 15
Let p(w) be the first derivative of 89*w**6/2 - 531*w**5/5 - 273*w**4/4 + 177*w**3 + 3*w**2 + 3779. What is t in p(t) = 0?
-1, -1/89, 0, 1, 2
Let z(g) be the second derivative of 2*g + 1/33*g**3 + 4 + 0*g**2 + 1/33*g**4 - 2/165*g**6 - 1/231*g**7 + 0*g**5. Solve z(n) = 0 for n.
-1, 0, 1
Let j be 638/32 - 204/(-3264). Let v(x) = x - 1. Let q be v(4). What is y in 2 + 117/2*y**2 - 81/2*y**q - j*y = 0?
2/9, 1
Let f(q) be the first derivative of -q**4/48 - q**3 - 23*q**2/8 - 42*q - 7. Let w(t) be the first derivative of f(t). Determine c, given that w(c) = 0.
-23, -1
Let q = 364 - 315. Let w be 16/(-28) + 175/q. Determine r so that 2/13*r**5 + 0 + 0*r + 2/13*r**2 - 2/13*r**4 - 2/13*r**w = 0.
-1, 0, 1
Suppose 45595*w = 45555*w. Let 6/5*d**2 + 2/5*d**4 + w + 6/5*d**3 + 2/5*d = 0. What is d?
-1, 0
Let 96*k**2 + 77*k**3 + 27/2*k**4 + 0 - 1/2*k**5 + 0*k = 0. Calculate k.
-3, -2, 0, 32
Suppose 0 = -4*z, 0 = -3*q - 4*z + z + 15. Factor -6*g**3 + 3 + 0*g + 1 + q - 12*g**2 + 6*g + 3*g**4.
3*(g - 3)*(g - 1)*(g + 1)**2
Let u(o) = -o**2 + 14*o - 39. Let b be u(9). Suppose -5*g = 3*w - b, -2*w - 5 = -g + 4. Solve -1/2*v**3 - g*v**2 - 2 - 9/2*v = 0 for v.
-4, -1
Let 1310/9*x**2 + 8/9*x**3 - 328/9*x + 0 = 0. Calculate x.
-164, 0, 1/4
Let k(u) be the third derivative of 0 - 1/15*u**5 + 283*u**2 + 1/42*u**7 + 0*u**4 - 1/120*u**6 + 0*u**3 + 0*u. Factor k(q).
q**2*(q - 1)*(5*q + 4)
Let u(g) = -1311*g + 34096. Let c be u(26). Solve j**4 - c*j**2 - 3 - 19/2*j - 3*j**3 + 1/2*j**5 = 0.
-2, -1, 3
Suppose -3*f - 181 + 184 = 0. Let h be (-1)/7*f + (-236)/(-84). Solve h*k**2 - 2/3*k**3 - 10/3*k + 4/3 = 0 for k.
1, 2
Suppose 20*g - 90 = 5*g. Solve 0*t**2 - 3634*t + 3618*t + g*t**2 - 2*t**4 + 8 + 4*t**3 = 0.
-2, 1, 2
Factor -14/5 - 10/3*r - 2/5*r**2 + 2/15*r**3.
2*(r - 7)*(r + 1)*(r + 3)/15
Let r be ((-28)/26 - -1)/(10/(-60)) - (-3592584)/442988. Factor -144/7 + 4/7*f**3 - r*f + 8/7*f**2.
4*(f - 4)*(f + 3)**2/7
Factor 2*r**3 - 6*r**3 - 166464*r + 72066*r**2 - 72882*r**2 + 3*r**3.
-r*(r + 408)**2
Let n = 5 - 4. Let a be (-4 + (0 - -9))/n. Find w such that -18*w**2 - 4 - 2*w**a - 21*w**2 + 8*w**4 + 10*w - 8*w**3 + 35*w**2 = 0.
-1, 1, 2
Suppose 3*h - 12 = -o, -5*h = -0*o + 5*o. Let b(z) be the second derivative of 1/16*z**5 + 0*z**2 + 5/24*z**3 - h*z + 0 + 5/24*z**4. What is p in b(p) = 0?
-1, 0
Let c(t) = -6*t**2 - 66*t - 84. Let k(w) = 7*w**2 + 72*w + 84. Let s(n) = -4*c(n) - 3*k(n). Factor s(q).
3*(q + 2)*(q + 14)
Let s(f) = 29*f**2 + 99 + 119468*f + 88 - 119657*f. Let r(x) = -7*x**2 + 47*x - 46. Let w(k) = -9*r(k) - 2*s(k). Factor w(j).
5*(j - 8)*(j - 1)
Let x be (-56)/(-21)*2/(-3)*(-36)/16. Let z(j) be the second derivative of -9*j - 8/15*j**3 + 19/30*j**x - 1/5*j**5 + 0 - 1/5*j**2. Find o such that z(o) = 0.
