et v be (-60)/330 - (-4163)/10615. Let r = v + -2/193. Factor -r*f**4 + 0 + 2/5*f**3 - 2/5*f + 1/5*f**2.
-f*(f - 2)*(f - 1)*(f + 1)/5
Let i(j) be the first derivative of j**4 - 84 + 0*j**3 + 0*j**2 + 0*j - 6/5*j**5 + 1/3*j**6. Let i(v) = 0. What is v?
0, 1, 2
Find g, given that 0*g - 65*g**2 + 1/3*g**4 - 2/3*g**3 + 0 = 0.
-13, 0, 15
Let k(c) be the second derivative of c**4/6 + 346*c**3/3 - 347*c**2 - 1704*c. Find f, given that k(f) = 0.
-347, 1
Let o(m) = 6*m**4 + 40*m**3 - 20*m**2 - 54*m. Let c = -202 + 205. Let w(b) = -b**4 - 8*b**3 + 4*b**2 + 11*b. Let n(y) = c*o(y) + 14*w(y). Factor n(q).
4*q*(q - 1)*(q + 1)*(q + 2)
Let b(k) = -9*k**2 + 42*k. Let n(o) = 7*o**2 - 41*o. Let x(h) = -13*h + 49. Let m be x(4). Let q(j) = m*n(j) - 2*b(j). Factor q(u).
-3*u*(u - 13)
Let b(f) be the first derivative of 0*f + 5/2*f**2 + 0*f**3 - 43 - 5/4*f**4. Suppose b(z) = 0. Calculate z.
-1, 0, 1
Let n(v) = 2*v**3 + 64*v**2 + 483*v. Let o(h) = 6*h**3 + 192*h**2 + 1450*h. Let g(q) = 10*n(q) - 3*o(q). Solve g(x) = 0.
-20, -12, 0
Let h(l) = l**3 + 4*l**2 + 3*l + 5. Let b be h(-4). Let s be ((-2)/b - -2) + (-4)/14. Find m such that -3*m**2 + 1648*m - 1648*m + s*m**2 = 0.
0
Let t(f) be the first derivative of -39/25*f**5 + 1/3*f**6 + 0*f - 6/5*f**2 + 16/15*f**3 + 33/20*f**4 + 138. Let t(h) = 0. Calculate h.
-3/5, 0, 1/2, 2
Determine r so that 0*r - 1/6*r**3 + 0 - 35/6*r**2 = 0.
-35, 0
Let q(u) = u**3 - 28*u**2 + 49*u - 39. Let n be q(26). Let z = -231/2 - n. Factor 2*c - 1/2*c**2 - z.
-(c - 3)*(c - 1)/2
Factor -542882/5 + 2084/5*h - 2/5*h**2.
-2*(h - 521)**2/5
Let z(a) be the first derivative of -2*a**6/9 + 32*a**5/5 - 31*a**4/4 + 23*a**3/9 + 3623. Factor z(w).
-w**2*(w - 23)*(2*w - 1)**2/3
Let i(p) be the second derivative of -p**4/3 - 88*p**3/3 - 680*p**2 + 2170*p. Find x such that i(x) = 0.
-34, -10
Let j(c) be the third derivative of c**5/12 + 935*c**4/24 - 800*c**3 - 2*c**2 - 2581*c. Determine d, given that j(d) = 0.
-192, 5
Let k(h) be the second derivative of h**4/3 - 578*h**3/3 - 580*h**2 - 132*h - 6. Find d, given that k(d) = 0.
-1, 290
Suppose 4*i + 4 = -2*k, 27 = k + i + 26. Let x(g) be the first derivative of 0*g - 21 - 1/12*g**k + 0*g**3 + 0*g**2. Suppose x(s) = 0. Calculate s.
0
Let m be ((-7)/392*7)/(3/(-18)). Let j(p) be the first derivative of 0*p - m*p**4 - 9/2*p**2 + 11 + 4*p**3. Factor j(z).
-3*z*(z - 3)*(z - 1)
Let m(c) be the third derivative of -1/105*c**7 - 8*c**3 + 5/12*c**4 - 102*c**2 - 1/12*c**6 + 0 + 5/6*c**5 + 0*c. Find z, given that m(z) = 0.
-8, -1, 1, 3
Factor -5060/3*z**3 + 0 - 2116/3*z**4 - 579*z**2 - 54*z.
-z*(z + 2)*(46*z + 9)**2/3
Let h(z) be the second derivative of z**5/160 + 887*z**4/32 + 73815*z**3/2 + 442225*z**2/4 - 37*z + 3. Find o such that h(o) = 0.
-1330, -1
Let i be 11 - 205458/(-1881) - (-4)/38. Factor -i - 1/3*x**2 + 38/3*x.
