3*v**l = 0?
-3, -1, 1
Factor -2270*w**3 - 58*w**2 + 114*w**2 - 54*w**2 + 2262*w**3 + 8*w**4.
2*w**2*(2*w - 1)**2
Solve 0 - 1/3*o**5 - 22/3*o + 5*o**4 + 19*o**2 - 49/3*o**3 = 0.
0, 1, 2, 11
Let m = 35 - 349/10. Let w(f) be the third derivative of 1/168*f**8 + 1/35*f**7 - 1/6*f**4 + 0*f**3 - 16*f**2 + 1/60*f**6 + 0 - m*f**5 + 0*f. Factor w(g).
2*g*(g - 1)*(g + 1)**2*(g + 2)
Let b = -2 + 4. Suppose 2*k - 7*k + 18 = -3*k. Factor -7*h**2 + h**2 + 30*h + k*h**b.
3*h*(h + 10)
Let z = 84999 + -84999. Find x such that 4/5*x**4 - 4*x**2 - 8/5*x - 12/5*x**3 + 4/5*x**5 + z = 0.
-1, 0, 2
Let c = 39 - 32. Let p(u) = -280*u**2 + 119*u - 19. Let l(m) = -186*m**2 + 79*m - 13. Let r(b) = c*l(b) - 5*p(b). Let r(t) = 0. What is t?
1/7, 2/7
Suppose 5*p = 2*d + 34, -5*d - 347*p = -348*p - 7. Let -2/13*f**2 - 2/13*f**d + 2/13 + 2/13*f = 0. What is f?
-1, 1
Let q be (2 + 117/(-52) - 506/72) + 8. Let l(j) be the second derivative of 1/3*j**2 - q*j**3 + 34*j + 1/6*j**4 + 0. Factor l(x).
(x - 2)*(6*x - 1)/3
Let y be 2 + -1 + (0 - 12) + 2. Let j be y/((-90)/8 - -6). Factor 30/7*s - 2/7*s**3 - 16/7 - j*s**2.
-2*(s - 1)**2*(s + 8)/7
Let s(p) = 22*p**2 - 80*p + 388. Let q(m) = -5*m**2 + 20*m - 97. Let g(x) = 9*q(x) + 2*s(x). Let b be g(9). Factor 0 + 0*t + 2/9*t**b.
2*t**2/9
Let w(t) be the third derivative of 0*t + 15/28*t**6 + 0 - 46*t**2 + 28/3*t**4 + 0*t**3 - 4/735*t**7 - 76/5*t**5. Solve w(j) = 0.
0, 1/4, 28
What is p in 0 + 75/2*p**3 + 3/2*p**4 + 0*p - 126*p**2 = 0?
-28, 0, 3
Let o(f) be the second derivative of f**7/126 - 2*f**6/15 - 41*f**5/12 - 85*f**4/9 + 34*f**3/3 + 176*f**2/3 - 48*f + 8. Determine k so that o(k) = 0.
-8, -2, -1, 1, 22
Suppose 0 = 4*x, 5787 = -3*p - 3*x + 5*x. Let t = -1927 - p. Solve 0 - 20/3*b**3 + 4/3*b**4 + 8*b**t + 0*b = 0 for b.
0, 2, 3
Suppose 3*z - 7*x - 19 = -3*x, -x = -4*z + 34. Suppose -3*k - r + 0*r + z = 0, 0 = 2*r. Factor -27*s**k - 4*s + 60*s**3 - 32*s**3.
s*(s - 2)*(s + 2)
Let m(p) be the first derivative of p**3/5 + 57*p**2/2 + 828*p/5 + 2737. Factor m(j).
3*(j + 3)*(j + 92)/5
Let j(m) be the second derivative of -20*m + 8/3*m**3 + 28/9*m**2 + 3 + 5/54*m**4. Factor j(q).
2*(q + 14)*(5*q + 2)/9
Let k(a) be the second derivative of 2*a**6/15 + 83*a**5/100 - 89*a**4/10 + 64*a**3/3 - 64*a**2/5 - 14*a - 16. Suppose k(p) = 0. Calculate p.
-8, 1/4, 8/5, 2
Let p = 223 + -224. Let g be 1/220*84 - p/(-5). Factor -g*u**2 + 12/11*u - 18/11.
-2*(u - 3)**2/11
Let i(l) be the first derivative of -l**5/6 - 67*l**4/24 - 113*l**3/9 - 20*l**2/3 + 2002. Factor i(r).
-r*(r + 5)*(r + 8)*(5*r + 2)/6
Suppose -82*n = -115*n + 46233. Suppose -n*a = -1396*a - 80. Determine g so that -a*g**2 - 32/5*g - 66/5*g**3 - 2/5*g**5 + 0 - 4*g**4 = 0.
-4, -1, 0
Let i = 59225 - 118449/2. Solve 0 + 3/2*g**2 + 1/2*g + i*g**4 + 3/2*g**3 = 0 for g.
-1, 0
Let l = 117 - 114. Factor -3*q**l + 22*q**2 - 6*q**2 - 19*q**2.
-3*q**2*(q + 1)
Let m(r) be the first derivative of 73 + 1/2*r**4 + 16*r + 17*r**2 + 20/3*r**3. Factor m(t).
2*(t + 1)**2*(t + 8)
Suppose 1110*n - 1109*n = 2. Let i(q) be the third derivative of 5/6*q**6 + 0 - 1/3*q**5 + 0*q + 0*q**4 + 0*q**3 - 25/42*q**7 + 4*q**n. Factor i(l).