-1/10, 1
Suppose 0 = -h + h + h. Suppose 0 = 5*p - 3*s - 15, h = 14*s - 11*s. Suppose 0 - 3/2*y**5 + 0*y**4 - 3/2*y + 0*y**2 + p*y**3 = 0. What is y?
-1, 0, 1
Solve 12*b**3 + 0 + 68/3*b**2 + 1/3*b**4 + 0*b = 0.
-34, -2, 0
Let r(a) be the third derivative of a**6/40 - 33*a**5/10 + 1089*a**4/8 + 5*a**2 - 73*a. Factor r(m).
3*m*(m - 33)**2
Let m(z) be the first derivative of -8*z**6/15 - 332*z**5/25 - 503*z**4/5 - 2212*z**3/15 + 2934*z**2/5 - 1296*z/5 + 1056. Suppose m(i) = 0. Calculate i.
-9, -4, 1/4, 1
Let m = 7664 + -367871/48. Let g(h) be the second derivative of 1/120*h**6 - 42*h + 1/40*h**5 + 0*h**2 + 0 + 0*h**3 + m*h**4. Factor g(n).
n**2*(n + 1)**2/4
Let x(y) = -y**3 - 4*y - 3. Let m be x(-1). Let 4*c + 12*c**2 - 27*c**m + 5*c + 12*c**2 = 0. What is c?
0, 3
Suppose 8*v + 420 = 5*a + 13*v, 4*v = -a + 75. Let i = -85 + a. Factor 2/3 + 14/3*g**i - 10/3*g - 2*g**3.
-2*(g - 1)**2*(3*g - 1)/3
Suppose -44 = -f - 2*t, 3*f - t - 2*t = 123. Solve -30 + 2*i**2 - 30 + f + 16*i = 0 for i.
-9, 1
Suppose 2*j - 96*i = -91*i + 41, -7 = i. Let y(a) be the first derivative of 0*a + 4/33*a**j - 31 - 1/22*a**4 - 1/11*a**2. Factor y(x).
-2*x*(x - 1)**2/11
Let g(p) be the second derivative of -p**7/189 + 17*p**6/135 - 31*p**5/90 + 5*p**4/18 - 394*p. Suppose g(z) = 0. What is z?
0, 1, 15
Let n(d) = d**2 - 11*d + 15. Let i be n(3). Let s(r) = -2*r**2 - 35*r - 24. Let w(y) = y**2 + 18*y + 13. Let p(f) = i*w(f) - 4*s(f). Factor p(q).
-(q + 1)*(q + 21)
Let d(r) = 3*r**2 + 102*r - 198. Let h(w) = -2*w**2 - 51*w + 100. Let g(n) = -5*d(n) - 9*h(n). Factor g(o).
3*(o - 15)*(o - 2)
Let i(k) be the first derivative of -5/4*k - 32 - 3/16*k**2 + 1/24*k**3. Factor i(x).
(x - 5)*(x + 2)/8
Let w be 7 + -4*(-5 - -6). Let h be (1/(-5) - w) + (8 - 3). Find z such that -h*z**2 + 51/5*z - 6 = 0.
2/3, 5
Let j be (28/1575)/((-9)/(324/(-8))). Let k(y) be the first derivative of -2/5*y**3 + 4/5*y + j*y**5 + 1/10*y**4 + 19 - 1/5*y**2. Let k(c) = 0. Calculate c.
-2, -1, 1
Let l(v) = -v**5 + 3*v**4 - 3*v**3 - v**2 + 2*v - 2. Suppose -21*w + 6 + 15 = 0. Let r(a) = a**5 - a**4 + a**3 - a + 1. Let c(n) = w*l(n) + 2*r(n). Factor c(k).
k**2*(k - 1)*(k + 1)**2
Suppose -5*s + 50 = -3*t + 4*t, 5*t = -s - 14. Let j be (-1)/(46 + -40 - s*1). Factor j*u**4 + 1/5*u - 1/5*u**3 + 0 - 1/5*u**2.
u*(u - 1)**2*(u + 1)/5
Solve 124/5*g + 32/5*g**3 - 48/5 - 2/5*g**4 - 106/5*g**2 = 0 for g.
1, 2, 12
Let d(b) = 7*b**3 + 70*b**2 - 26*b + 563. Let v be d(-11). Factor -15/4*g + 1/4*g**v - 17/2.
(g - 17)*(g + 2)/4
Let w be 159/(-4) - (-1)/(-4). Let a = -33 - w. Factor f**3 + 0*f**3 - 4*f**3 + f**2 - a*f**2.
-3*f**2*(f + 2)
Let w(j) = 6*j + 40. Let s be w(-5). Solve -3*f**3 + s*f**3 + 36*f**2 + 45*f - 6*f**2 - 2*f**3 = 0 for f.
