1
Determine x, given that 974/9*x + 16/9*x**2 - 122/9 = 0.
-61, 1/8
Let t(b) be the third derivative of 0*b**3 + 3/4*b**4 + 1/168*b**8 + 4/105*b**7 - 2/5*b**5 - 1/30*b**6 + 0*b - 157*b**2 + 0. Solve t(s) = 0.
-3, 0, 1
Solve -1543/9*j - 23/9*j**2 - 134/9 = 0 for j.
-67, -2/23
Let d(g) be the first derivative of 5*g**3/3 - 315*g**2 - 1280*g + 6427. Factor d(a).
5*(a - 128)*(a + 2)
Suppose -12 = -12*u, -4*u + 21 - 8 = 3*i. Let r(v) be the second derivative of i*v**2 + 19*v - 3/2*v**3 + 0 + 1/4*v**4. Solve r(g) = 0.
1, 2
Suppose p = -82*n + 88*n - 23, -2*n = 4*p - 38. Factor -1/4*t**n - 1/2 - t**3 - 1/2*t**2 + 5/4*t + t**4.
-(t - 2)*(t - 1)**3*(t + 1)/4
Let k(c) = c**3 + 9*c**2 + 3*c - 13. Let x be k(-9). Let y = x - -42. Determine r so that -3*r**y + 2*r + r**2 - 3*r**2 + 3*r = 0.
0, 1
Suppose 0 = -2631*h + 886 + 4376. Determine k, given that -6/7*k + 2/7*k**3 + 0 - 4/7*k**h = 0.
-1, 0, 3
Determine t, given that 136/7 - 6*t + 2/7*t**2 = 0.
4, 17
Let w(y) be the second derivative of -y**4/3 + 3208*y**3/3 - 1286408*y**2 + 10*y + 6. Factor w(r).
-4*(r - 802)**2
Suppose 7*s + 9 + 5/3*s**2 + 1/9*s**3 = 0. Calculate s.
-9, -3
Let k(p) be the third derivative of p**8/112 - 9*p**7/70 - 2*p**6/5 + 14*p**5/5 + 6*p**4 - 40*p**3 + 1889*p**2. Solve k(t) = 0 for t.
-2, 1, 2, 10
Factor -1/3*x**3 + 480 + 52/3*x**2 - 172*x.
-(x - 40)*(x - 6)**2/3
Let x be (3/21)/(-1*31/(-434)). Suppose 40 + 5/2*a**x - 25*a = 0. Calculate a.
2, 8
Let y(x) be the second derivative of -3/100*x**5 - 5/2*x**3 - 1/2*x**4 + 0*x**2 - 58*x + 0. Find w, given that y(w) = 0.
-5, 0
Find q, given that 15*q + 4*q**2 - 91 - 38 + 29 - 3*q**2 = 0.
-20, 5
Factor 2561328 + 4/3*d**2 + 3696*d.
4*(d + 1386)**2/3
Let g(b) be the third derivative of 8/21*b**3 + 3*b**2 + 1/210*b**5 + 1/14*b**4 - 8 + 0*b. Solve g(a) = 0 for a.
-4, -2
Factor 4460*o + 7*o**2 + 164794 - 110525 - 2*o**2 + 639112 + 301199.
5*(o + 446)**2
Let j = -83 - -90. Let g(h) = 24*h**2 + 774*h + 14433. Let n(c) = 13*c**2 + 388*c + 7216. Let o(m) = j*n(m) - 4*g(m). Factor o(t).
-5*(t + 38)**2
Factor -25920 + 12993 + 12927 - 1380*h + 2*h**2.
2*h*(h - 690)
Let w be (12/15)/((9/(-345))/(-3)). Let q = 94 - w. Factor 3 + 6*g**2 - 4 + 2*g**3 - q*g - 3 - 2.
2*(g - 1)*(g + 1)*(g + 3)
Suppose 2*b + 25 - 35 = 0. Let v be (-18)/(-3) - (b + -2). Factor -7*x - 2*x**v - 2*x**2 - x + 7*x + 5*x.
-2*x*(x - 1)*(x + 2)
Let s be (-26)/(-1430)*-30*33/(-15). What is o in 3/5*o - s*o**3 - 6/5 + 3/5*o**5 + 12/5*o**2 - 6/5*o**4 = 0?
-1, 1, 2
Let l(g) be the first derivative of -g**4/12 + 10*g**3/9 - 7*g**2/6 - 6*g - 1665. Find t such that l(t) = 0.
-1, 2, 9
Suppose 5 = -3*v - 3*y + 38, -3*v + 19 = -4*y. Let a be ((-648)/(-80))/v - (-2)/4. Factor -2/5 - 3/5*z**2 + a*z.
