- 12*a**3 - 9*a**4 + 24*a**2 = 0. Calculate a.
-2, 2
Let i be (-10 - -3) + 23 + -14. Let k(h) be the second derivative of -1/10*h**5 - 1/30*h**6 + 0 + 0*h**i - 5/48*h**4 - 25*h - 1/24*h**3. Factor k(y).
-y*(y + 1)*(2*y + 1)**2/4
Let o be 507 - (50/15)/(8/12). Suppose 8 = o*s - 498*s. Factor 3/7*z**s + 3/7*z**4 + 9/7*z**3 - 9/7*z - 6/7.
3*(z - 1)*(z + 1)**2*(z + 2)/7
Let k(v) = -7*v**3 - 2*v**2 - v. Let o be k(2). Let x = 90 + o. Solve -4*q + 16*q**2 + 30*q**3 + x*q**2 - 21*q - 10*q**4 - 30 - 5*q**5 = 0.
-3, -1, 1, 2
Let j be 0 + (-2018)/5 + (-2 - -3). Let r = j - -403. Let 0*c - 2/5*c**2 + 0 - r*c**3 = 0. What is c?
-1, 0
Solve 9*u + 1173/2 - 3/2*u**2 = 0 for u.
-17, 23
Let c = -24 - -26. Suppose 842*u + 50 - 787*u + 3*u**2 + u**2 + u**c = 0. What is u?
-10, -1
Let z(l) = 5*l**3 - 110*l**2 - 1608*l - 6905. Let s(a) = -a**3 + 2*a**2 + 24*a - 1. Let c(y) = 14*s(y) + 2*z(y). Suppose c(q) = 0. Calculate q.
-24, -12
Let s(m) be the first derivative of 5/24*m**4 + 1/30*m**5 + 0*m - 1/36*m**6 + 51 + 0*m**2 + 1/6*m**3. Let s(i) = 0. What is i?
-1, 0, 3
Let h(s) be the second derivative of 0 + 0*s**4 + 17*s - 1/10*s**3 + 1/100*s**5 - 1/5*s**2. Factor h(y).
(y - 2)*(y + 1)**2/5
Let d(x) be the second derivative of x**6/3 - 3*x**5/4 - 35*x**4/3 - 55*x**3/2 - 25*x**2 + 530*x + 1. Find p, given that d(p) = 0.
-2, -1, -1/2, 5
Let j(f) be the first derivative of 3*f**5/20 - 13*f**4/4 + 11*f**3 - 174*f + 103. Let g(r) be the first derivative of j(r). Solve g(t) = 0 for t.
0, 2, 11
Find q, given that -2401073*q**4 + 0*q**3 + 2401048*q**4 - 10*q**3 = 0.
-2/5, 0
Determine k, given that -5*k**2 + 10*k**2 + 1034*k**3 + 9*k**2 - 1020*k**3 - 4*k**2 = 0.
-5/7, 0
What is u in -321 - 44*u**2 - 854 - 1385*u - 2*u**3 - 161*u**2 - 2*u**3 + 9*u**3 = 0?
-5, -1, 47
Let z(s) = 16*s - 429. Let v be z(27). Let j(r) be the second derivative of -10*r**v - 20*r**2 - 17*r - 1/4*r**5 + 0 - 5/2*r**4. Find h such that j(h) = 0.
-2
Suppose -415 = 26*u - 31*u. Factor 27*j + 39*j**3 + 12*j**5 + 173*j**2 + 4*j**4 - 64*j**4 - u*j**2.
3*j*(j - 3)**2*(2*j + 1)**2
Let r(x) be the third derivative of -x**5/15 - 127*x**4/3 - 506*x**3/3 + 2241*x**2. Let r(a) = 0. What is a?
-253, -1
Factor 29*n - 50*n**3 - 30*n**4 - 184*n**2 + 6*n**4 - 128 + 19*n**4 + 771*n + 17*n**4.
2*(n - 4)**2*(n + 4)*(6*n - 1)
Let w(q) be the second derivative of -q**4/42 - 4*q**3/21 - 4*q**2/7 - 2*q + 58. Factor w(i).
-2*(i + 2)**2/7
Let w(c) = -c**3 + c**2 - 15*c + 1. Let i(a) = -168*a**3 - 649*a**2 - 572*a - 1. Let r(x) = -i(x) + 5*w(x). Let r(f) = 0. What is f?
-3, -1, -2/163
Factor -45*i + i**4 - 49*i**2 - 12655*i**3 + 6*i + 25289*i**3 - 12643*i**3.
i*(i - 13)*(i + 1)*(i + 3)
Let v(o) be the second derivative of -o**5/110 + o**4/22 - o**3/11 + o**2/11 + 5*o + 435. Solve v(z) = 0.