-3, 0
Let -4*d**2 - 124*d + 47*d + d**2 + 53*d = 0. What is d?
-8, 0
Let d(k) = 8*k**3 - 158*k**2 - 553*k - 550. Let t(m) = 5*m**3 - 80*m**2 - 275*m - 274. Let y(r) = 3*d(r) - 5*t(r). Factor y(u).
-(u + 2)**2*(u + 70)
Factor 16*q**2 + 8*q**2 + 1076*q - 54*q**2 + 1075 + 19*q**2 + 12*q**2.
(q + 1)*(q + 1075)
Suppose 2*w = -7*x + 5*x, 7*w - 29*x - 15 = -31*x. Factor 2/13*u**w + 0 - 2/13*u + 0*u**2.
2*u*(u - 1)*(u + 1)/13
Let a(z) be the first derivative of -z**6/100 + 71*z**5/150 + 8*z**4/15 - 149*z**3/3 - 93. Let v(n) be the third derivative of a(n). Factor v(q).
-2*(q - 16)*(9*q + 2)/5
Let g = 8629121/11505484 + -2/2876371. Find f such that 3*f + 0 - 9/8*f**4 + 9/2*f**2 - 3/8*f**5 + g*f**3 = 0.
-2, -1, 0, 2
Let n(y) = 9*y**3 - 75*y**2 - 75*y + 795. Let o be n(8). Factor -3/5 - 1/5*j**4 + 6/5*j**o - 12/5*j**2 + 2*j.
-(j - 3)*(j - 1)**3/5
Let y(u) be the third derivative of u**5/2 - 209*u**4/8 - 21*u**3/2 + 680*u**2. Factor y(j).
3*(j - 21)*(10*j + 1)
Suppose -3*k + 267 = -3*y, 6*k = 4*k - 5*y + 213. Let n = k - 92. Factor 4*c**n + 20*c - 42 + 98 - 32.
4*(c + 2)*(c + 3)
Let u(l) be the second derivative of l**7/504 + l**6/8 + 29*l**5/80 + 43*l**4/144 + 2*l - 6. Factor u(d).
d**2*(d + 1)**2*(d + 43)/12
Determine d so that -26/9*d - 112/9 - 16/9*d**3 + 23/3*d**2 + 1/9*d**4 = 0.
-1, 2, 7, 8
Let x(g) be the third derivative of g**7/1260 - 5*g**6/144 + 47*g**5/120 - 31*g**4/16 + 9*g**3/2 + g**2 - 7*g - 4. Let x(o) = 0. Calculate o.
1, 3, 18
Let i(y) = -11*y + 80. Let c be i(7). Factor -s**3 - 7*s**c + 32*s + 68*s**2 - 4*s**3 + 0*s**3 - 48.
-4*(s - 6)*(s + 1)*(3*s - 2)
Let w = -72 + 89. Let w - 28*s + 15 + 2*s - 4*s**3 + 40*s**2 - 42*s = 0. What is s?
1, 8
Let d be (11 - -4) + (0 - 4). Suppose 0 = 4*f - 17 - d. Find w such that -31*w**2 + f*w**2 + 4*w**3 + 2 - 18 + 36*w = 0.
1, 4
Let c(v) be the third derivative of 5/17*v**3 - 1/510*v**5 - 58 + 0*v + 2*v**2 + 1/102*v**4. Find y such that c(y) = 0.
-3, 5
Let l(z) be the second derivative of -z**5/5 - 53*z**4 - 4650*z**3 - 101250*z**2 - 6569*z - 1. Factor l(t).
-4*(t + 9)*(t + 75)**2
Suppose -3*j = -3*t - 330, -4*j - 3*t + 2*t = -430. Factor -245 - 864*o**2 - 39*o + 4*o**5 - 403 - 56*o**4 + 1227*o + j*o**3 + 204*o**3.
4*(o - 3)**4*(o - 2)
Factor 2768*d + 4*d**2 + 1204 - 1128 - 2848.
4*(d - 1)*(d + 693)
Let s(u) be the third derivative of 0 + 56*u**3 + 9*u**4 + 1/40*u**6 + 3/4*u**5 + u + 2*u**2. Factor s(f).
3*(f + 4)**2*(f + 7)
Let v(h) = 9*h**4 - 30*h**3 - 5*h**2 + 30*h + 2. Let d(c) = -2*c**4 - 1. Let q be (-40)/(-15)*(-9)/12. Let b(f) = q*d(f) - v(f). Factor b(l).
-5*l*(l - 6)*(l - 1)*(l + 1)
Solve 0 - 10/11*j**4 + 10/11*j**2 + 12/11*j - 2/11*j**5 - 10/11*j**3 = 0 for j.
-3, -2, -1, 0, 1
Let l(d) = -d**3 + 18*d**2 - d + 27. Let m be l(18). Let h = m - 9. Factor 2/9*j*