 324*x + 335 + 54*x**2 - 3*x**3.
-3*(x - 6)**3
Let n = -25390 + 25393. Let b(v) be the second derivative of 0 + 1/8*v**4 - v + 3/4*v**2 + 1/2*v**n. Solve b(q) = 0 for q.
-1
Let z(a) be the first derivative of -3*a**3 - a**2/3 - 4340. Suppose z(h) = 0. Calculate h.
-2/27, 0
Let g(b) = 3*b**4 - 406*b**3 - 40374*b**2 + 253364*b - 385633. Let i(s) = -2*s**4 - s**3 + 2*s - 4. Let x(c) = -3*g(c) - 6*i(c). Determine r so that x(r) = 0.
-207, 3
Let p be (-126)/28*72/(-162). Suppose 4/15*y**p + 0*y**3 + 0*y - 2/15*y**4 - 2/15 = 0. What is y?
-1, 1
Let u be 31 + 11849/(-451) - 6/3. What is v in 6/11*v**2 + 36/11*v + u = 0?
-5, -1
Let b(x) be the third derivative of -x**6/30 - 9*x**5/5 - 45*x**4/2 - 126*x**3 + 867*x**2. Factor b(n).
-4*(n + 3)**2*(n + 21)
Let w be (-2)/8 + (-2)/(-4). Suppose 4*t + 32 = -4*q, 275*t - 277*t - 26 = -3*q. Factor 1/4*p**q - w + 0*p.
(p - 1)*(p + 1)/4
Let n(b) = 7*b**3 + b**2 + 6*b**2 + 3*b**2 - 7*b**3 - b**3 + 11*b. Let w(f) = f**3 - 8*f**2 - 9*f. Let a(j) = 3*n(j) + 4*w(j). Let a(v) = 0. Calculate v.
-1, 0, 3
Suppose -27*k = -67 - 338. Let w be (-1 - (-18)/k)/1. Factor -3/5*j**4 - w*j**2 + 0*j - 3/5*j**3 - 1/5*j**5 + 0.
-j**2*(j + 1)**3/5
What is p in -15*p**3 + 728 + 450*p**4 - 9444*p + 8640*p + 254*p**2 - 451*p**4 = 0?
-26, 2, 7
Factor -y**2 - 101 - 223 + 138 - 16*y + 53*y.
-(y - 31)*(y - 6)
Find y, given that -2/5*y**4 - 68/5*y**3 + 68/5*y + 128/5 - 126/5*y**2 = 0.
-32, -2, -1, 1
Let x(d) be the third derivative of -d**7/140 + 3*d**6/80 - d**5/20 + 2*d**2 + 895. Let x(b) = 0. What is b?
0, 1, 2
Suppose 0*i + 0 - 7/8*i**3 + 5/4*i**2 + 1/8*i**4 = 0. What is i?
0, 2, 5
Let p = -80 + 80. Let y be 2*(-6 - -2)*(-1 + p). Let -16*v**2 + 2 + 7*v**4 + 0 - y*v**3 - v**5 - 2 = 0. Calculate v.
-1, 0, 4
Find z such that -333/4*z + 1/4*z**2 + 331/2 = 0.
2, 331
Factor -2034/5*d + 1034289/5 + 1/5*d**2.
(d - 1017)**2/5
Let w(f) = -5*f**3 - 4. Let k(o) = 39*o**3 - 147*o**2 - 5175*o + 16907. Let a(s) = 3*k(s) + 24*w(s). Find d such that a(d) = 0.
-75, 3
Let j be (-2 - -11) + (54 - 50). Let y(i) be the first derivative of j - 12/5*i**5 - 47/4*i**4 - 52/3*i**3 + 64*i - 1/6*i**6 + 24*i**2. Solve y(g) = 0.
-4, -1, 1
Find f such that -5 - 1/3*f**2 + 16/3*f = 0.
1, 15
Let i be 3 + (5 - (-30)/(-6)). Factor -r**2 + 7*r**2 + 0*r**3 + 40*r - 31*r - i*r**3.
-3*r*(r - 3)*(r + 1)
Determine g so that -4/9*g**2 + 4568/9 - 4564/9*g = 0.
-1142, 1
Let y(m) be the second derivative of -1/15*m**4 + 1/50*m**5 - 1/15*m**3 - 28*m + 0 + 2/5*m**2. Let y(l) = 0. What is l?
-1, 1, 2
Let w(d) be the second derivative of 9*d**5/22 + d**4/11 - 2*d + 589. Suppose w(p) = 0. What is p?
-2/15, 0
Factor 48*w**3 + 48*w**4 + 2 - 71*w**4 + 26*w**4 + 240*w - 228*w**2 - 2.