-(z - 2)*(3*z - 1)/5
Let l(r) = -11 - 18 + 28 - r. Let w(j) = -j**2 + 9*j - 15. Let b(d) = 5*l(d) + 5*w(d). Suppose b(y) = 0. Calculate y.
4
Let j(p) be the first derivative of -p**5/15 + 31*p**4/4 + 128*p**3/3 + 194*p**2/3 + 2672. Factor j(m).
-m*(m - 97)*(m + 2)**2/3
Let u(m) = 2*m**2 - 3*m + 16. Let t be u(-3). Factor 36 + 14*f - 100*f**3 + 50*f + 11*f - 6*f + f**4 + 111*f**3 + t*f**2.
(f + 1)*(f + 3)**2*(f + 4)
Let z be (-2142)/234 + 2 - (-2)/13. Let t be z/((-63)/339) + -11. Determine o so that -179/3*o**2 + t*o + 47*o**3 - 25/3*o**5 - 4 - 5/3*o**4 = 0.
-3, 2/5, 1
Let r(k) be the second derivative of 800/3*k**2 + 1 + 40/9*k**3 + 1/36*k**4 + 29*k. Factor r(p).
(p + 40)**2/3
Let w be (-484)/(-5)*((-25)/10)/(-1). Suppose -324*z - 8630*z**2 - 36*z**3 - 1 - w + 8468*z**2 - 3*z**4 = 0. What is z?
-3
Let u be (60/(-30))/((4/(-7))/2). Factor 26*v**3 + u*v**2 + 5*v**2 - 22*v**3 + 12*v + 3 + 1.
4*(v + 1)**3
Let s(x) be the second derivative of x**6/30 + 4*x**5/5 - 377*x**4/6 + 2728*x**3/3 - 4719*x**2/2 + 556*x. Solve s(b) = 0 for b.
-39, 1, 11
Suppose 21*b = -14*b - 70. Let s be (38/228)/(b/(-24)). What is c in 3/10*c - 1/10*c**s + 0 = 0?
0, 3
Let k(x) be the first derivative of -x**6/840 + x**5/35 - x**4/8 - 2*x**3 - 2*x + 74. Let r(g) be the third derivative of k(g). What is o in r(o) = 0?
1, 7
Factor 477388 - 2*r - 7*r - 2*r**2 + 2*r**2 + r**2 - 478490.
(r - 38)*(r + 29)
Let z = -295672 + 295675. Factor -18/13*x**4 - 68/13*x**2 + 4*x**z + 42/13*x + 2/13*x**5 - 10/13.
2*(x - 5)*(x - 1)**4/13
Determine w so that -22*w**2 - 16*w**2 + 42*w**2 + 88804 - 1192*w = 0.
149
Suppose 5*a - 2*b = -3*b + 19, -3*a + 2*b + 1 = 0. Factor 79 - 22*o + 10*o - 2*o**a - 10*o**2 - 79.
-2*o*(o + 2)*(o + 3)
Factor 19002/7*g**2 + 2/7*g**4 + 356/7*g**3 + 281240/7*g + 1248200/7.
2*(g + 10)**2*(g + 79)**2/7
Let v(h) = h**3 + 12*h**2 + 21*h + 12. Let p be v(-10). Suppose 7*m - 17*m**3 - m**2 + 18*m**3 - 2*m**2 - 3 - 2*m**p = 0. Calculate m.
1, 3
Let v(o) be the third derivative of -o**7/210 + o**6/20 + 7*o**5/60 - 369*o**2. Factor v(q).
-q**2*(q - 7)*(q + 1)
Let i be -1 + 5/7 - (22 + (-6288)/252). Let a(t) be the first derivative of -15 + 3*t**2 - i*t**3 + 0*t + 1/2*t**4. Factor a(n).
2*n*(n - 3)*(n - 1)
Let d be 2 + (89120/(-24))/4. Let w = d + 928. Factor 0 - 8/3*o**3 + 4/3*o**2 - w*o**4 + 0*o.
-o**2*(o + 2)*(5*o - 2)/3
Let s(w) be the first derivative of -w**5/15 + 2*w**4/3 - 8*w**3/3 + 17*w**2/2 - 4*w - 163. Let y(t) be the second derivative of s(t). Factor y(p).
-4*(p - 2)**2
Let y = 364661 + -364659. Factor -20*d**y - 4/7*d**3 + 144/7*d + 0.
-4*d*(d - 1)*(d + 36)/7
Let u(g) be the third derivative of g**6/30 - 58*g**5/5 + 115*g**4/2 - 344*g**3/3 + 2067*g**2. Factor u(n).
