, 1/34, 1
Let j(y) be the third derivative of -y**5/120 - 223*y**4/96 - 37*y**3/8 + 768*y**2. What is u in j(u) = 0?
-111, -1/2
Solve -623 - 408*o**3 + 918*o**2 - 20*o**4 + 1550 - 621 - 78*o - 807*o + 92*o**4 - 3*o**5 = 0 for o.
1, 2, 3, 17
Suppose -200/13*u - 582/13 - 2/13*u**2 = 0. What is u?
-97, -3
Let l(g) = -g**2 - 9*g - 5. Let u be l(-8). Let p = -1 + u. Factor -10*d**3 + 4*d**4 + 0*d**4 - 5 + p*d**4 + 10*d - d**4.
5*(d - 1)**3*(d + 1)
Let g be 7 + (50 - -6)/(-7). Let f be 255/(-357)*(g + 4/10). Factor 1/7*h**4 + 12/7*h**2 + f - 6/7*h**3 - 10/7*h.
(h - 3)*(h - 1)**3/7
Let p = -23755/12 - -1980. Let m(n) be the third derivative of p*n**5 - 115/24*n**4 + 0 + 0*n - 12*n**2 - 25/3*n**3. Factor m(j).
5*(j - 5)*(5*j + 2)
Let j(u) = u**2 + 6*u - 24. Let g be j(-11). Let p = g + -29. Factor -2*b + 6*b**4 + b - 3*b**5 - 6*b**p + 6*b - 2*b.
-3*b*(b - 1)**3*(b + 1)
Suppose -308*q = -305*q. Suppose q = 5*o - 1150 + 70. Suppose 4*c**4 - 212 - 8*c**5 + 5*c**2 - 8*c + o + 16*c**3 - 13*c**2 = 0. Calculate c.
-1, 1/2, 1
Let o = 8 + -12. Let n be -2 - (-2 + 3 + o). Factor 25*u + u**4 + n + 24*u - u**5 - 50*u + 2*u**3 - 2*u**2.
-(u - 1)**3*(u + 1)**2
Let x(t) = -2*t**3 - 34*t**2 - 58*t + 100. Let n(b) = -5*b**3 - 101*b**2 - 173*b + 300. Let g(h) = 2*n(h) - 7*x(h). Factor g(f).
4*(f - 1)*(f + 5)**2
Let v(h) be the third derivative of 0 + 0*h - h**3 - 66*h**2 + 1/140*h**5 - 13/56*h**4. Determine n, given that v(n) = 0.
-1, 14
Suppose -940*v = -953*v - 1144. Let d be v/(-39) - 116/87. Let d*x + 10/13 + 2/13*x**2 = 0. Calculate x.
-5, -1
Let j be 128/5*(-5025)/938. Let d = -135 - j. Determine o, given that 12/7*o**2 + d*o + 6/7 + 3/7*o**3 = 0.
-2, -1
Let p(n) be the third derivative of 1/130*n**5 + 0 + 0*n - 5/78*n**4 + 1/780*n**6 - 8/13*n**3 + 88*n**2. Find c, given that p(c) = 0.
-4, -2, 3
Factor -2/5*v**3 + 222/5*v + 112/5 + 108/5*v**2.
-2*(v - 56)*(v + 1)**2/5
Suppose -5*r - 8 = 2*z - 27, -3*r = -2*z - 5. Factor 1 + 50*c + 235*c**2 - 466*c**2 - 1 + 236*c**z.
5*c*(c + 10)
Let k(m) = 6*m - 62. Let u be k(11). Find z, given that -5*z**4 - 1157*z**3 - 3*z**2 + 1153*z**3 + u*z**4 = 0.
-3, -1, 0
Factor 48427*j**2 - 48422*j**2 + 58 - 265*j - 608.
5*(j - 55)*(j + 2)
Let a = -38 + 35. Let i = a - -8. Factor -18*w**3 + 9*w**3 - 13*w**3 + 15*w**4 - 4 - 26*w + 8*w**i - 46*w**2 - 5*w**4.
2*(w - 2)*(w + 1)**3*(4*w + 1)
Find p such that 2/15*p**2 + 572/15*p - 574/15 = 0.
-287, 1
Let p(t) be the third derivative of -t**6/900 - t**5/50 - 3*t**4/20 - 37*t**3/3 - 81*t**2. Let h(x) be the first derivative of p(x). Factor h(d).
-2*(d + 3)**2/5
Let n(k) = -8729*k - 32. Let o be n(-2). Factor -5 + 6 - 3021*t**2 - 480*t - 2785*t**3 - 5 + o*t**3 - 11136*t**2.
(t - 1)*(121*t + 2)**2
Let f(n) = -7*n + 3. Let r be f(-13). Let w = -91 + r. Solve -6*g + 8*g**2 + 4 - 687*g**3 - 4*g + 685*g**w = 0.
