 1)**2
Let p(a) be the third derivative of -a**5/105 + 1747*a**4/21 - 6104018*a**3/21 + a**2 + 30*a + 5. Determine b, given that p(b) = 0.
1747
Let a(h) be the third derivative of 0 + 7/48*h**4 + 1/105*h**7 + 0*h - 7/60*h**5 + 1/672*h**8 - 30*h**2 - 1/30*h**6 + 5/6*h**3. Solve a(f) = 0.
-5, -1, 1, 2
Find m such that -183/4*m**2 + 0 + 0*m + 1/4*m**3 = 0.
0, 183
Let f = 1147/1722 + 1/1722. Let v(c) be the first derivative of 0*c**2 + 16 + f*c - 2/9*c**3. Find l, given that v(l) = 0.
-1, 1
Let a be (-2 + 2 + 1)/(24 - 25). Let r be 2/((-20)/(-12) + a). Factor 2/7*x**4 + 4/7*x**r - 4/7*x - 2/7 + 0*x**2.
2*(x - 1)*(x + 1)**3/7
Let p(n) be the third derivative of 0*n**3 - 1/140*n**5 + 0*n + 3*n**2 - 3/28*n**4 - 33. Solve p(g) = 0 for g.
-6, 0
Let x(v) be the third derivative of -v**7/420 + v**5/10 - v**4/3 + 876*v**2. Determine t, given that x(t) = 0.
-4, 0, 2
Let r = -1952 + 66369/34. Let k(z) be the third derivative of 0*z + 1/510*z**5 - 5*z**2 - r*z**4 + 3/17*z**3 + 0. Suppose k(u) = 0. Calculate u.
3
Factor 4/13*d**2 + 2/13*d**3 - 98/13*d - 196/13.
2*(d - 7)*(d + 2)*(d + 7)/13
Let t be (-50)/50 - (-1*161/(-42) - 5). Factor 5/6*v - 2/3 - t*v**2.
-(v - 4)*(v - 1)/6
Let p(h) = h**3 + 5*h**2 - 3*h - 11. Let t be p(-5). Suppose t*u + 606 = 618. Factor 0*z - 4/7*z**2 + 2/7*z**4 + 2/7 + 0*z**u.
2*(z - 1)**2*(z + 1)**2/7
Let r(j) = -j**2 - j + 3. Let m = 1 - -20. Let l(y) = -5*y**3 + 25*y**2 - 5*y - 29. Let q(z) = m*r(z) + 3*l(z). Factor q(w).
-3*(w - 2)**2*(5*w + 2)
Let j(w) be the first derivative of w**4/38 + 20*w**3/19 + 131*w**2/19 + 300*w/19 + 2989. Factor j(y).
2*(y + 2)*(y + 3)*(y + 25)/19
Let m be ((-102)/((-238)/7))/((-63)/(-243)). Factor -m*l + 30/7 + 15/7*l**2.
3*(l - 5)*(5*l - 2)/7
Let q = 233668 + -233666. Let -1/2*u**4 + 0*u + 2*u**q + 3/2*u**3 + 0 = 0. What is u?
-1, 0, 4
Let d(k) = -2*k**5 - k**4 + k**2 - k. Let f(t) = -2*t**5 + 4*t**5 + t + 0*t**5 - 2*t - 5*t**5 + t**3. Let l(p) = 5*d(p) - 5*f(p). Factor l(m).
5*m**2*(m - 1)**2*(m + 1)
Let u(r) = 14*r + 59. Let a be u(-4). What is j in -43*j**2 + 29*j**4 - 83*j**4 + 60*j - 16 + 53*j**2 - 120*j**a = 0?
-2, -1, 1/3, 4/9
Let y(f) be the first derivative of 1/10*f**5 + 47/21*f**3 + 22/21*f**4 + 10/7*f**2 + 16 - 23*f. Let z(k) be the first derivative of y(k). Factor z(j).
2*(j + 1)*(j + 5)*(7*j + 2)/7
Let u(c) = 3*c**2 - 7*c + 6. Let m be u(2). What is b in 4*b**4 + 6*b**4 + m*b**5 - 3*b**5 + 0*b**4 = 0?
-10, 0
Suppose 0 = -11*n + 22 + 143. Factor 13*p**2 - 25*p + 10*p**2 - n*p - 28*p**2.
-5*p*(p + 8)
Let c(f) be the first derivative of 5*f**4/4 + 55*f**3/3 - 215*f**2 - 480*f - 7967. Factor c(m).
5*(m - 6)*(m + 1)*(m + 16)
Let t(l) = -2*l**3 - l**2 - l. Let q(k) = 45*k**3 + 480*k**2 - 1377*k + 936. Let n(b) = q(b) + 21*t(b). Find p such that n(p) = 0.
