 1)**2
Determine v, given that 968*v + 2116*v - 792 + 87*v + 7*v**3 - 3180*v**2 + 5*v**3 = 0.
1/2, 264
Let h be 0 + 0 - (52 + -52). Let z(j) be the second derivative of h + 1/21*j**4 + 16/21*j**3 + 32/7*j**2 - 19*j. Factor z(t).
4*(t + 4)**2/7
Suppose -h = 6*h + 490. Let s = 86 + h. Factor 8*x**2 - 3*x**3 + 4*x**3 - s*x**2 + 3*x**2.
x**2*(x - 5)
Let i = -10 - -37. Suppose 23*u = i*u - 12. Find a, given that 0*a**5 + 60*a + 4*a**2 + a**5 - 59*a - 2*a**u - 2 - 2*a**4 = 0.
-1, 1, 2
Let a(j) be the first derivative of 0*j**3 + 3/2*j**2 + 1/2*j**6 - 37 + 0*j + 0*j**5 - 3/2*j**4. Factor a(u).
3*u*(u - 1)**2*(u + 1)**2
Let d be (-3315)/(-325) - (4 - (7 + -13)). Determine g so that 0 - 3/5*g - d*g**2 = 0.
-3, 0
Find b such that -43*b**2 + 284258*b**3 + 222*b + 284253*b**3 - 568510*b**3 = 0.
0, 6, 37
Suppose 17 = -3*d + 3*i + 71, -d + 10 = -5*i. Factor -41*z**2 - d - 2*z + 38*z**2 + 29*z - 4.
-3*(z - 8)*(z - 1)
Suppose 3*g - 2*x - 1 = 0, -17*g + 21*g + 2*x = 20. Suppose -4*f + 5*f + d = 3, g*f - 4*d = 2. Factor -f*q + 0 - 3/2*q**3 - 13/2*q**2.
-q*(q + 4)*(3*q + 1)/2
Let u(h) be the first derivative of 24649*h**4/42 + 27318*h**3/7 - 523*h**2/7 + 10*h/21 - 3274. Find k, given that u(k) = 0.
-5, 1/157
Let d = -121896/7 - -17414. Let q(u) be the first derivative of -18 + 0*u**3 - 4/35*u**5 + 4/7*u**2 - d*u**4 + 4/7*u. Factor q(m).
-4*(m - 1)*(m + 1)**3/7
Let s = -52 - -55. Factor 15*z - z**4 - 23*z + 12*z**2 - s*z**4.
-4*z*(z - 1)**2*(z + 2)
Let g(k) be the third derivative of -k**7/210 + 7*k**6/60 - 7*k**5/12 - 25*k**4/12 - 19*k**2. Determine c, given that g(c) = 0.
-1, 0, 5, 10
Let k(b) be the second derivative of 4/9*b**3 - 11/9*b**4 - 1/10*b**6 + 19/30*b**5 + 0*b**2 - 28*b + 0. Factor k(m).
-m*(m - 2)**2*(9*m - 2)/3
Suppose -30752/17*i**2 - 338/17 + 6448/17*i = 0. What is i?
13/124
What is q in -4618*q + 4978*q - 179 + 298 + 239 + 2*q**2 = 0?
-179, -1
Let s(c) be the first derivative of 2*c**5/5 - 7*c**4 + 38*c**3 - 36*c**2 - 216*c - 217. Let s(b) = 0. Calculate b.
-1, 3, 6
Let s(x) be the third derivative of -x**5/40 + 78*x**4 - 480*x**2. What is r in s(r) = 0?
0, 1248
Let s(p) be the second derivative of 1/6*p**6 + 0 + 0*p**2 + 37*p + 5/2*p**5 + 125/12*p**4 + 0*p**3. Factor s(n).
5*n**2*(n + 5)**2
Let j(b) be the third derivative of 0*b - 131*b**2 - 1/672*b**8 + 0*b**3 - 25/6*b**4 - 27/40*b**6 + 17/6*b**5 + 23/420*b**7 + 0. Let j(d) = 0. What is d?
0, 1, 2, 10
Let l(d) be the first derivative of 5*d**3/6 + 145*d**2/2 + 285*d/2 + 3635. Factor l(j).
5*(j + 1)*(j + 57)/2
Let g(v) be the first derivative of 2/21*v**3 + 0*v**4 - 1/35*v**5 - 15*v - 1/105*v**6 - 15 + 1/7*v**2. Let o(r) be the first derivative of g(r). Factor o(p).
-2*(p - 1)*(p + 1)**3/7
Suppose v = 6*i - 3*i - 7, v - 5 = -3*i. Let 20 + 68 - 8 - 38*r + 4*r**2 + i*r = 0. What is r?
