 7 = y + 14. Let v be 6/4 - (-6 + (-74)/y). Factor 1/3*j**2 - v - j.
(j - 4)*(j + 1)/3
Let y be (-202)/(-20) - (-280)/(-11 - 17). Factor 1/10*d**2 - 1/10 - y*d + 1/10*d**3.
(d - 1)*(d + 1)**2/10
Let y(t) = t + 9. Let c be y(-7). Let h(s) = s + 6. Let u be h(-2). Factor 3*i**2 - 4*i**4 + i**2 + i**4 + c*i**u.
-i**2*(i - 2)*(i + 2)
Let s(z) be the second derivative of -z**7/2520 + z**3/3 + 8*z**2 + 18*z. Let u(l) be the second derivative of s(l). Find r, given that u(r) = 0.
0
Let h = 133885 + -133880. Suppose 0 + 15/2*o**4 + 18*o**3 - 6*o + 3/2*o**2 - 3*o**h = 0. Calculate o.
-1, 0, 1/2, 4
Let p(b) be the second derivative of -b**6/150 + 3*b**5/25 + b**4/20 - 19*b**3/15 + 12*b**2/5 + 581*b. Factor p(m).
-(m - 12)*(m - 1)**2*(m + 2)/5
Let y(a) be the first derivative of 4/5*a**5 - 27 + 0*a + 0*a**3 - 7*a**4 + 0*a**2. Factor y(p).
4*p**3*(p - 7)
Factor -539328/5 - 3/5*p**2 - 2544/5*p.
-3*(p + 424)**2/5
Determine a, given that -1 + 128*a + 1 + 16*a + 376*a**3 + 44*a**4 + 276*a**2 - 204*a**3 + 4*a**5 = 0.
-4, -3, -1, 0
Let z(p) = -p**2 + 1093. Let w be z(-33). Factor -1/2*k + 1/6*k**2 - 1/6*k**w + 0 + 1/2*k**3.
-k*(k - 3)*(k - 1)*(k + 1)/6
Let g(o) = -90*o - 898. Let h be g(-10). Suppose 0 = 2*q - 6. Determine f, given that -2*f**4 + 41*f**5 + 0*f**2 + 2*f**q + 2*f**h - 3*f**3 - 40*f**5 = 0.
-1, 0, 1, 2
Suppose 0 = -23*r + 38*r - 60. Factor -2*g**2 + 29*g**r + 3*g**5 - 2*g - 2*g**5 + g - 27*g**4.
g*(g - 1)*(g + 1)**3
Let n(x) be the second derivative of -x**7/168 + 4*x**6/15 + 17*x**5/40 - 2*x**4/3 - 11*x**3/8 - 10*x - 190. Find w, given that n(w) = 0.
-1, 0, 1, 33
Suppose 602*q**4 + 474*q**2 + 304*q**3 - 590*q**4 + 54*q**2 - 4*q**5 = 0. What is q?
-6, -2, 0, 11
Let v(t) be the first derivative of 4*t**5/5 + 63*t**4 + 1644*t**3 + 15066*t**2 + 52488*t - 1070. What is q in v(q) = 0?
-27, -6, -3
Let n be 6/(-21) + 258/21. Suppose 0 = n*j - 10*j - 4. Factor -314 + 4*r**j + 12*r + 314.
4*r*(r + 3)
Let g be (-96)/(-56)*(-42)/(-9). Let c(m) be the first derivative of 1/18*m**3 - 1/2*m + g - 1/6*m**2. Factor c(j).
(j - 3)*(j + 1)/6
Let b(u) be the second derivative of -u**6/120 - 3*u**5/40 - 5*u**4/48 + u**3 + 9*u**2/2 + 1237*u. Solve b(i) = 0.
-3, -2, 2
Suppose -12*v + 58 = 17*v. Suppose 0 = -136*d + 126*d + 50. Solve -6/5*l - 21/5*l**v - 3*l**4 - 3/5*l**d + 0 - 27/5*l**3 = 0 for l.
-2, -1, 0
Let h(s) be the third derivative of -s**6/420 + 17*s**5/210 + 43*s**4/28 + 69*s**3/7 - 57*s**2 + 3*s + 1. Factor h(d).
-2*(d - 23)*(d + 3)**2/7
Let k(d) = 12*d - 67. Let g be k(6). Suppose 634 = -g*a + 644. Let 0 + 4/9*t**5 + 0*t + 20/9*t**3 + 16/9*t**4 + 8/9*t**a = 0. Calculate t.
-2, -1, 0
Determine h, given that -11028*h**3 - 337 + 650 + 151 - 604*h**2 - 243*h**5 + 4576*h - 4185*h**4 + 880 = 0.
