5*q**5 + 18*q. Find i such that r(i) = 0.
-6, -1, 1/3
Let v(r) be the third derivative of r**8/1344 - r**7/120 - 7*r**6/480 + 79*r**5/240 + r**4/16 - 3*r**3 + 729*r**2. Solve v(g) = 0 for g.
-3, -1, 1, 4, 6
Let n(m) = 29*m**3 - 83*m**2 + 804*m - 750. Let i(q) = -16*q**3 + 42*q**2 - 402*q + 376. Let x(g) = -11*i(g) - 6*n(g). Factor x(l).
2*(l - 7)*(l - 1)*(l + 26)
Let j(c) be the first derivative of 51 - c**3 + 0*c + 3*c**2 - 3/4*c**4. Factor j(f).
-3*f*(f - 1)*(f + 2)
Let n be 2232/720 - 2/((-40)/(-2)). Suppose 0*b = b - 2. Factor 11 - 14*u**b - 2*u**n + 10 - 30*u - 39.
-2*(u + 1)*(u + 3)**2
Suppose -2*b = -u + 4, 0 = u - 10*b + 5*b - 16. Let i be (-1)/(-3 + -44*u/60). Solve -7*g**2 - 2*g - 4 + 6*g**3 + 0*g + i*g**2 = 0.
-1, 2/3
Factor -64*d - 241*d - d**2 + 265 - 34*d + 21*d + 375.
-(d - 2)*(d + 320)
Let x(p) = -p - 3. Let r be -12 + 0 + 3 - (-4 - 0). Let v be x(r). Factor -14*l**2 + 10*l**v + 6*l**2 + 0*l**2.
2*l**2
Let n be (10 - 5120/500)*(32/(-9) - -3). Let -4/3 - n*o**2 - 14/15*o = 0. What is o?
-5, -2
Solve -18/23 - 22898/23*h**2 - 1284/23*h = 0 for h.
-3/107
Let p(o) = -o**2 + 14*o. Let a be p(14). Suppose 61 = -a*m + 5*m + 4*w, 3*w = -3*m + 39. Factor -c - m*c**2 - 6 + 7*c**2 + c**3 + 8.
(c - 2)*(c - 1)*(c + 1)
Let b(o) be the first derivative of o**4/2 + 94*o**3/9 + 640*o**2/9 + 200*o + 4634. Determine a, given that b(a) = 0.
-9, -10/3
Suppose 92 = 5*m + 5*r - 28, 0 = 5*m + r - 112. Let g(n) = 5*n**2 + 3*n + 2. Let t be g(-1). Factor m*q**3 - 8*q**4 + 2*q**t - 15*q - 16*q**2 + 7*q.
-2*q*(q - 2)**2*(3*q + 1)
Factor -640*w + 5*w**3 + 533 + 165*w**2 - 1170 + 2215*w + 4012.
5*(w + 3)*(w + 15)**2
Let a(u) be the first derivative of 14*u**3/27 - 2039*u**2/9 + 388*u/3 - 2822. Factor a(w).
2*(w - 291)*(7*w - 2)/9
Let r(y) be the second derivative of y**4/6 - 31*y**3/3 + 130*y**2 - 1561*y. Factor r(o).
2*(o - 26)*(o - 5)
Solve 2187/4*g + 3/4*g**5 - 729/4*g**3 + 0 + 8019/8*g**2 + 3/8*g**4 = 0.
-18, -1/2, 0, 9
Let g(v) be the first derivative of 9/5*v**5 + 17/2*v**4 - 42 + 4*v**2 - 4*v + 37/3*v**3. Find u such that g(u) = 0.
-2, -1, 2/9
Suppose -5*b + 5 + 10 = 0. Suppose 2*t + 3*m - 19 = 0, b*t + 4*m + 5 = 32. Determine l, given that 6*l**5 + 24*l**4 - 13*l**t - 18*l**4 - 8*l**5 = 0.
0, 2/5
Let t(b) be the first derivative of b**6/72 - 5*b**5/12 + 15*b**4/8 + 21*b**3 - 2*b - 83. Let f(g) be the third derivative of t(g). Factor f(h).
5*(h - 9)*(h - 1)
Let g = -109725/2 + 219465/4. Factor 0*n**2 - g*n**3 + 0*n + 0 + 5/4*n**4.
5*n**3*(n - 3)/4
Let u be 2/(-13) + ((-6886)/(-143) - -6). Let j(o) be the first derivative of 9*o**2 - 1/2*o**3 + 12 - u*o. Factor j(a).
-3*(a - 6)**2/2
Let z(x) be the first derivative of 10/3*x + 2/45*x**3 - 2/3*x**2 + 9. Solve z(k) = 0 for k.