1, 2
Solve -12 - 2/9*i**5 - 14*i + 0*i**4 + 32/9*i**3 + 4/3*i**2 = 0.
-3, -2, -1, 3
Let v = 15094 + -15088. Let r(c) be the first derivative of -1/3*c**v + 0*c + 24 - 3/2*c**4 + 2/3*c**3 + 6/5*c**5 + 0*c**2. Determine k so that r(k) = 0.
0, 1
Let l be (-5)/(20/(-8)) - (0 - 2). Let v(z) be the first derivative of -3 + 8*z**2 - 4*z**3 - z**4 - l*z + 0*z**3 - 9 - 14*z**2. Factor v(d).
-4*(d + 1)**3
Let n(v) be the first derivative of -v**5/5 + 117*v**4/4 - 1254. Factor n(w).
-w**3*(w - 117)
Let u = 36540 - 36537. Find y such that 1/6*y**u + 1/6*y**2 - 1/6 - 1/6*y = 0.
-1, 1
Let g be 4/(-6) - (-14)/12. Suppose -318*u = -347*u. Factor -g*y**2 + y + u.
-y*(y - 2)/2
Let k be 14/6*-3 - 47/(-6). Let n(w) be the second derivative of -5/12*w**4 - 2*w + 5*w**2 + 0 - k*w**3. Solve n(q) = 0 for q.
-2, 1
Let w(d) = -8*d**4 - 18*d**3 + 9*d**2 + 23*d + 4. Let t(f) = -1 - f + 1 - 727*f**2 + 726*f**2. Let p(i) = -5*t(i) - w(i). What is l in p(l) = 0?
-2, -1, -1/4, 1
Let x = -225 - -216. Let d be 40 + -38 - (-10)/x. Determine a so that -d*a**2 + 2/9*a - 4/9*a**3 + 4/9 + 4/9*a**4 + 2/9*a**5 = 0.
-2, -1, 1
Let g(q) be the third derivative of 1/54*q**6 + 1/945*q**7 + 0 - 11/54*q**4 - 3*q**2 - 13/270*q**5 + 0*q**3 + 41*q. Let g(d) = 0. Calculate d.
-11, -1, 0, 2
Let i(c) = -39*c**2 - 806*c - 162466. Let l(u) = -2*u**2 - 3. Let o(j) = 2*i(j) - 38*l(j). Let o(x) = 0. What is x?
-403
Determine u so that 153/7*u - 132/7*u**2 - 54/7 - 3/7*u**5 + 18/7*u**4 + 18/7*u**3 = 0.
-3, 1, 6
Suppose 0 = -4*w + 3*w - 4*u - 3, u + 2 = 0. Suppose -4*h - w*f + 28 = -9, -5*h + 35 = 4*f. Find j, given that 0*j + 0 + 8/9*j**2 - 8/9*j**h + 2/9*j**4 = 0.
0, 2
Factor 8/3*o**3 + 10/3*o**2 - 8 - 94/3*o.
2*(o - 3)*(o + 4)*(4*o + 1)/3
Factor -9/2*b**3 + 6*b + 0 + 26*b**2.
-b*(b - 6)*(9*b + 2)/2
Suppose -5*f - 340 = -790. Let 183*i - f + 1145*i**2 - 46 - 50 - 1142*i**2 = 0. What is i?
-62, 1
Let o(u) be the first derivative of u**6/24 + 7*u**5/20 + 7*u**4/16 - 5*u**3/4 - 2172. Determine z, given that o(z) = 0.
-5, -3, 0, 1
Let j(r) be the second derivative of 25/6*r**4 + 0*r**2 + 5/3*r**6 - 5/28*r**7 - 59/12*r**5 - 5/4*r**3 + 0 + 291*r. Determine n, given that j(n) = 0.
0, 1/3, 3
Let k = -46 + 48. Factor 2*f - 10*f + 2*f**k - 12 - 2*f + 2*f**2 + 2*f**3.
2*(f - 2)*(f + 1)*(f + 3)
Let b = 32 - 29. Let a be 19 - 18 - (-2)/(b - 2). Factor -a*p + 3 - 3*p**2 + p**3 + 5*p - 3.
p*(p - 2)*(p - 1)
Let x(n) be the first derivative of -n**3/15 - 149*n**2/5 + 1278. Factor x(m).
-m*(m + 298)/5
Suppose -2*g + 2*c - 8 = -5*g, 3*g - c - 14 = 0. Let n(q) = -q**2 + 5*q - 1. Let m be n(g). Determine l so that -3*l + 0 - 4*l + 2 + l + 6*l**2 - 2*l**m = 0.