-5*l**2*(5*l - 2)**2
Suppose 3*k - 6326 = -x, k - x = -4*k + 10546. What is h in -65*h**4 + 32*h**2 - k*h**3 + 2181*h**3 - 67*h**4 + 28*h**5 = 0?
-2/7, 0, 1, 4
Let j(k) = k + 8. Let n be j(-10). Let x be (n/(-4))/((-6)/(-24)). Find d, given that 3*d**3 - 948 + 52*d - 42*d**x - 5*d**3 - 346*d + 262 = 0.
-7
Suppose 44 = -5*l + 59. Suppose p**2 - 12*p**3 + 11*p**2 - 67*p**2 - 40*p + 0*p**l + 20 - 3*p**3 = 0. Calculate p.
-2, 1/3
Let b(m) be the third derivative of 1/48*m**5 + 0*m + 35/96*m**4 + 25/12*m**3 + 0 + 31*m**2. Suppose b(u) = 0. Calculate u.
-5, -2
Let g(p) be the first derivative of -2*p**7/63 + 2*p**6/15 - p**5/5 + p**4/9 - 82*p + 215. Let r(v) be the first derivative of g(v). Factor r(u).
-4*u**2*(u - 1)**3/3
Let s(q) be the second derivative of -1/2*q**3 + 2 + 1/5*q**5 + q**2 - 1/42*q**7 - 1/6*q**4 + 0*q**6 + 12*q. Factor s(o).
-(o - 1)**3*(o + 1)*(o + 2)
Suppose h**3 - 288 + 61988*h**2 + 69*h - 5*h + 61946*h**2 - 123896*h**2 = 0. What is h?
-36, -4, 2
Let g = 943/4300 + 33/1075. Let c(l) be the third derivative of -33/20*l**5 - 2*l**2 + g*l**4 + 22 + 0*l**3 + 0*l. Let c(z) = 0. What is z?
0, 2/33
Factor -16245*w - 2246*w**4 + 747*w**4 - 16815*w**2 - 575*w**3 + 746*w**4 + 748*w**4.
-5*w*(w + 1)*(w + 57)**2
Suppose 1 = 36*x - 35. Let q be x + -5 + 13/3. Let 0 + 1/3*j**4 + 0*j + q*j**3 - 2/3*j**2 = 0. What is j?
-2, 0, 1
Let c(j) be the second derivative of 2*j**7/21 + 4*j**6/15 - 13*j**5/5 - 14*j**4/3 + 16*j**3 + 3*j - 1226. Let c(m) = 0. Calculate m.
-4, -2, 0, 1, 3
Let z(p) be the first derivative of -p**4/5 - 706*p**3/3 - 882*p**2/5 + 3434. Suppose z(a) = 0. Calculate a.
-882, -1/2, 0
Suppose -48020/3 + 980/3*v - 5/3*v**2 = 0. Calculate v.
98
Let f(o) be the third derivative of -o**11/831600 + o**10/94500 + o**5/12 + o**3/3 + 57*o**2 + 2. Let d(a) be the third derivative of f(a). Factor d(l).
-2*l**4*(l - 4)/5
Factor 0*x**2 + 6*x**2 - 12*x - 6*x**2 + 1258*x + x**2.
x*(x + 1246)
Let x = -887 - -939. What is j in -38*j**2 - 506 + 4*j**3 - 462 - 6*j**3 - 1056*j - x*j**2 = 0?
-22, -1
Factor -7/2*x + 245/8 - 1/8*x**2.
-(x - 7)*(x + 35)/8
Let u(t) = -t**3 + 10*t**2 + 4*t - 30. Let o be u(9). Let l = o - 82. Find x, given that -2*x**4 + 0 + 0*x**2 - 1/4*x**l - 9/2*x**3 + 27/4*x = 0.
-3, 0, 1
Let l(t) = -8*t**3 + 3690*t**2 - 10909*t + 7297. Let m(q) = 11*q**3 - 4920*q**2 + 14548*q - 9729. Let b(s) = -9*l(s) - 7*m(s). Factor b(g).
-5*(g - 243)*(g - 2)*(g - 1)
Let g(i) be the third derivative of i**6/80 + 949*i**5/40 - 475*i**4/8 - 8631*i**2. What is p in g(p) = 0?
-950, 0, 1
Let b(k) = 7*k**5 - 17*k**4 + 2*k**3 + 14*k**2 - 13*k - 5. Let p(n) = 14*n**5 - 33*n**4 + 3*n**3 + 28*n**2 - 24*n - 9. Let a(h) = -7*b(h) + 4*p(h). Factor a(w).
(w - 1)**3*(w + 1)*(7*w + 1)
Factor 266*w + 108 - 1/2*w**5 + 171/2*w**3 + 10*w**4 + 233*w**2.
-(w - 27)*(w + 1)*(w + 2)**3/2
Solve 0 - 12/7*w**4 - 18/7*w**3 + 24/7*w + 8/7*w**2 - 2/7*w**5 = 0 for w.
-3, -2, 0, 1
Find p, given that -293378/5 + 1532/5*p - 2/5*p**2 = 0.
383
Let i be (-5 + -10 + 13)/(-1). Let r(j) be the first derivative of -16*j - 9/2*j**4 + 20*j**i - 2 - 4*j**3. Factor r(b).
-2*(b + 2)*(3*b - 2)**2
Suppose -3*m + 63 = 4*v - 3*v, -m - v = -21. Let b(t) be the first derivative of 1/3*t**2 - 1/9*t**3 + m + 0*t. Factor b(h).
-h*(h - 2)/3
Let l(w) be the second derivative of w**8/1680 + w**7/105 + w**6/20 - w**4/12 + 9*w**3 - 