-156, 1, 2
Let h = -121902/17 - -853382/119. Factor -h*w + 3/7 + 4/7*w**3 - 2/7*w**2 - 1/7*w**4.
-(w - 3)*(w - 1)**2*(w + 1)/7
Let q = -511 + 601. Suppose 17*d + 5 = q. Solve 0*y**3 - 2/3*y**d + 2/3*y + 4/3*y**4 - 4/3*y**2 + 0 = 0.
-1, 0, 1
Let j = 832/165 + -140/33. Let l(r) be the second derivative of j*r**2 - 4/15*r**3 - 1/30*r**4 + 1/50*r**5 + 0 - 12*r. Factor l(b).
2*(b - 2)*(b - 1)*(b + 2)/5
Let o(s) be the first derivative of -2*s**6 - 724*s**5/5 - 3660*s**4 - 41600*s**3 - 200000*s**2 - 120000*s - 580. Solve o(x) = 0 for x.
-30, -10, -1/3
Suppose 5*q - 32*q**5 - 8*q**3 + 14*q**2 - 14*q**4 - 2*q**5 + 37*q**5 = 0. What is q?
-1, -1/3, 0, 1, 5
Let y = -1844 + 1842. Let n be 24/(-72)*(y + 1). Find x, given that 1/3*x - 1/3*x**2 + n - 1/3*x**3 = 0.
-1, 1
Let d(w) be the third derivative of 1089/2*w**3 + 0*w + 33/4*w**4 + 9*w**2 + 11 + 1/20*w**5. Factor d(j).
3*(j + 33)**2
Let d(s) be the first derivative of s**3/7 + 255*s**2/7 + 881. What is o in d(o) = 0?
-170, 0
Let k(v) be the first derivative of 3/13*v**2 + 36/13*v - 2/39*v**3 - 19. Factor k(q).
-2*(q - 6)*(q + 3)/13
Let 0 + 247808/3*t + 2/3*t**3 + 1408/3*t**2 = 0. What is t?
-352, 0
What is x in 1/2*x**5 + 11/2*x**4 - 13*x**3 + 25/2*x + x**2 - 13/2 = 0?
-13, -1, 1
Factor 481 + 496*a - 285*a - 1137 + 449*a - 6*a**2 + 2*a**2.
-4*(a - 164)*(a - 1)
Let m(t) be the second derivative of t**5/5 - 26*t**4/3 - 58*t**3/3 + 108*t**2 + 999*t - 2. Find p, given that m(p) = 0.
-2, 1, 27
Factor -9956 - 124733 + 268644*b - b**4 - 106*b**3 - 133222*b**2 - 493*b**3 - 133*b**3.
-(b - 1)**2*(b + 367)**2
Let k be 60/(-50) - (-11984)/20. Let r = k + -8962/15. Let 32/15*i - r + 6/5*i**3 - 14/5*i**2 = 0. What is i?
2/3, 1
Let w(q) be the first derivative of 0*q**3 - 5/2*q**2 + 0*q + 5/4*q**4 + 156. Factor w(z).
5*z*(z - 1)*(z + 1)
Let w(r) be the third derivative of r**6/1020 + 29*r**5/510 - 70*r**4/51 + 592*r**3/51 + 1094*r**2 + 1. Factor w(y).
2*(y - 4)**2*(y + 37)/17
Find b, given that -36*b**2 - 35*b**2 + 5484975 + 75*b**2 + 10296*b + 1128487 + 12014 = 0.
-1287
Suppose -8*r = 2*r - 60. Suppose 3 + 15 = r*y. Factor 23*c**4 - 8*c - c**2 + 2*c**5 - 10*c - 11*c**2 + 16*c**y - 11*c**4.
2*c*(c - 1)*(c + 1)*(c + 3)**2
Let r(y) be the first derivative of -y**5/5 + y**4 + 8*y**3/3 - 37*y + 100. Let z(q) be the first derivative of r(q). Factor z(f).
-4*f*(f - 4)*(f + 1)
Let a(b) be the third derivative of 11*b**5/12 - 1085*b**4/48 - 25*b**3/2 - 63*b**2 + b - 2. Factor a(m).
5*(m - 10)*(22*m + 3)/2
Let l(b) be the second derivative of b - 1/50*b**5 + 0*b**2 + 1/5*b**3 + 1/15*b**4 + 15. Suppose l(k) = 0. Calculate k.
-1, 0, 3
Let s = 78267 - 78267. Determine g so that 4*g**2 + s*g + 0 - g**4 + 1/4*g**5 - g**3 = 0.
