5
Suppose 3*d - 60 = -31*d + 22*d. Suppose -3*n**d + 33/5*n**3 + 18/5*n**2 + 0 - 36/5*n**4 + 0*n = 0. Calculate n.
-3, -2/5, 0, 1
Let i(f) be the first derivative of f**3/18 - f**2/2 + 6354. Factor i(y).
y*(y - 6)/6
Let f(h) be the first derivative of -h**4/30 + 36*h**3/5 - 2916*h**2/5 + 104976*h/5 + 616. Let f(b) = 0. Calculate b.
54
Let x be 105705/20007 + (33/12 - 2)/(1235/(-380)). Suppose -94/19*z**3 + 6/19*z + x*z**4 + 26/19*z**2 - 32/19*z**5 - 2/19 = 0. What is z?
-1/4, 1/4, 1
Factor 10*k + 20*k**2 + 86*k + 0*k**3 - 2*k**3 + 106*k**2 + 184 - 216*k**2.
-2*(k - 2)*(k + 1)*(k + 46)
Let v be ((-45)/(2475/(-22)))/(2*-4). Let d = 193/20 + v. Find h such that 24/5*h**3 + 72/5*h**2 + 3/5*h**4 + 96/5*h + d = 0.
-2
Find n such that 25/2*n**3 - 1/4*n**5 + 45/2*n**2 - 69/4 - 21/4*n**4 - 49/4*n = 0.
-23, -1, 1, 3
Let y(u) be the first derivative of -u**4/10 + 4*u**3/5 - 3*u**2/5 - 4*u + 1393. Determine j so that y(j) = 0.
-1, 2, 5
Solve 71/2 + 1/10*j**2 - 38/5*j = 0.
5, 71
Let v(n) be the third derivative of n**5/45 + 23*n**4/18 + 28*n**3 + 3*n**2 + 2*n + 2083. Suppose v(l) = 0. Calculate l.
-14, -9
Let b = -202 + 836. Let y be b - -2 - (9 - 7). Suppose -t**2 - 5*t**2 - 632*t**3 + y*t**3 = 0. Calculate t.
0, 3
Let n = -67409/70 + 963. Let t(h) be the second derivative of 0*h**2 + 1/42*h**4 - n*h**5 - 1/105*h**6 + 1/21*h**3 - 4*h + 0. Factor t(w).
-2*w*(w - 1)*(w + 1)**2/7
Let u = -383461 + 1910419/5. Let k = u + 1382. Determine o, given that -9*o**4 + 126/5*o**3 + 0 - 5*o**5 + k*o + 116/5*o**2 = 0.
-3, -2/5, 0, 2
Factor 196*k**2 + 930 - 195*k**2 + 245*k + 686*k.
(k + 1)*(k + 930)
Let c(f) = -38*f**4 + 12*f**3 + 186*f**2 - 466*f - 28. Let z(p) = 8*p**4 - 2*p**3 - 37*p**2 + 93*p + 6. Let o(s) = 3*c(s) + 14*z(s). Solve o(g) = 0 for g.
-4, 0, 2, 6
Let b(d) = -d**2 - 2806*d - 1960336. Let w(f) = 2*f**2 + 5613*f + 3920728. Let x(q) = -13*b(q) - 6*w(q). Solve x(k) = 0 for k.
-1400
Let o(b) = 2*b**2 + 296*b + 316. Let u(j) = -6*j**2 - 883*j - 954. Let x(a) = 7*o(a) + 2*u(a). Suppose x(t) = 0. What is t?
-152, -1
Suppose 3*z - 59 = -3*u - 53, -u + 3*z = -14. Let k(v) be the third derivative of 0*v + 0 + 5/96*v**4 + 0*v**3 - 1/60*v**u - 1/480*v**6 - 39*v**2. Factor k(f).
-f*(f - 1)*(f + 5)/4
Let a(g) be the first derivative of 4/5*g**5 + 128*g + 56*g**3 - 128*g**2 + 39 - 11*g**4. Factor a(h).
4*(h - 4)**2*(h - 2)*(h - 1)
Let d(g) be the third derivative of 0 + 3/2*g**5 + 0*g + 7/8*g**6 + 4/21*g**7 + 0*g**4 + 0*g**3 - 66*g**2 + 5/336*g**8. Factor d(r).
5*r**2*(r + 2)*(r + 3)**2
Let -11*z**3 + 0 + 8/3*z - 130/3*z**2 = 0. What is z?
-4, 0, 2/33
Let r(n) be the third derivative of -1/60*n**6 + 0*n + 1 + 5/4*n**4 + 1/15*n**5 - 12*n**3 - 49*n**2. Factor r(q).