-(x - 19)**2/3
Let z(x) = 2*x**2 + 7*x - 18. Let r be z(13). Let p = 1237/3 - r. Factor 4/3*o**2 + 0 + 4/3*o**5 + 0*o - 4/3*o**4 - p*o**3.
4*o**2*(o - 1)**2*(o + 1)/3
Let p = 238/183 - -2/61. Suppose -53*q = 5*q - 109 - 7. Factor -16/3*o**q - 7/3*o**3 - p*o + 0.
-o*(o + 2)*(7*o + 2)/3
Suppose 205*f**5 + 7*f + 1894*f**4 - 20*f**2 + 39*f**3 - 1694*f**4 + 35*f**5 - 2*f - 104*f**3 = 0. Calculate f.
-1, -1/3, 0, 1/4
Factor -148*k**2 - 792*k**3 + 312987 + 334*k**2 - 2121*k**2 - 311049*k + 789*k**3.
-3*(k - 1)*(k + 323)**2
Let d = 91109 + -91106. Determine y, given that 2/3*y**d - 2/3*y - 2/3*y**2 + 2/3 = 0.
-1, 1
Let j(t) = t**3 + 214*t**2 + 3179*t + 2181. Let c be j(-198). Let 2/9*b**5 + 0 - 2/3*b**c + 16/9*b + 20/9*b**2 - 8/9*b**4 = 0. What is b?
-1, 0, 2, 4
Suppose -21 - 507 = -12*k. Let h be ((-429)/k - -11)*(-4)/(-3). Factor 10/3*d**2 + 0*d**3 - 5/3*d**4 - h + 0*d.
-5*(d - 1)**2*(d + 1)**2/3
Factor -12/17*g**2 + 0 + 2/17*g**3 + 10/17*g.
2*g*(g - 5)*(g - 1)/17
Let h = 4466389/205437 - -26/2209. Let a = 49/31 + h. Suppose a*x + 50/3 + 22/3*x**2 + 2/3*x**3 = 0. What is x?
-5, -1
Let h be 134/10 - 10/25. Suppose 5*s + 3*v = 9*s - h, -4*s - 2*v - 2 = 0. Factor 4/3*p - s - 1/3*p**2.
-(p - 3)*(p - 1)/3
Let j = -419 - -422. Find f such that -160*f**j + 9600*f**2 - 256000*f + 1175462 + f**4 + 1374819 + 9719 = 0.
40
Let p be (-43)/(-129)*(-1 - -529)/2. Solve p*s**3 - 85*s**3 - 7 - 3*s**2 + 7 = 0.
0, 1
Suppose -1678112/7 + 3664/7*d - 2/7*d**2 = 0. Calculate d.
916
Let p(k) be the third derivative of k**8/12096 + k**7/432 + k**6/72 - k**5/3 - k**4/24 + 53*k**2. Let y(l) be the third derivative of p(l). Factor y(o).
5*(o + 1)*(o + 6)/3
Factor -26500/7*m**2 + 112500/7 + 256/7*m**5 + 5700/7*m**3 + 2880/7*m**4 - 7500*m.
4*(m + 5)**3*(8*m - 15)**2/7
Let f(i) be the second derivative of 5*i**7/49 - 104*i**6/105 + 11*i**5/70 + 191*i**4/21 + 108*i**3/7 + 72*i**2/7 - 2646*i. Let f(j) = 0. What is j?
-1, -2/3, -2/5, 3, 6
Let u = -5522 + 5522. Let j(r) be the second derivative of u + 0*r**3 + 2/5*r**5 - 2/5*r**6 + 0*r**4 - 18*r + 2/21*r**7 + 0*r**2. Factor j(y).
4*y**3*(y - 2)*(y - 1)
Let -20*z + 2*z**5 - 30*z**3 + 17556*z**2 - 2*z**4 - 8779*z**2 - 8823*z**2 = 0. Calculate z.
-2, -1, 0, 5
Let m(v) = 278*v**3 + 13644*v**2 + 10840*v + 2160. Let q(n) = 56*n**3 + 2728*n**2 + 2168*n + 432. Let o(d) = -6*m(d) + 28*q(d). Let o(t) = 0. Calculate t.
-54, -2/5
Let s(u) be the first derivative of -1/4*u**3 + 72 - 3/8*u**2 + 3/2*u. Factor s(l).
-3*(l - 1)*(l + 2)/4
Let j(v) be the first derivative of v**6/14 - 123*v**5/35 + 501*v**4/14 - 734*v**3/7 - 1005*v**2/14 + 2325*v/7 + 651. Let j(d) = 0. What is d?
-1, 1, 5, 31
Let l(k) = 5*k + 32. Let o be l(10). Factor 3*a + 5*a - 192*a**2 + o*a**2 - 16*a**2.