-14, -3, -4/9, 2/3
Solve 15/4*p + p**2 - 9/2 - 1/4*p**3 = 0.
-3, 1, 6
Suppose 0 = 225*k - 240*k. Let d(h) be the first derivative of 1/15*h**2 + 10 - 1/30*h**4 + k*h**3 + 0*h. Let d(i) = 0. What is i?
-1, 0, 1
Let y = 317 - -19. Let f = -328 + y. Factor f*a + 2*a**2 + 8/3 - 10/3*a**3.
-2*(a - 2)*(a + 1)*(5*a + 2)/3
Let g be ((-2)/13)/(((-12)/20)/(3/5)). Let r be (-40)/78 + (-2)/(-3). Factor -2/13*n + r + 2/13*n**3 - g*n**2.
2*(n - 1)**2*(n + 1)/13
Let c(y) be the second derivative of y**5/90 + 797*y**4/54 + 159991*y**3/27 + 157609*y**2/3 - 2*y + 731. Find a, given that c(a) = 0.
-397, -3
Let x(f) be the first derivative of 207 + 0*f + 3/10*f**4 - 12/5*f**3 + 3*f**2. Find m such that x(m) = 0.
0, 1, 5
Let q(s) = s**2 - 1190*s + 1308. Let u(c) = -c**2 + 587*c - 654. Let h(z) = -4*q(z) - 7*u(z). Factor h(n).
3*(n - 1)*(n + 218)
Let c(j) = -5*j + 52. Let z be c(10). Find w such that -8*w**2 + 4*w**z - 7*w + 5*w - 18*w = 0.
-5, 0
Let l(y) be the first derivative of -y**6/21 - 2*y**5/5 - 15*y**4/14 - 6*y**3/7 + 740. Suppose l(p) = 0. What is p?
-3, -1, 0
Let m(a) = -4*a**2 + 26*a - 25. Let c be m(5). Suppose 7 = h + c*q, -5*h - 5*q = -6*h - 3. Let 3/5*p**3 + 5*p**h + 16/5 + 56/5*p = 0. Calculate p.
-4, -1/3
Let z = -42 + 56. Let s be 4/(-14) + (1 - (-18)/z). Factor -2 + 4 + s*o + o**3 + 2*o**2 - 4 - 3*o**3.
-2*(o - 1)**2*(o + 1)
Let f(i) be the third derivative of -2*i**7/5 - 149*i**6/30 - 329*i**5/15 - 73*i**4/2 - 12*i**3 + 4124*i**2. Solve f(y) = 0 for y.
-3, -1, -2/21
Let m be -7 - ((-1379)/168 + 0 + (-1)/8). Determine i so that 0 + m*i**2 - 8/3*i = 0.
0, 2
Let q(c) be the third derivative of -c**6/180 - 956*c**5/45 - 304007*c**4/12 + 203522*c**3 + 2222*c**2. What is v in q(v) = 0?
-957, 2
Let o(i) be the third derivative of -i**8/420 - i**7/105 + i**6/90 + i**5/15 + 10*i**3 - 78*i**2. Let h(d) be the first derivative of o(d). Factor h(v).
-4*v*(v - 1)*(v + 1)*(v + 2)
Let m(c) be the first derivative of -c**4/8 - 14*c**3 - 81*c**2/4 + 83*c - 284. Determine t, given that m(t) = 0.
-83, -2, 1
Suppose -2346*b = -1153*b - 1165*b - 84. Determine o so that 24/5*o + 1/5*o**b - 9/5*o**2 - 4 = 0.
2, 5
Suppose -383*u + 804 = -379*u. Suppose u - 193 = 4*j. Suppose 2/15*i**j + 8/15 + 8/15*i = 0. Calculate i.
-2
Let m(w) be the third derivative of -86*w**2 - 2/75*w**5 - 2/525*w**7 + 0*w**3 + 0*w + 0 + 0*w**4 + 1/50*w**6. Suppose m(d) = 0. Calculate d.
0, 1, 2
Let 505521/4 - 711/2*i + 1/4*i**2 = 0. What is i?
711
Let g(d) = 27*d + 83. Let x be g(-3). Determine j, given that 21*j**2 + 2874*j - 3029*j + 4*j**x = 0.
0, 31/5
Let i(s) be the second derivative of -82*s - 1/20*s**5 + 0 + 5/6*s**3 + 1/3*s**4 + 0*s**2. Suppose i(b) = 0. What is b?
-1, 0, 5
Let g(h) be the second derivative of h**7/42 - 7*h**6/30 + 9*h**5/10 - 11*h**4/6 + 13*h**3/6 - 3*h**2/2 + 17*h - 2. Find w such that g(w) = 0.