-2*(q - 3)**2*(q + 4)
Let w = 50 + -45. Let m = -1315/2 + 658. Suppose 0 - m*x - 69/4*x**4 - 59/4*x**3 - 19/4*x**2 - 27/4*x**w = 0. What is x?
-1, -1/3, -2/9, 0
Let i = -3 - -158. Factor 45*b**3 - 12*b**4 + 52*b**2 - 60 + 7*b**4 - 187*b**2 + i*b.
-5*(b - 4)*(b - 3)*(b - 1)**2
Suppose -102*k = 8*k - 550. Let l(r) be the second derivative of 0*r**2 - 2*r + 0*r**3 + 0 - 1/12*r**k - 5/36*r**4 + 5/126*r**7 + 1/18*r**6. Solve l(p) = 0.
-1, 0, 1
Let c = -40267/3 + 13424. Factor 1/6*r - 1/3*r**2 + c.
-(r + 2)*(2*r - 5)/6
Let m = -11/556 - -54/973. Let a(x) be the first derivative of -4/7*x + 0*x**2 - 15 - m*x**4 + 1/7*x**3. Determine w so that a(w) = 0.
-1, 2
Let z(q) be the second derivative of -q**4/72 + 37*q**3/12 - 27*q**2 - 1043*q. Suppose z(b) = 0. What is b?
3, 108
Let o(b) = b**2 - 6*b - 3. Suppose -27 = -92*i + 89*i. Let q be o(i). Find f, given that 12*f**2 + 8*f**2 - 96*f - 576 - q*f**2 = 0.
-12
Suppose -5000 = 29*s + 7499. Let l = s - -437. Let -15/2*c + l + 3/2*c**2 = 0. Calculate c.
1, 4
Let g = 223 + -229. Let x be (g/12)/((-14)/16). Determine h so that -x*h + 6/7 - 2/7*h**2 = 0.
-3, 1
Let t(d) be the first derivative of -d**4/2 - 716*d**3/3 - 3505*d**2 - 17400*d + 11498. Let t(h) = 0. Calculate h.
-348, -5
Suppose 35*k**3 - 66026*k**5 + 15*k**4 - 30*k + 35 + 66021*k**5 + 5 - 55*k**2 = 0. What is k?
-2, -1, 1, 4
Factor 0 + 10*t**2 + 19/2*t + 1/2*t**3.
t*(t + 1)*(t + 19)/2
Let t(d) be the first derivative of 1/20*d**4 - 7/10*d**2 - 2/5*d**3 - 27 + 0*d. Factor t(h).
h*(h - 7)*(h + 1)/5
Let c = -346 + 9344/27. Let o(h) be the first derivative of c*h**3 - 18 + 4/9*h**2 + 8/9*h. Factor o(a).
2*(a + 2)**2/9
Suppose -k + 0*k = -4*x + 41, 4*k + 65 = 5*x. Suppose 0 = -3*y + x. Factor 9*f**3 + 20*f - f**2 - 4*f**y + 12*f**2 + 14*f**2.
5*f*(f + 1)*(f + 4)
Factor -3844*x + 0 + 62*x**2 - 1/4*x**3.
-x*(x - 124)**2/4
Let v(c) be the second derivative of -348*c**5/5 + 113*c**4/2 - 13*c**3 - 9*c**2/16 + 286*c - 1. Factor v(r).
-3*(4*r - 1)**2*(232*r + 3)/8
Let t(h) = -1. Let r(s) = 2*s**2 - 112*s + 1571. Let q be (-16)/(-3) - (3 + 66/(-18)). Let y(l) = q*t(l) + 2*r(l). Factor y(a).
4*(a - 28)**2
Solve -134*y**4 + 88*y**2 - 438*y**3 - 4*y**5 - 229110*y - 60 - 638*y**2 + 228808*y = 0 for y.
-30, -1, -1/2
Let l = -7277 + 7277. Let n(j) be the third derivative of 0 + 1/320*j**6 + 1/32*j**4 - 19*j**2 + 0*j**3 + 3/160*j**5 + l*j. Factor n(z).
3*z*(z + 1)*(z + 2)/8
Let v = 625244/7 - 89318. Factor -48/7*n - 2/7*n**3 - 40/7 - v*n**2.
-2*(n + 2)**2*(n + 5)/7
Suppose -646*t - 550 + 1778 + 2002 = 0. Let 12/5*i**4 - 12/5*i**3 + 4/5*i**t - 44/5*i**2 - 24/5*i + 0 = 0. What is i?
-3, -1, 0, 2
Let m(r) be the first derivative of 140*r**2 + 74 - 275/3*r**3 - 60*r - 125/4*r**4. Let m(d) = 0. Calculate d.
-3, 2/5
Let g(w) be the second derivative of w**4/3 + 146*w**3 - 884*w**2 + 870*w + 1. Factor g(u).