5
Let o(h) be the second derivative of 2*h**6/15 + 81*h**5/5 + 589*h**4 - 9610*h**3/3 - 714984*h**2 - 2*h + 1180. Let o(a) = 0. What is a?
-31, 12
Let r = -2261 - -2266. Let h(i) be the second derivative of -29*i + i**2 + 1/50*i**r + 7/30*i**4 + 11/15*i**3 + 0. Factor h(b).
2*(b + 1)**2*(b + 5)/5
Factor 968/9 + 808/3*i + 10/9*i**2.
2*(i + 242)*(5*i + 2)/9
Suppose s - 2 = 2*t, -45 - 1 = -5*s - 8*t. Let b(k) be the first derivative of 3 + 2*k + 4/3*k**3 - 1/3*k**s - 6/5*k**5 - k**4 + 3*k**2. Factor b(f).
-2*(f - 1)*(f + 1)**4
Suppose 24 = 4*o - 428. Solve 336*f**3 + 4*f**4 - o*f**3 - 167*f**3 = 0.
-14, 0
Let k = -58095 - -522901/9. Find m, given that -2/9*m**3 + 26/9*m**2 + 22/9 - k*m = 0.
1, 11
Let o be ((-250)/(-6) + 48/36)*4. Factor -183*j**2 - o*j**2 + 116*j + 118 + 531*j**2 - 178*j**2.
-2*(j - 59)*(j + 1)
Factor -2*m**4 - 40/7*m**2 + 52/7*m**3 - 16/7*m + 0.
-2*m*(m - 2)**2*(7*m + 2)/7
Suppose z = 3*n - 9, -4*z - 1 = 3*n - 10. Factor 7*y**2 - 18*y**n + 17*y**2 - 10*y + 14*y**3 - 2*y**2.
-2*y*(y - 5)*(2*y - 1)
Let r(w) be the second derivative of w**6/75 - 69*w**5/50 + 77*w**4/2 + 245*w**3/3 + 713*w. Find c such that r(c) = 0.
-1, 0, 35
Let r = 3/11 - -5/22. Let a = 13619 + -13617. Let 1/2*x**a + r + x = 0. Calculate x.
-1
Let s(y) = y**3 - 14*y**2 + y - 11. Let h be s(14). Suppose 3*f + 6*m = 5*m + 3, -4*f = h*m + 1. Factor -4/7*n**5 + 0 - 4/7*n**4 + 8/7*n**3 + 0*n**f + 0*n.
-4*n**3*(n - 1)*(n + 2)/7
Suppose 105*d + 110 = 115*d. Suppose 5*u + d = 21. Find a, given that -2/3*a - 1/6*a**u - 2/3 = 0.
-2
Let y(s) be the second derivative of -s**5/90 - 2*s**4/9 - 35*s**3/27 - 295*s + 2. Find c such that y(c) = 0.
-7, -5, 0
Let k be 4*14/4*(-390)/(-364). Let i(d) be the first derivative of k + 4/7*d - 1/21*d**6 - 9/7*d**2 + 12/35*d**5 + 32/21*d**3 - d**4. What is p in i(p) = 0?
1, 2
Let b = 4/15389 - -61544/46167. Factor 8/3*p**3 - 2/3 + 14/3*p**2 + b*p.
2*(p + 1)**2*(4*p - 1)/3
Suppose -26*s + 89 = -41. Solve 210*k - 5*k**s - 65*k**3 + 60*k**2 + 52*k**4 - 111*k - 119*k - 22*k**4 = 0.
0, 1, 2
Let g(i) be the first derivative of -5*i**3/3 + 3810*i**2 - 2903220*i + 944. Solve g(l) = 0.
762
Let k(a) be the third derivative of -29*a**6/24 + 7*a**5/6 + 145*a**4/24 - 35*a**3/3 - 3521*a**2. Solve k(x) = 0 for x.
-1, 14/29, 1
Suppose -u - 1 = 2*k, -2*k = 4*u - 0 + 16. Suppose 2 - 16 + 111 + 185*m**k + 300*m + 50*m**3 + 83 + 5*m**4 = 0. What is m?
-3, -2
Let g = -5321/5 - -5324/5. Factor -24/5*s - 27/5 + g*s**2.
3*(s - 9)*(s + 1)/5
Let w = -14591 + 291823/20. Let c(o) be the second derivative of 0 + 1/2*o**3 + o**2 - 1/30*o**6 - 1/12*o**4 - w*o**5 - 28*o. What is h in c(h) = 0?
-2, -1, 1
Suppose -w + 21 = -2*v + 5, -17 = -2*w - v. Let p(a) be the first derivative of -20*a + 45/2*a**2 - w*a**3 + 5/4*a**4 + 2. Factor p(i).