4*(n - 172)*(n - 1)**2
Let a(m) be the third derivative of -m**6/360 - 17*m**5/90 + 149*m**4/72 - 19*m**3/3 - m**2 - 2934*m. Let a(q) = 0. Calculate q.
-38, 1, 3
Let a be -2 + (-72)/(-28) - (-7094)/7. Let i be (-15 + a/70)*(-1 - 6). Suppose 81/5 - i*y + 1/5*y**2 = 0. Calculate y.
9
Suppose -3/5*c**3 - 108 + 27/5*c + 87/5*c**2 - 3/5*c**4 = 0. What is c?
-5, -3, 3, 4
Let u be ((-453)/27)/(-1) - (-114)/513. Let v(t) be the first derivative of u - 2/3*t**3 + 0*t - 3/4*t**2 - 1/8*t**4. Factor v(o).
-o*(o + 1)*(o + 3)/2
Suppose 0 = 4*d - 2*i - 100, 75 = -138*d + 141*d + 3*i. Suppose -d*h + 117 = 67. Factor 2/9*b**3 - 2/9*b - 4/9 + 4/9*b**h.
2*(b - 1)*(b + 1)*(b + 2)/9
Let h(o) be the third derivative of -o**8/48 + 9*o**7/35 + 43*o**6/60 - 3*o**5/5 - 79*o**4/24 - 3*o**3 - 31*o**2 - 101*o. Solve h(r) = 0 for r.
-1, -2/7, 1, 9
Let d(y) be the first derivative of -y**6/300 - y**5/50 + y**4/40 + 3*y**3/10 - 61*y - 5. Let l(h) be the first derivative of d(h). Factor l(c).
-c*(c - 2)*(c + 3)**2/10
Suppose 14641/4 - 6959/2*j**3 - 239/4*j**4 - 43681/4*j + 21599/2*j**2 - 1/4*j**5 = 0. Calculate j.
-121, 1
Let n = 26263 - 709097/27. Let w(z) be the first derivative of 0*z - 31 - n*z**3 - 1/9*z**4 + 4/9*z**2. Suppose w(b) = 0. What is b?
-2, 0, 1
Let r(x) = -65*x - 2396. Let i be r(-37). Let m(d) be the first derivative of 0*d - 4*d**5 - 10/3*d**3 - 25/4*d**4 + i - 5/6*d**6 + 0*d**2. Factor m(k).
-5*k**2*(k + 1)**2*(k + 2)
Let s(b) = -23*b**3 - 5*b**2 - 102*b - 12. Let n(l) = -61*l**3 - 15*l**2 - 304*l - 34. Let i(y) = 6*n(y) - 17*s(y). Determine o, given that i(o) = 0.
-9/5, 0, 2
Suppose 1/4*v**3 - 41/4 + 41/4*v**2 - 1/4*v = 0. Calculate v.
-41, -1, 1
Let l(t) be the first derivative of -2*t**2 + 0*t - 80 + 1/6*t**4 - 2/9*t**3. What is u in l(u) = 0?
-2, 0, 3
Let m = -512 + 510. Let v(b) = -b**4 + 29*b**3 - 269*b**2 + 973*b - 731. Let z(g) = -g**3 - g**2 - g + 2. Let i(l) = m*v(l) - 2*z(l). Factor i(x).
2*(x - 9)**3*(x - 1)
Let o(n) be the third derivative of -7*n**8/12 + 8*n**7/15 + 32*n**6/5 - 112*n**5/15 + 8*n**4/3 - 1876*n**2 + 3*n. Determine m, given that o(m) = 0.
-2, 0, 2/7, 2
Find d, given that -14*d**2 + 53*d**2 - 2499 - 14*d**2 + 8759 - 3140*d - 20*d**2 = 0.
2, 626
Solve 159*h**2 - 79*h**2 - 79*h**2 - h - 11 - 199 = 0 for h.
-14, 15
Let c = 560 + -5041/9. Let k = c + 17/18. Suppose 11/3*n**2 + 14/3*n + k*n**3 + 4/3 = 0. Calculate n.
-2, -2/5
Let f be (-64800)/7560*((-64)/70 + 14/(-49)). Determine q so that 3674/7*q**2 + 984/7*q + 338/7*q**4 + f + 2132/7*q**3 = 0.
-3, -2/13
Let n(y) be the third derivative of y**6/180 - y**5/10 + 2*y**4/9 + 722*y**2. Factor n(l).
2*l*(l - 8)*(l - 1)/3
Let h(y) = -y**2 + 3*y - 1. Suppose 13 = -b - 3*j, 1 + 2 = -b - j. Let m(i) = 5*i**3 - 3*i**2 - 76*i + 122. Let g(d) = b*h(d) + m(d). Let g(z) = 0. Calculate z.
-4, 2, 3
Let o(k) 