4*(u - 2)*(u + 221)
Let g(n) be the second derivative of 0 - 16*n**3 + 23/4*n**4 + 18*n**2 + 248*n - 9/20*n**5. Factor g(p).
-3*(p - 6)*(p - 1)*(3*p - 2)
Let u = -302801 + 302801. Factor -2/21*h**4 + u - 2/7*h**2 - 2/21*h - 2/7*h**3.
-2*h*(h + 1)**3/21
Let m(t) = t**4 - t**3 + 2*t**2. Let k(u) = u**4 - 15*u**3 + 28*u**2 + 8*u - 40. Let h = 403 - 404. Let l(y) = h*m(y) - k(y). Factor l(x).
-2*(x - 5)*(x - 2)**2*(x + 1)
Let p = -412 + 420. Let 4*m**2 + 3*m**2 + p*m**2 + 6*m**3 - 18*m**2 - 3*m**4 = 0. What is m?
0, 1
Let l(o) be the second derivative of -o**4/120 + o**3/4 + 46*o**2/5 - 1531*o. Solve l(z) = 0 for z.
-8, 23
Factor 2366 - 52*c + 2/7*c**2.
2*(c - 91)**2/7
Factor 2/7*p**3 - 2/7*p + 54/7*p**2 - 54/7.
2*(p - 1)*(p + 1)*(p + 27)/7
Determine n so that 628*n**3 + n**5 - 60*n**4 - 2408*n**2 + 2499 + 3086 - 294*n + 12190 - 2683 + n**5 = 0.
-2, 7, 11
Suppose -225*j = -3*c - 222*j + 51, -4*c - 2*j + 38 = 0. Factor -c - 1/3*v**2 + 4*v.
-(v - 6)**2/3
Let q be (30/(-5) - -4)*-1. Suppose -20 = -4*r - 4*i, -2*i = r + q*r - 12. Suppose 4*a**4 + 8 - 4*a**3 - 8*a**r - 17 + 9 = 0. What is a?
-1, 0, 2
Suppose -4*x = 5*f - 37, -x = f + x - 11. Factor 4*k**4 - 3*k**5 + 2*k**3 + k**f - 3*k**4 - k**3.
-k**3*(k - 1)*(2*k + 1)
Factor -17*j**2 + 0 + 1/3*j**4 - 30*j - 4/3*j**3.
j*(j - 10)*(j + 3)**2/3
Let 1/2*u**2 + 2047761/2 - 1431*u = 0. Calculate u.
1431
Suppose 0*u + 4*z + 12 = 4*u, z = -u - 3. Let p(v) be the second derivative of 2/21*v**3 - 19*v + u + 1/7*v**2 + 1/42*v**4. Factor p(b).
2*(b + 1)**2/7
Let c = -4533 - -1400698/309. Let z = 722/309 - c. Factor -z*h + 2 - h**2.
-(h + 3)*(3*h - 2)/3
Let s be (-5 - (-10)/15 - -4)*-9. Suppose s*j - 18 = 3*f + 9, 5*j - 13 = -3*f. Factor 8/3*y**4 - 4/3*y + 4/3*y**j + 0 - 8/3*y**2 + 0*y**3.
4*y*(y - 1)*(y + 1)**3/3
Let y(k) be the first derivative of -k**8/616 + 3*k**6/220 - k**5/55 + 3*k**2/2 - 12*k + 61. Let d(o) be the second derivative of y(o). Factor d(q).
-6*q**2*(q - 1)**2*(q + 2)/11
Let k(z) be the third derivative of -z**7/42 - 244*z**6/3 - 238144*z**5/3 + 6317*z**2. Find s such that k(s) = 0.
-976, 0
Let a be 490/20*(3 + -1). Factor -60*i + a - 31 - 36 - 50*i**2.
-2*(5*i + 3)**2
Let z(l) be the first derivative of -2*l**6/3 - 16*l**5/5 + 12*l**4 + 128*l**3/3 - 128*l**2 + 125. Solve z(b) = 0 for b.
-4, 0, 2
Suppose -v = -2*t + 4*t - 92, -t = v - 44. Let w = t - 46. Determine u so that w*u**4 - 21*u**2 + 3 - 1 + 17*u**2 = 0.
-1, 1
Let l(m) = 30*m**2 + 15*m + 3. Let j be l(-12). Determine a so that 5*a**4 + 40*a**2 - j*a - 45*a**3 + 4143*a = 0.
0, 1, 8
Let v(d) = 3. Let o(q) = q**2 - 102*q - 193. Let g(i) = -o(i) + 5*v(i). Factor g(x).
-(x - 104)*(x + 2)
Let v(n) = 2*n - 24. Let i be v(15). Let f be 