-2*a*(63*a - 4)
Let h = 1 + 1. Let u be 6/((-105)/(-45) - 1/3). Factor 13/2*z**2 - 2 + h*z + 5/2*z**u.
(z + 1)*(z + 2)*(5*z - 2)/2
Let b be (-20)/200*3/(-2). Let i(n) be the second derivative of 0 + 0*n**2 + 1/10*n**6 - 2*n + 1/2*n**3 - b*n**5 - 1/4*n**4. Factor i(j).
3*j*(j - 1)**2*(j + 1)
Let n(g) be the second derivative of g**6/45 - g**4/6 + 2*g**3/9 + 246*g. Suppose n(h) = 0. What is h?
-2, 0, 1
Let 1132/7*s - 162 + 2/7*s**2 = 0. Calculate s.
-567, 1
Let r be (-18)/(-100) - 4/50. Let i(z) be the second derivative of 0 - 9*z + 3/5*z**2 + r*z**4 - 1/2*z**3. Factor i(x).
3*(x - 2)*(2*x - 1)/5
Factor 5196/7*k - 3374802/7 - 2/7*k**2.
-2*(k - 1299)**2/7
Let y be 4/(-14) + 31284/126. Factor 6*z - 6*z - 3*z**2 - 248 + y.
-3*z**2
Let m be 2/(-2)*(0/(-3) + -3). Suppose 4*g**2 + 7*g**4 + 8*g**m + 8*g**4 + 2*g**2 - 13*g**4 = 0. What is g?
-3, -1, 0
Let q(r) = 103*r**2 - 217*r + 233. Let h(s) = -18*s**2 + 36*s - 39. Let u(o) = 17*h(o) + 3*q(o). Factor u(j).
3*(j - 12)*(j - 1)
Suppose -76 + 98*g + 40 - 2*g - 15*g**3 + 75*g + 24*g**2 - 72 = 0. Calculate g.
-3, 3/5, 4
Let o be (-15)/12 - (-3 + (-11)/(-4)). Let v be o - -32 - 3/1. Factor -144*d + 164*d + 8 + 0 - v*d**2.
-4*(d - 1)*(7*d + 2)
Let d(h) be the third derivative of -h**5/60 + 141*h**4/8 + 212*h**3/3 + 134*h**2. Factor d(j).
-(j - 424)*(j + 1)
Factor 292/11 - 442/11*k + 152/11*k**2 - 2/11*k**3.
-2*(k - 73)*(k - 2)*(k - 1)/11
Let n(i) be the third derivative of -i**5/12 - 35*i**4/8 - 95*i**3/3 + i**2 + 83*i. Factor n(o).
-5*(o + 2)*(o + 19)
Let z(n) = -4*n**3 - 20*n**2 - 48*n - 26. Let s(a) = 16*a**3 + 78*a**2 + 194*a + 105. Let i(y) = 2*s(y) + 9*z(y). Solve i(q) = 0.
-3, -2, -1
Suppose -14 = -3*o + 4*n, 0 = 14*o - 12*o - 5*n - 7. Suppose -3 = -b, 11*r - 31 = o*r - 2*b. Factor -2/5*v**r + 7/5*v**4 - 9/5*v**3 - 1/5*v + 0 + v**2.
-v*(v - 1)**3*(2*v - 1)/5
Find s, given that 76*s - 464/3 + 2/3*s**2 = 0.
-116, 2
Let o(y) be the second derivative of -y**4/4 - 244*y**3 - 89304*y**2 - 218*y - 2. Find d such that o(d) = 0.
-244
Let p(d) be the second derivative of -48*d**5/5 - 26*d**4 - 169*d**3/8 + 781*d. Factor p(t).
-3*t*(16*t + 13)**2/4
Suppose -4*c + 42 = 5*j - 66, 86 = 4*j + 3*c. Suppose -2*q - 8 = -j. What is f in 18 + 1/2*f**2 - q*f = 0?
6
Suppose 59443 = -53*y + 59602. Factor 3/2*v**y - 9/2*v**2 - 3/2*v + 9/2.
3*(v - 3)*(v - 1)*(v + 1)/2
Factor -194/13*j - 90/13*j**2 + 2/13*j**3 + 282/13.
2*(j - 47)*(j - 1)*(j + 3)/13
Let u(d) be the third derivative of -d**8/336 - d**7/60 + 3*d**6/10 + 197*d**5/120 - 85*d**4/6 - 100*d**3 + 15*d**2 - 2*d + 10. Solve u(f) = 0.
-5, -3/2, 4
Let r = 379989 + -759977/2. Determine w so that -7*w - 33/2 - r*w**2 = 0.
-11, -3
Let t(v) be the second derivat