5*(i - 4)*(i - 1)**2
Let s be ((-2896)/241)/2 + 7 + -1. Let a = s + 982/2169. Find p, given that -16/9*p**2 - 2/3*p - 4*p**4 + 44/9*p**3 + 10/9*p**5 + a = 0.
-2/5, 1
Let p be 8/8 + ((-81)/(-9) - 11/((-110)/(-80))). Factor -7/2*r**3 - 6 - 16*r + 33/2*r**p.
-(r - 3)*(r - 2)*(7*r + 2)/2
Let b(r) be the third derivative of -r**7/735 - r**6/70 + 4*r**5/35 - 13*r**4/42 + 3*r**3/7 + 6200*r**2. Find h such that b(h) = 0.
-9, 1
Let h(o) be the first derivative of 136*o**3/3 - 46*o**2 - 80*o - 1393. Factor h(i).
4*(2*i + 1)*(17*i - 20)
Suppose -2*q - 1 = -m, 5*m - 100 + 89 = 4*q. Solve 17/3*a + 3*a**5 + 52/3*a**2 + 70/3*a**m + 2/3 + 14*a**4 = 0 for a.
-2, -1, -1/3
Let y(p) be the second derivative of 1 + 1/4*p**3 + 0*p**2 + 1/24*p**4 - 33*p. Factor y(b).
b*(b + 3)/2
Let m(c) = -2*c - 6. Let j be m(-4). Suppose 2*k - 8 = -j*h, -5*h + 2*k - 9 = -29. What is y in 2*y**3 + 0*y**3 + 4*y**3 - 3*y**h = 0?
0, 2
Suppose -50*a + 54*a - 3*h - 50 = 0, -a - 68 = 5*h. What is f in 3*f + 4*f**2 + a*f**3 - 1/5*f**5 + 0*f**4 + 4/5 = 0?
-1, 4
Suppose 2*p - 25 = -11*z, 52*z - 50*z = 4*p + 22. Let k(j) be the first derivative of 6/11*j - 4/11*j**2 + 2/33*j**z - 48. Factor k(m).
2*(m - 3)*(m - 1)/11
Let o be (-8 + -5 + 12)*(2 + -2). Let x be 0 + 2/6*(o - -6). Find j such that -j + 1 + 1/4*j**x = 0.
2
Suppose -t + 16 = 3*t. Let u = -23 - -28. Factor j**3 - 2*j**2 + 11*j**u - 12*j**5 - 2*j**t + 4*j**2.
-j**2*(j - 1)*(j + 1)*(j + 2)
Let u(f) = f**3 - 70*f**2 + 972*f - 1677. Let y(r) = r**3 - 72*r**2 + 975*r - 1676. Let q(n) = 6*u(n) - 5*y(n). Factor q(m).
(m - 29)**2*(m - 2)
Find g, given that -13/4*g**3 - 84*g + 1/4*g**4 + 0 - 38*g**2 = 0.
-4, 0, 21
Let u(m) be the second derivative of -2/5*m**5 + 0 + 4/5*m**2 + 11/10*m**4 - 4/3*m**3 + 4/75*m**6 - 18*m. Factor u(v).
2*(v - 2)**2*(2*v - 1)**2/5
Let r(h) = -h**2 + 107*h - 1378. Let p be r(92). Let l(k) be the third derivative of -6*k**p + 3/20*k**5 - 1/4*k**4 + 0 - 1/2*k**3 + 0*k. Factor l(t).
3*(t - 1)*(3*t + 1)
Let j(d) be the third derivative of -d**5/60 + 125*d**4/24 + 3174*d**2. Factor j(l).
-l*(l - 125)
Let k = 551 + -455. Factor -59*d - 2*d**2 + k*d - d.
-2*d*(d - 18)
Suppose -4*b = 2*y - 11 + 5, 4*b + 3*y = 3. Let t(n) be the first derivative of -8*n + 5*n**2 - 2/3*n**b + 13. Factor t(r).
-2*(r - 4)*(r - 1)
Let 113/7 - 1/7*n**3 - 113/7*n**2 + 1/7*n = 0. Calculate n.
-113, -1, 1
Let y(v) = -2*v**3 + v**2 - 1. Let c be y(-1). Let i be (-4 - -3) + 2 - 36/(-2). Suppose -i - 5*p**3 + 3 - 4 + 15*p**c = 0. Calculate p.
-1, 2
Let f(y) be the first derivative of y**7/1155 - y**6/165 + y**5/66 - y**4/66 + y**2 + 49*y - 55. Let z(t) be the second derivative of f(t). Factor z(k).
2*k*(k - 2)*(k - 1)**2/11
Suppose 4*v + 2712*o - 2715*o = -8, 0 = 2*v + 3*o - 32. F