1
Suppose -3*v + 42 = 3*s, -5*s - 12*v - 59 = -206. Suppose 0 + 6*w - 3/2*w**s - 9/2*w**2 = 0. Calculate w.
-4, 0, 1
Let m(b) be the second derivative of -25*b**5/4 - 3675*b**4/4 + 1480*b**3 - 890*b**2 - 74*b + 20. Solve m(k) = 0 for k.
-89, 2/5
Let r(t) be the second derivative of t**4/3 - 432*t**3 + 209952*t**2 + 513*t. Factor r(y).
4*(y - 324)**2
Let p(k) = 25*k**3 + 925*k**2 + 956*k + 8. Let c(b) = -3*b**3 + 5*b**2 + b - 1. Let w(t) = -8*c(t) - p(t). Factor w(h).
-h*(h + 1)*(h + 964)
Let m(s) = -s**3 + 6*s**2 + 8*s - 11. Let n be m(5). Let w = n - 45. Factor -12*z**2 + w*z + 7*z + 4*z**3 + 9*z - 17*z.
4*z*(z - 2)*(z - 1)
Let w(n) = 11*n**3 - 225*n**2 - 823*n - 62. Let u(x) = 22*x**3 - 451*x**2 - 1644*x - 126. Let b(p) = 5*u(p) - 9*w(p). Factor b(k).
(k - 24)*(k + 3)*(11*k + 1)
Let 1881 - 625*a**2 - 1215*a - 36 - 60*a**3 - 66*a**3 + 121*a**3 = 0. What is a?
-123, -3, 1
Let z(l) = l**4 - 84*l**3 + 82*l**2 + 86*l - 83. Let c(m) = 6*m**4 - 420*m**3 + 408*m**2 + 431*m - 414. Let w(h) = 2*c(h) - 11*z(h). Factor w(b).
(b - 1)**2*(b + 1)*(b + 85)
Suppose 0 = -23*k + 121 - 6. Suppose 0 = -k*v + 5*x + 40, -v + 10 = -6*v - 5*x. What is g in 1/4*g**4 + 0 - 1/4*g**2 + 3/4*g**v - 3/4*g = 0?
-3, -1, 0, 1
Let v be (9/(-864))/((-16)/48). Let d(m) be the third derivative of -2*m**2 + v*m**4 + 0*m + 0*m**3 + 1/240*m**5 + 0. Determine p, given that d(p) = 0.
-3, 0
Let y(z) = 9*z**2 - 274*z - 915. Let j(i) = -17*i**2 + 547*i + 1815. Let k(p) = 4*j(p) + 7*y(p). Factor k(n).
-5*(n - 57)*(n + 3)
Solve -128/5*o - 4/5*o**4 + 128/5 + 28/5*o**3 - 24/5*o**2 = 0.
-2, 1, 4
Let x(j) = 2*j**2 - 1. Let y(d) = 5*d**3 - 300*d**2 - 345*d + 655. Let r(h) = 15*x(h) - y(h). Factor r(v).
-5*(v - 67)*(v - 1)*(v + 2)
Suppose -10*r = 180 - 120. Let i be ((-10)/(-48))/(-5)*r. Factor -5/4*h + 1/4*h**3 + 3/4 + i*h**2.
(h - 1)**2*(h + 3)/4
Let n(u) be the first derivative of -u**5/510 + 11*u**4/204 - 28*u**3/51 + 241*u**2/2 + 246. Let l(y) be the second derivative of n(y). Factor l(s).
-2*(s - 7)*(s - 4)/17
Suppose 164*q - 34 = 950. Let t(r) be the second derivative of 0 + 4/5*r**4 - 8/75*r**q + 2/25*r**5 + 0*r**2 - 6/5*r**3 - 23*r - 2/105*r**7. Factor t(j).
-4*j*(j - 1)**2*(j + 3)**2/5
Let z be 1752/511 - 252/147. Factor -24/7*u + z*u**2 - 2/7*u**3 + 16/7.
-2*(u - 2)**3/7
Suppose 62 = 9*q + 62. Let w(s) be the third derivative of q*s + 0 + 13*s**2 + 1/24*s**8 + 0*s**3 - 2/7*s**7 + 3/5*s**6 + 0*s**4 - 4/15*s**5. Factor w(v).
2*v**2*(v - 2)**2*(7*v - 2)
Let n be 8/(-7) - 5/(-35). Let a be n/4 + 3/12. Find v such that 2 + 12*v**2 + a - 13*v**2 + v = 0.
-1, 2
Suppose 0 = -61*y + 68*y + 1806. Let z = -258 - y. Suppose 0 + z*x**2 + 2*x**3 + 0*x + 2/3*x**4 = 0. What is x?
-3, 0
Factor 2/17*l**3 + 76/17 + 32/17*l**2 - 110/17*l.