3*w*(w - 2)**2*(w + 20)
Let k(z) be the first derivative of -z**5/60 - 11*z**4/36 - 19*z**3/18 - 3*z**2/2 + 43*z + 25. Let i(n) be the first derivative of k(n). Factor i(g).
-(g + 1)**2*(g + 9)/3
Let w(m) be the first derivative of 5*m**4 - 4*m**3 - 64*m**2 - 48*m + 2892. Factor w(p).
4*(p - 3)*(p + 2)*(5*p + 2)
Let v = 192578/45 - 4280. Let y = v + 8/9. Factor 0 + 0*g + y*g**2.
2*g**2/5
What is a in 4/3*a**4 + 19/3*a**3 + 14/3*a**2 + 0 + a - 4/3*a**5 = 0?
-1, -1/2, 0, 3
What is m in -1/7*m**2 + 1686/7*m - 710649/7 = 0?
843
Let m(u) = u + 2. Let p be m(-5). Let y(t) = -5*t - 6. Let s be y(p). Factor 13*o**2 - 12*o - s - 6*o**3 - 4 + 17 + o**4.
(o - 2)**2*(o - 1)**2
Let z(x) = 707*x - 65042. Let g be z(92). Factor -6/5*k**g + 8/5 - 1/5*k**4 - k**3 + 4/5*k.
-(k - 1)*(k + 2)**3/5
Suppose 84*w + 1340 = -20*w + 1548. Find o, given that 0 - 3/5*o**3 + 0*o + 18/5*o**w = 0.
0, 6
Let j(z) be the first derivative of 2*z**6/3 + 892*z**5/5 + 662*z**4 + 1760*z**3/3 + 2416. Suppose j(d) = 0. What is d?
-220, -2, -1, 0
Let j(p) = 23*p**2 - 10*p + 3. Let t be j(3). Let d be (-4)/3 - t/(-54). Factor 1 - h**d + 7/2*h - 7/2*h**3.
-(h - 1)*(h + 1)*(7*h + 2)/2
Let c(w) = 185*w**2 - 6*w - 7. Let r be c(-1). What is n in -559*n**2 + r*n**2 + 191*n**2 + 188*n**2 = 0?
0
Let k(f) = 4*f**2 + 16*f - 7. Let d be k(-6). Suppose n + 3*n + t - 208 = 0, -n + d = 3*t. Factor -4 + 8*h - 35*h**2 + 21*h - n*h.
-(5*h + 2)*(7*h + 2)
Let y(i) = i**3 + 9*i**2 - 11*i - 6. Let m be y(-10). Suppose m*h = 11*h - 210. Factor 18*g**4 - 4*g**3 - 2*g**3 + 14*g**4 - h*g**4 + 4*g**2.
2*g**2*(g - 2)*(g - 1)
Let d(c) be the second derivative of c**6/15 - 3*c**5 + 193*c**4/6 + 160*c**3 + 256*c**2 - 909*c. Factor d(m).
2*(m - 16)**2*(m + 1)**2
Let u = 9147 + -9145. Let j(p) be the second derivative of 0 - 7*p - 3*p**u + 5/6*p**3 + 1/12*p**4. Factor j(y).
(y - 1)*(y + 6)
Let 0 + 69/7*k**2 + 36/7*k**3 + 1/7*k**4 + 34/7*k = 0. What is k?
-34, -1, 0
Let u(r) be the first derivative of -r**4/2 + 302*r**3 - 7030. Let u(x) = 0. What is x?
0, 453
Let 136/15 - 6/5*p**3 + 184/5*p - 274/15*p**2 = 0. What is p?
-17, -2/9, 2
Let t = -2761 + 2761. Let w(b) be the third derivative of 1/45*b**7 + 1/15*b**6 - 1/18*b**4 + 1/30*b**5 - 11*b**2 + 0 + t*b**3 + 0*b. Factor w(o).
2*o*(o + 1)**2*(7*o - 2)/3
Let j(r) be the second derivative of -r**4/24 - 325*r**3/12 - 323*r**2/2 + 3*r + 725. Factor j(b).
-(b + 2)*(b + 323)/2
Suppose 0 = -2792*a + 18710 - 7542. Solve -6/5*u - 2/5*u**a + 0 + 6/5*u**3 + 2/5*u**2 = 0 for u.
-1, 0, 1, 3
Let b(o) be the third derivative of -o**5/180 + 77*o**4/36 + 155*o**3/18 + 576*o**2. Factor b(m).
-(m - 155)*(m + 1)/3
Let k(b) be the second derivative of 5*b**4/24 - 3655*b**3/6 + 2671805*b**2/4 + 5938*b. Factor k(q).