1
Suppose -5*x + 14*v = 18*v - 68, -5*v = -3*x - 11. Let g(k) be the second derivative of -5/57*k**3 - 4/19*k**2 + x*k - 1/114*k**4 + 0. Factor g(b).
-2*(b + 1)*(b + 4)/19
Suppose 89*g - 11956 + 11778 = 0. Find u such that 3*u + 0 + 1/3*u**g = 0.
-9, 0
Suppose -1577 = 255*n - 2342. Find r, given that 6/13*r**4 - 32/13 + 48/13*r**2 + 32/13*r**n + 0*r = 0.
-2, 2/3
Factor 1/7*u**3 - 5/7*u**2 + 1/7*u**4 + 0 + 3/7*u.
u*(u - 1)**2*(u + 3)/7
Solve 0*u + 174724*u**2 + 0 - 418*u**3 + 1/4*u**4 = 0 for u.
0, 836
Let k be (-75)/(-125) + 1*-12. Let s = k - -176/15. Factor -1/3*g**3 + 0 - s*g**2 + 1/3*g**4 + 1/3*g.
g*(g - 1)**2*(g + 1)/3
Let y(v) be the first derivative of -140*v + 5/3*v**3 + 30*v**2 - 24. Factor y(g).
5*(g - 2)*(g + 14)
Let i(u) be the first derivative of -4*u**5/5 + 67*u**4 + 1408*u**3/3 + 1144*u**2 + 1152*u + 1929. Suppose i(m) = 0. Calculate m.
-2, -1, 72
Let t = -771077/11 - -70098. Let 0*y**2 + 12/11*y - t*y**3 + 16/11 = 0. What is y?
-2, 4
Factor 503*t + 184 - 624 + 511*t - 1421*t + 499*t + 12*t**2.
4*(t + 11)*(3*t - 10)
Let v(c) be the second derivative of c**8/26880 + 19*c**7/10080 + c**6/45 + c**5/8 - 8*c**4/3 + 124*c. Let y(b) be the third derivative of v(b). Solve y(g) = 0.
-15, -2
Let t(a) = -31*a**2 + 35*a + 112. Let l be t(-3). Let z = l - -549/2. Let 0 - 5/2*f**2 + z*f = 0. Calculate f.
0, 1
Let v(n) be the first derivative of 1/7*n**5 + 2/7*n**2 - 8/21*n**3 - 1/4*n**4 + 0*n + 6. Factor v(u).
u*(u - 2)*(u + 1)*(5*u - 2)/7
Let p(u) = 645*u - 6448. Let l be p(10). Let m(y) be the first derivative of 11/3*y**3 - 11 - 2*y - 9/2*y**l. Factor m(f).
(f - 1)*(11*f + 2)
Factor -62/5 + 1/5*q**2 - 61/5*q.
(q - 62)*(q + 1)/5
Suppose -49*m + 25*m - 9 = -81. Let r be (-28)/52*12/(-14). Determine j, given that 6/13*j - 2/13 - r*j**2 + 2/13*j**m = 0.
1
Suppose -134 - 997 = -5*g + 3*h, 0 = 2*g + 4*h - 442. Factor -25*n**3 + 441*n**2 - 156*n**2 - g*n**2 + 45*n.
-5*n*(n - 3)*(5*n + 3)
Let q(s) be the second derivative of s**6/210 + 31*s**5/140 + 53*s**4/28 + 229*s**3/42 + 50*s**2/7 + 4*s - 194. Let q(h) = 0. Calculate h.
-25, -4, -1
Let m(l) = -17*l**3 + 16*l**2 + 9*l - 9. Let u(g) = 15*g**3 - 16*g**2 - 8*g + 8. Let d(b) = -8*m(b) - 9*u(b). Solve d(f) = 0 for f.
-16, 0
Let n(z) be the first derivative of -z**4 + 12*z**3 - 30*z**2 - 100*z + 41. Find k, given that n(k) = 0.
-1, 5
Let g = -294 - -299. Let m be ((-7)/3)/(6/(-18)) - g. Factor -16/5*b - 4/5 - 16/5*b**3 - 4/5*b**4 - 24/5*b**m.
-4*(b + 1)**4/5
Let f(r) = -1 - r**3 + 18*r**4 + r - 17*r**4 + 0*r. Let m(c) = -8*c**4 - 52*c**3 - 196*c**2 - 4*c + 4. Let w(j) = 4*f(j) + m(j). Let w(g) = 0. What is g?
-7, 0
Let x(f) = -10*f**2 + 6*f + 4. Let r(z) = -4 + 13 + 0 + 1 - z**2 - 9. Let w be 1/(1 - (-18)/(-16)). Let t(q) = w*r(q) + x(q). Factor t(y).
-2*(y - 2)*(y -