2*(l - 2)*(l - 1)*(l + 19)/17
Let s be (-4)/(-22) - (-775)/275. Let j be 9 - 1 - 3/1. Factor -3*h**s + h**j - 3*h**4 + 4*h**4 + 2*h**5 - 2*h**5 - 5*h**2 - 2*h.
h*(h - 2)*(h + 1)**3
Let l(y) = 16*y**3 + 6*y**2 + 9*y**3 - 32*y**3 + 8*y**3 + 14 + 2*y. Let x be l(-6). Find p such that 10*p**2 + 2*p**3 + 8 + 18*p - 4*p**x + 6*p**2 = 0.
-4, -1
Let i = 1064 - 1007. Let d be -6 - (-19)/(i/18). Factor 8/15 - 2/15*t**2 + d*t.
-2*(t - 2)*(t + 2)/15
Let y be -87 - -89 - (236/10)/((-36)/30). Factor 7/3*n**2 + y*n + 6.
(n + 9)*(7*n + 2)/3
Let v(q) = 5*q + 9. Let l = 67 - 66. Let c be v(l). Suppose -4*u - c*u + 2*u**2 + u + 3*u = 0. Calculate u.
0, 7
Let o = 3301 - 3301. Let x(q) be the third derivative of 19*q**2 - 1/40*q**5 - 1/480*q**6 - 1/8*q**4 + o*q - 1/3*q**3 + 0. Solve x(g) = 0.
-2
Suppose -3*b - 3*j - 42 = 0, 22316*b - j = 22319*b + 10. Factor -8/3*u + 0 + 2/3*u**4 + 16/3*u**b - 10/3*u**3.
2*u*(u - 2)**2*(u - 1)/3
Let q(w) = -10*w**2 + 212*w - 10. Let h be q(21). Suppose 0 = -18*l - 25*l + h*l. Let 2/13*z**4 + 2/13*z - 2/13*z**3 - 2/13*z**2 + l = 0. What is z?
-1, 0, 1
Let w(j) = -12*j + 245. Let v be w(22). Let q be v/((-304)/112) + -1 + -1. Factor -2/3*x - 8/3*x**q + 0 - 10*x**3 + 26/3*x**4 + 14/3*x**2.
-2*x*(x - 1)**3*(4*x - 1)/3
Let y(l) = 2*l**2 - 58. Let r be y(-7). Let s be (-16)/40*r/(-56). Let -2/7 + 4/7*u - s*u**2 = 0. Calculate u.
1
Let l(k) be the first derivative of -10/9*k**2 + 21 + 2*k + 2/27*k**3. Factor l(x).
2*(x - 9)*(x - 1)/9
Let k(f) be the first derivative of -f**4/14 + 96*f**3/7 + 1836*f**2/7 + 11232*f/7 - 1924. Factor k(o).
-2*(o - 156)*(o + 6)**2/7
Let t(b) be the first derivative of 8/7*b**5 + 108/7*b**2 - 218 - 1296/7*b + 1/21*b**6 + 36*b**3 + 141/14*b**4. Factor t(a).
2*(a - 1)*(a + 3)*(a + 6)**3/7
Suppose 32 = y - 4*m, 5*y - 559*m = -556*m + 41. Suppose l + 0*l**3 + 3/4*l**2 + 3/8 - 1/8*l**y = 0. Calculate l.
-1, 3
Suppose -s - 179 = -3*v, 10*v - 6*v - 230 = -3*s. Determine x, given that -5*x**3 + 8*x**2 - v*x**2 + 11*x**2 + 15*x**2 = 0.
-5, 0
Let f(v) be the third derivative of -v**5/240 - 7*v**4/32 - 49*v**3/12 - 360*v**2 + v - 2. Factor f(i).
-(i + 7)*(i + 14)/4
Let o(u) = 2*u**2 - 85*u - 99. Let g be o(48). Let m be (g/36 - 12) + 1/4. Determine h so that -m + 1/3*h - 1/6*h**2 = 0.
1
Let t be (-35)/(-56)*1888/295. Suppose 0*q**t + 0*q + 2/3*q**2 - 1/3*q**5 + 0 + q**3 = 0. What is q?
-1, 0, 2
Let l(g) be the first derivative of g**5/5 + g**4 + 4*g**3/3 + 50*g + 5. Let j(r) be the first derivative of l(r). Factor j(o).
4*o*(o + 1)*(o + 2)
Let i(k) be the second derivative of -k**7/84 + 7*k**6/60 - 9*k**5/20 + 11*k**4/12 - 13*k**3/12 + 3*k**2/4 + 3943*k - 2. What is f in i(f) = 0?
1, 3
Suppose 96*n**3 - 5998 - 276*n**2 - 22*n**4 + 18*n**4 - 4