4, 5
Let q(b) be the first derivative of 2*b**3/33 + 158*b**2/11 - 640*b/11 - 1752. Factor q(h).
2*(h - 2)*(h + 160)/11
Let i = -162524 - -1137728/7. Let -9/7*x**2 + 96/7*x - i - 30/7*x**3 + 3/7*x**4 = 0. Calculate x.
-2, 1, 10
Let x(h) = 45*h**3 + 5239*h**2 - 2128*h. Let p(f) = 68*f**3 + 7852*f**2 - 3192*f. Let t(c) = -5*p(c) + 8*x(c). Factor t(s).
4*s*(s + 133)*(5*s - 2)
Factor -2646 + 5376*s + 4/3*s**3 - 506/3*s**2.
2*(s - 63)**2*(2*s - 1)/3
Let o = -31192/15 + 2080. Let k(f) be the third derivative of 0 - 7/6*f**4 + 2/3*f**3 + o*f**5 - f**2 + 8/15*f**6 + 0*f. Factor k(c).
4*(c + 1)*(4*c - 1)**2
Let c(d) be the third derivative of -20*d**3 + 11/12*d**5 + 57*d**2 + 0*d + 0 + 1/24*d**6 - 35/12*d**4. Factor c(t).
5*(t - 2)*(t + 1)*(t + 12)
Suppose -194*o**2 + 177 + 454 + 403*o**2 - 204*o**2 + 335*o + 19 = 0. Calculate o.
-65, -2
Let l(w) = -298*w - 4467. Let z be l(-15). Factor 2*g**2 + 8/3*g**z + 0 + 2/3*g**4 + 0*g.
2*g**2*(g + 1)*(g + 3)/3
Let c(f) be the second derivative of 2/3*f**3 + 2/3*f**4 + 0 - 40*f - 4/15*f**6 + 0*f**2 - 1/5*f**5. Solve c(s) = 0.
-1, -1/2, 0, 1
Let o(d) be the first derivative of d**7/3360 - 7*d**6/1440 - d**5/480 + 7*d**4/96 + 163*d**3/3 + 12. Let k(p) be the third derivative of o(p). Factor k(s).
(s - 7)*(s - 1)*(s + 1)/4
Suppose -19*m + 3 = 3. Factor m - 5*p + 6 - 2*p**2 + 0 + p**2.
-(p - 1)*(p + 6)
Factor 6*d**2 - 3*d**2 - 94161*d**5 + 94158*d**5 - 21*d**3 + 6*d**2 + 15*d**4.
-3*d**2*(d - 3)*(d - 1)**2
Let n = -888/373 - -7708/2611. Let -n*h**2 + 0 - 108/7*h = 0. Calculate h.
-27, 0
Let c(z) = -z**2 + 43*z - 63. Let r be c(37). Let o = -157 + r. Factor 2/17*k**4 + 16/17*k**o + 8/17*k + 0 + 10/17*k**3.
2*k*(k + 1)*(k + 2)**2/17
Let i be 2/(-2) - (6 - -19 - (-1254)/(-44)). Factor 9/4 - i*a + 1/4*a**2.
(a - 9)*(a - 1)/4
Let f = 204 + -196. Find p such that f*p**5 - 6*p**5 + 10*p**3 + 12*p**2 - 8*p**2 + 8*p**4 = 0.
-2, -1, 0
Let n = -2284 + 976. Let w = 1311 + n. Factor 7/2*b**2 + 1/2 + 5/2*b + 3/2*b**w.
(b + 1)**2*(3*b + 1)/2
Suppose -x + 938 + 459 = -2*i, -4*x + 5538 = 2*i. Let l = 1389 - x. Factor 0 + 0*n + 1/3*n**l + 1/3*n**3 - 1/3*n**4 - 1/3*n**5.
-n**2*(n - 1)*(n + 1)**2/3
Let w(u) be the third derivative of -u**6/48 - 7*u**5/12 + 50*u**4/3 - 440*u**3/3 - 279*u**2. Find l such that w(l) = 0.
-22, 4
Let t(y) be the second derivative of -7/4*y**2 - 1/4*y**4 + 11*y + 0 + 43/12*y**3. Factor t(v).
-(v - 7)*(6*v - 1)/2
Let a be (-8256)/258 - 208/(-6). Let -a*p + 4 + 1/3*p**2 = 0. Calculate p.
2, 6
Suppose 3*t = 2*w - w + 4, 5*t + 5*w - 40 = 0. Let j = -4094 + 36850/9. Let -j*x**t + 0 - x**2 - 2/9*x = 0. What is x?