1, 3
Let n(a) = 3*a**2 - 10*a. Let y(j) be the first derivative of -7*j**3/3 + 21*j**2/2 - 65. Let t(u) = 5*n(u) + 2*y(u). Factor t(w).
w*(w - 8)
Let g(j) be the first derivative of 4/7*j - 1/14*j**4 - 103 - 5/7*j**2 + 8/21*j**3. Determine w so that g(w) = 0.
1, 2
Let s be 5/(315/441)*(-6)/(-14). Let v(y) be the first derivative of -19 - 3/8*y**4 - 9/2*y**s - 45/4*y**2 + 75/2*y. Factor v(o).
-3*(o - 1)*(o + 5)**2/2
Let m = 28137/5 + -84361/15. Find j such that -2*j**3 + m*j + 0 + 4/3*j**2 = 0.
-1, 0, 5/3
Let b = -13 - -22. Suppose 3*j + 20 - 43 = 5*v, 5*j + 2*v = 28. Factor j*m - 4*m + 4*m + b*m**2 + 3*m**3.
3*m*(m + 1)*(m + 2)
Solve 608*w - 612 + 2053*w**2 - 1036*w**2 - 1013*w**2 = 0.
-153, 1
Let h(b) be the second derivative of b**9/1008 - 3*b**8/560 + b**6/30 + 13*b**3/2 + b + 12. Let o(q) be the second derivative of h(q). Factor o(i).
3*i**2*(i - 2)**2*(i + 1)
Suppose -84 = -o - 4*u, -52*o = -48*o + 5*u - 105. Let l = 0 - -2. Factor -2/3*v**3 - 2*v**l + 0*v + o.
-2*v**2*(v + 3)/3
Let i = 317 - 207. Let y = 114 - i. Factor y + 6*m + 1771*m**2 - 1771*m**2 - 2*m**3.
-2*(m - 2)*(m + 1)**2
Let n = 47 - 39. Let q(c) be the first derivative of -3 - 2/5*c**5 + c**4 + n*c + 2*c**3 - 8*c**2. Factor q(s).
-2*(s - 2)*(s - 1)**2*(s + 2)
Solve 136161 - 369*l + 1/4*l**2 = 0.
738
Let u(f) be the second derivative of -11*f - 1/80*f**5 + 1/2*f**3 + 0 + 3/32*f**4 + 6*f**2. Let v(j) be the first derivative of u(j). Let v(s) = 0. What is s?
-1, 4
Let v(f) = 19*f**4 - 5*f**4 + f**4 + 12 - 11*f**4 + 3*f - 10*f**2. Let t(d) = d**4 + d + 1. Let g(q) = 3*t(q) - v(q). Solve g(b) = 0.
-3, -1, 1, 3
Let c(v) be the third derivative of -5 + 0*v**4 + 1/6*v**3 - v**2 - 1/60*v**5 + 0*v. Determine u, given that c(u) = 0.
-1, 1
Solve -192/7*t**3 + 0 + 386/7*t**2 - 2/21*t**4 - 580/21*t = 0.
-290, 0, 1
Let y(u) be the first derivative of -u**7/1260 - u**6/360 + u**5/360 + u**4/72 - 16*u**2 - 69. Let m(r) be the second derivative of y(r). Factor m(p).
-p*(p - 1)*(p + 1)*(p + 2)/6
Factor 8*h**5 - 6*h**5 - 1412*h**3 + 183*h**4 + 101*h**4 + 1412*h**3.
2*h**4*(h + 142)
Let v = -397 + 405. Let n be (-10)/9*v/(-10). What is k in -8/9*k + 2/9*k**4 + 8/9*k**3 - n + 2/3*k**2 = 0?
-2, -1, 1
Suppose -f = -16 + 11. Let y(o) = -o**2 + 7*o - 2. Let b be y(6). Factor -33*k**b + 13*k**4 - 28*k**2 + 32*k**3 + 8*k + 4*k**3 + 4*k**f.
4*k*(k - 2)*(k - 1)**3
Let t = 27 - 14. Suppose -2*v + 28 = 3*u, -3*u + t = 6*v - 7*v. Determine r so that -r**2 + 27*r - 70 + u - 11*r = 0.
8
Let 64*y + 320/3 + 12*y**2 + 2/3*y**3 = 0. What is y?
-10, -4
Let d(q) = 105*q**2 + 170*q - 1520. Let a(c) = 69 - 8*c**2 - 18*c - 22*c + 27*c + 48. Let n(t) = 40*a(t) + 3*d(t). Solve n