-2, 0, 2, 4
Suppose -6*u = -3 - 9. Suppose 3*l = 30*z - 34*z + 194, -4*z = u*l - 128. Factor 0 + 2*p + 14/3*p**2 - l*p**4 - 26*p**3.
-2*p*(3*p + 1)**2*(11*p - 3)/3
Suppose -x + 6 = 4. Let h(g) = g**2 - 2. Let j be h(x). Let -4*s**2 - 50*s + 50*s + 2*s**4 + j*s**3 = 0. What is s?
-2, 0, 1
Let p(o) be the second derivative of 3*o**5/4 - 95*o**4/12 - 55*o**3/3 + 140*o**2 + 2760*o. What is l in p(l) = 0?
-2, 4/3, 7
Suppose -c = 1, -5*n = 28*c - 23*c - 70. Let j(v) be the first derivative of 1/35*v**5 + 3/7*v**3 + 1/2*v**2 + n + 2/7*v + 5/28*v**4. Solve j(m) = 0.
-2, -1
Let t(x) be the third derivative of -x**5/30 - 35*x**4/6 - 136*x**3/3 - 615*x**2. Factor t(f).
-2*(f + 2)*(f + 68)
Let o be -3 + 13 - 2/12*57. Let u(v) be the first derivative of -2*v + o*v**4 - v**2 - 24 + 2/3*v**3. What is s in u(s) = 0?
-1, 1
Let j = 46141 - 138319/3. Suppose 70*q**4 + 394/3*q**2 + 8/3 + 508/3*q**3 + j*q = 0. Calculate q.
-1, -2/7, -2/15
Factor 127/3*q - 2 + 43/3*q**2.
(q + 3)*(43*q - 2)/3
Let p be (90/(-24))/((-7375)/2360). Let 0 - 2/5*f**3 + 8/5*f**2 - p*f = 0. What is f?
0, 1, 3
Let f(l) = 4*l**4 - 19*l**3 - 35*l**2 - 21*l + 18. Let s(u) = -14*u**4 + 77*u**3 + 141*u**2 + 83*u - 66. Let r(x) = 22*f(x) + 6*s(x). Let r(n) = 0. Calculate n.
-9, -1, 0
Let g(y) = -2*y**2 + 453*y - 973. Let z(p) = -p**2 - 71. Let h(a) = 2*g(a) - 2*z(a). Determine w so that h(w) = 0.
2, 451
Let a(g) = -9*g**2 + 37*g - 6. Let t be a(4). Let x be 8/t - (-11 + (13 - 11)). Suppose 45/2 + x*d**4 + 185/2*d**2 - 75/2*d**3 - 165/2*d = 0. Calculate d.
1/2, 1, 3
Let c = -69 + 72. Suppose 6*d = -5*g + c*d + 18, 3*g - 3*d = 30. Factor 18*u**2 - 49*u + 89*u + g + 2.
2*(u + 2)*(9*u + 2)
Let k = 71 - 62. Suppose 0 = -5*u + 3*c + 13, -1 = 2*u - 4*c - k. Factor 3 - 31 + 13 + 4*g**u - 8*g + 3.
4*(g - 3)*(g + 1)
Let u(f) be the first derivative of -f**3 - 45*f**2/2 + 162*f + 1129. Factor u(s).
-3*(s - 3)*(s + 18)
Let v(r) be the first derivative of r**5/10 - r**4/8 - r**3 - 725. What is z in v(z) = 0?
-2, 0, 3
Factor -902*i + 1/2*i**2 + 406802.
(i - 902)**2/2
Let t(c) be the second derivative of -c**4/96 - 13*c**3/24 - 9*c**2 - 160*c. Suppose t(p) = 0. What is p?
-18, -8
Factor 25*h**2 - 237*h**4 + 704*h**4 - 13*h - 7*h**3 - 231*h**4 - 237*h**4 - 4*h**3.
-h*(h - 1)**2*(h + 13)
Let r(i) be the third derivative of 52/9*i**3 - 1/45*i**5 + 0*i + 0 - 11/18*i**4 + 42*i**2. Find o, given that r(o) = 0.
-13, 2
Suppose 0 = 408*d - 405*d + 423. Let l = d + 1552/11. Solve -2/11*f**2 + 0 - 1/11*f - l*f**3 = 0 for f.
-1, 0
Suppose 5*j + 3*k + 63 - 93 = 0, -3*j - 4*k = -29. Let o(q) be the first derivative of 1/12*q**j + 1/2*q**2 + q - 8. Suppose o(y) = 0. Calculate y.
-2
Factor 22496*p + 55*p**3 - 178*p**3 + 64*p**3 + 60*p**3 + 46208 + 148*p**2 - 450*p**2.
(p - 152)**2*(p + 2)