-2, -1/4, 0
Let x(j) be the second derivative of -11*j**10/6048 + j**9/1512 - 5*j**4/6 + 114*j. Let o(y) be the third derivative of x(y). Find b, given that o(b) = 0.
0, 2/11
Let k(x) = -5*x**2 + 140*x + 1669. Let v(n) = -35*n**2 + 980*n + 11685. Let i(d) = -15*k(d) + 2*v(d). Determine j, given that i(j) = 0.
-9, 37
Factor -685*j + 3*j**2 - 299*j + 226*j - 69192 - 5*j**2 + 14*j.
-2*(j + 186)**2
Let d be (0 + 46/6)/((-14)/252). Let h = d - -207. Find n, given that -6*n**4 + 57*n**2 - h*n**2 + 24*n**3 - 3*n - 39*n**3 = 0.
-1, -1/2, 0
Determine o, given that -410/11*o**3 + 3456/11 - 64/11*o**4 - 2/11*o**5 + 144*o - 564/11*o**2 = 0.
-24, -4, -3, 2
Let y(s) be the first derivative of -s**3/7 + 3135*s**2/14 - 894*s + 2043. Determine c so that y(c) = 0.
2, 1043
Let a(t) be the first derivative of 2*t**3/39 - 1168*t**2/13 + 2334*t/13 + 14114. Factor a(c).
2*(c - 1167)*(c - 1)/13
Let o = 766153 - 766149. Factor 2/7*c**2 - 30/7*c + o.
2*(c - 14)*(c - 1)/7
Suppose -3*k**2 + 33091769 - 21672*k - 3*k**2 - 3737045 + 13*k**2 - 3*k**2 = 0. What is k?
2709
Let n be 141/282 + -5*1/14. Let l(a) be the first derivative of -1/14*a**4 + 0*a + 2/35*a**5 - 17 - 2/21*a**3 + n*a**2. Solve l(v) = 0.
-1, 0, 1
Let k(o) = 5*o**4 - 63*o**3 - 20*o**2 - 2*o - 22. Let i(p) = -61*p**4 + 755*p**3 + 239*p**2 + 25*p + 275. Let d(g) = -6*i(g) - 75*k(g). Solve d(c) = 0.
-1/3, 0, 22
Let z(w) be the second derivative of -70/3*w**3 - 5/12*w**4 - 375/2*w**2 + 132*w - 1. Solve z(v) = 0 for v.
-25, -3
Let -3/2*p**3 + 0 + 9*p + 3/2*p**2 = 0. What is p?
-2, 0, 3
Let o(w) be the second derivative of w**8/84 - 2*w**7/105 - w**6/30 + w**5/15 - 100*w**2 - 2*w + 37. Let f(r) be the first derivative of o(r). Factor f(t).
4*t**2*(t - 1)**2*(t + 1)
Let -160/9*o**3 - 4/3*o**2 + 488/9*o - 320/9 + 4/9*o**4 = 0. Calculate o.
-2, 1, 40
Let m be 18*(-6 - (-560)/63). Let n = -94 - -190. Suppose -16*v**2 - n*v + m*v**4 - 52*v**5 + 60*v**5 + 88*v**3 - 18 - 18 = 0. What is v?
-3, -1, -1/2, 1
Suppose 0 = 2*p + r + 3, r + 3 = 5*p. Suppose -7*u + 8*u - 4 = p. Let 53*y**2 - 12*y**3 + 3*y**u - 45*y**2 + 5*y**4 - y**5 - 2*y**4 = 0. Calculate y.
0, 2
Suppose -4*y + 9*y + 74 = 4*f + 73, -10*y = -30. Find q such that 0 - 33/7*q**2 + 18/7*q + 18/7*q**3 - 3/7*q**f = 0.
0, 1, 2, 3
Let o = -1271 + 1274. Let d(k) be the first derivative of 0*k + 14/25*k**5 - 2/15*k**o - 8 + 0*k**2 + 4/15*k**6 + 1/5*k**4. Factor d(w).
2*w**2*(w + 1)**2*(4*w - 1)/5
Let r(i) be the second derivative of 2*i**6/3 - 561*i**5/4 + 8225*i**4 - 12250*i**3/3 - 5860*i. Factor r(w).
5*w*(w - 70)**2*(4*w - 1)
Let g(z) = -12*z**2 + 204*z - 2240. Let y(m) = 22*m**2 - 407*m + 4481. Let q(n) = -7*g(n) - 4*y(n). Find x such that q(x) = 0.
17, 33
Let w = -1504 + 1534. Suppose 26 - w = -2*o. Factor -65/3*f**o - 20/3 - 50*f**3 + 100/3*f - 15*f**4.
-5*(f + 2)**2*(3*f - 1)**2/3
Suppose -r**2