5*(q - 731)**2/2
Let u(g) = 3*g**3 + 3*g**2 - 6*g + 3. Let x = -519 + 516. Let r(f) = f**2 + 2*f - 1. Let c(v) = x*r(v) - u(v). Factor c(s).
-3*s**2*(s + 2)
Let f(h) be the second derivative of -3 + 1/2*h**2 + 1/84*h**4 - 4/21*h**3 - 6*h. Suppose f(r) = 0. Calculate r.
1, 7
Suppose -2*v + 7 = -3*b, -3*v + 4*b = 53 - 63. Determine w, given that -70/3*w - 1/6*w**4 + 1/2*w**v - 98/3 + 5/3*w**3 = 0.
-2, 7
Let u(a) = -19*a**3 - 136*a**2 - 90*a + 256. Let j(t) = 28*t**3 + 204*t**2 + 136*t - 384. Let x(g) = 11*j(g) + 16*u(g). Factor x(b).
4*(b - 1)*(b + 2)*(b + 16)
Suppose 5*y = -8*r - 28, -82*r + 85*r + 2 = -4*y. Suppose -16/5*h**2 + 16/5*h**y + 2/5*h**5 + 0*h + 0 - 2/5*h**3 = 0. What is h?
-8, -1, 0, 1
Let o(k) be the third derivative of k**8/6720 - k**6/240 + k**5/10 - k**3/2 + 24*k**2. Let x(z) be the third derivative of o(z). Find w, given that x(w) = 0.
-1, 1
Let g be (-6 - 1008/(-60))/(9*(-28)/(-120)). Factor 0 + 4*t**3 + g*t + 60/7*t**2 + 4/7*t**4.
4*t*(t + 1)*(t + 3)**2/7
Let q(f) = 9*f**2 + 240*f + 144. Let i(r) = -46*r**2 - 1232*r - 720. Let v(s) = -6*i(s) - 31*q(s). Suppose v(a) = 0. Calculate a.
-12, -4
Let s(q) = -52*q**2 + 103*q + 7. Let u be s(2). Let g(d) be the first derivative of u*d**2 + 0*d + 5/3*d**3 - 15 - 5/4*d**4. Suppose g(c) = 0. What is c?
-1, 0, 2
Let u = -45 + 47. Suppose -u + 4 - 668*w + 655*w - 24*w**2 - 9*w**3 - 4 = 0. What is w?
-2, -1/3
Factor 2/5*r**2 + 34*r + 3348/5.
2*(r + 31)*(r + 54)/5
Let g be 32/(6 + -2) - 5. Determine q so that -80*q**2 + 23*q**3 - 120*q + 25 + 14*q**g - 36*q**2 - q**3 + 7 = 0.
-1, 2/9, 4
Let o(v) = -v**3 - v**2 + 5*v + 3. Let b be o(-3). Let w be b - 10/5 - -3. Factor w*z - 2 - 19/2*z**2 + 25/4*z**3 + 1/4*z**5 - 2*z**4.
(z - 2)**3*(z - 1)**2/4
Let f(v) = -22*v**3 - 24*v**2 - 8*v + 4. Let m = -634 - -631. Let j(y) = 21*y**3 + 24*y**2 + 8*y - 3. Let u(p) = m*f(p) - 4*j(p). Factor u(w).
-2*w*(3*w + 2)**2
Let c = 585366 - 5267788/9. Factor -376/9*j + 1936/9*j**3 - c*j**2 - 40/9.
2*(8*j - 5)*(11*j + 2)**2/9
Let x(b) be the first derivative of -b**4/20 - 748*b**3/15 - 3136. Factor x(k).
-k**2*(k + 748)/5
Let h = 680073/13 - 52313. Factor -16/13*m**2 - h + 4/13*m**3 + 14/13*m + 4/13*m**4 - 2/13*m**5.
-2*(m - 1)**4*(m + 2)/13
Let b(q) = 224*q**2 + 3*q + 4. Let u be b(-1). Let h = u - 223. Factor -6/5*l**h + 22/5*l - 12/5.
-2*(l - 3)*(3*l - 2)/5
Let c = 961/12 - 229/3. Suppose 5/4*m**3 - 5/4*m**5 + 55/4*m**2 - c*m**4 + 15*m + 5 = 0. Calculate m.
-2, -1, 2
Let t(d) be the third derivative of d**7/11340 + d**6/3240 - d**5/90 + 17*d**4/24 + d**3/6 - d**2 - 10. Let m(o) be the second derivative of t(o). Factor m(j).
2*(j - 2)*(j + 3)/9
Suppose 79200*j**3 + 2*j**5 + 1855*j**4 + 1556*j**4 + 80000*j**2 - 4209*j**4 = 0. What is j?
-1, 0, 200
Suppose -58 = -9*d - 4*g, 10 = -5*d + 254*g - 252*g. Factor -2/11