*(-4)/6. Find p such that -2/3*p - 2/3*p**4 - 4/3*p**3 - l*p**2 - y - 2/15*p**5 = 0.
-1
Let u(s) be the third derivative of s**6/540 + s**5/15 + 5*s**4/9 - 47*s**3/3 - 124*s**2. Let w(n) be the first derivative of u(n). Solve w(a) = 0.
-10, -2
Let u = 93041/40 + -2326. Let d(m) be the third derivative of -1/8*m**4 + 0 + 0*m + 1/20*m**5 - 1/2*m**3 + m**2 + u*m**6. Suppose d(s) = 0. Calculate s.
-1, 1
Factor -48*h**2 + 7028*h - 766 - 46*h**2 - 2042 + 74*h**2.
-4*(h - 351)*(5*h - 2)
Let s(n) be the first derivative of n**6/2 + 63*n**5/5 + 54*n**4 + 68*n**3 + 3699. Suppose s(g) = 0. What is g?
-17, -2, 0
Let o(u) = u**2 + 80*u + 1348. Let j be o(-24). Let g(t) be the second derivative of 0 + 4/9*t**3 - 4/3*t**2 - 1/18*t**j + 20*t. Suppose g(c) = 0. Calculate c.
2
Let z(i) be the second derivative of i**5/210 - i**4/84 + 17*i**2 - 72*i. Let f(v) be the first derivative of z(v). Factor f(q).
2*q*(q - 1)/7
Let s = 278 + -174. Factor -12*a - a**4 + 7*a**4 - 24*a**2 + s*a**3 + 3*a**5 - 113*a**3.
3*a*(a - 2)*(a + 1)**2*(a + 2)
Let w(l) = -22*l**3 - 93*l**2 - 779*l - 9. Let c(b) = 19*b**3 + 91*b**2 + 778*b + 8. Let f(r) = -9*c(r) - 8*w(r). Factor f(v).
5*v*(v - 22)*(v + 7)
Suppose -17*h**3 + 0 + 88/3*h**2 + 4*h**4 - 16*h - 1/3*h**5 = 0. Calculate h.
0, 1, 3, 4
Let o = 3949780/11 - 359060. What is c in -6/11*c**3 + o*c**2 - 114/11*c + 0 = 0?
0, 1, 19
Let d(c) be the third derivative of -c**5/60 + 2*c**4/3 + 6*c**2 + 69. Factor d(t).
-t*(t - 16)
Let s(x) be the third derivative of x**7/420 - 31*x**6/240 + 7*x**5/10 + x**4/12 - 28*x**3/3 - 2524*x**2. Factor s(h).
(h - 28)*(h - 2)**2*(h + 1)/2
Determine d, given that 128/3 + 8*d - 2/3*d**2 = 0.
-4, 16
Let p = -14/2735 + 16508/19145. Let n(c) be the first derivative of -4/7*c**2 + 2/21*c**3 - 17 + p*c. Find u, given that n(u) = 0.
1, 3
Suppose 3*u - 2*r = 1562, 2*u + r = 3*u - 522. Factor 10 - 269*p + u*p + 2*p**2 - 261*p.
2*(p - 5)*(p - 1)
Let i = -7400 - -7400. Let f(x) be the second derivative of -1/100*x**5 + 1/150*x**6 - 10*x + 0 + 0*x**2 + i*x**3 - 1/30*x**4. Suppose f(b) = 0. What is b?
-1, 0, 2
Let y(h) be the second derivative of -h**4/3 + 12*h**3 - 34*h**2 - h - 337. Suppose y(s) = 0. Calculate s.
1, 17
Let c(f) be the third derivative of f**5/20 - 3*f**4/8 - 5*f**3 + 4*f**2 - 590*f. Let c(a) = 0. What is a?
-2, 5
Let x be ((-8 - -20602)/(-7))/2. Let j = 1475 + x. Solve -2*p + 0 + 10/3*p**2 + 38/3*p**j + 8/3*p**5 + 46/3*p**3 = 0.
-3, -1, 0, 1/4
Let v be (13/(312/11) + (-3)/24)/36. Let y(u) be the second derivative of v*u**4 - 5/18*u**2 + 30*u + 0 + 2/27*u**3. Factor y(c).
(c - 1)*(c + 5)/9
Let r(w) be the first derivative of 13 - 1/4*w**4 - 21/20*w**5 + 0*w - 17/2*w**2 + 0*w**3. Let d(l) be the second derivative of r(l). Factor d(j).
-3*j*(21*j + 2)
Let d = -144 + 194. Suppose 83*j**2 - 36*j - 19*j**3 + j**2 + 169*j**5 - 172*j**5 - d*j**3 + 24*j**4 = 0. Calculate j.
0, 1, 2, 3
Let r = 3/23707 - 7752966/6140113. Let z = -15/37 - r. Let -12/7 + z*m**3 + 4*m**2 + 26/7*m = 0. Calculate m.
-3, -2, 1/3
Let p = -32089/77 - -2921/7. Factor p*d**2 + 4/11 - 2/11*d**3 + 10/11*d - 2/11*d**4.
-2*(d - 2)*(d + 1)**3/11
Let a(j) be the third derivative of 7*j**6/80 - 11*j**5/8 + 13*j**4/2 + 4*j**3 + 15*j**2 - 59*j. Factor a(m).
3*(m - 4)**2*(7*m + 1)/2
Let y be (56/294)/((-2)/(-3)). Let a(s) = 2*s**2 - 24*s + 24. Let v be a(11). Factor -2/7*n**v + 0 + 0*n - y*n**3.
-2*n**2*(n + 1)/7
Let q(l) be the first derivative of -l - 16 - 1/17*l**3 - 1/170*l**5 - 1/17*l**2 - 1/34*l**4. Let g(b) be the first derivative of q(b). Let g(w) = 0. What is w?
-1
Determine i so that -327*i**4 + 556*i**5 - 4374 - 1383*i**2 - 1663*i**5 + 4521*i**3 + 552*i**5 - 10611*i + 561*i**5 = 0.
-1, -1/2, 2, 27
Let t(h) be the third derivative of h**7/1050 - 7*h**6/200 + 2*h**5/5 - 5*h**4/6 - 4*h**2 - 1. Factor t(b).
b*(b - 10)**2*(b - 1)/5
Let b(x) = -3*x + 72. Let d be b(15). Factor d*z - 22*z**2 + 9*z - 2*z**4 - 7*z**3 - z**3 + 28*z**2.
-2*z*(z - 2)*(z + 3)**2
Let x(p) = 8*p**4 - p**3 - 47*p**2. Let c(r) = -r**4 - 2*r**3 - r**2. Let a(i) = 7*c(i) + x(i). Factor a(u).
u**2*(u - 18)*(u + 3)
Let s = -3/251 + 2023/1255. Let m(a) be the first derivative of -s*a**5 - 8/3*a - 6*a**2 - 14/3*a**4 - 64/9*a**3 - 23 - 2/9*a**6. Solve m(c) = 0 for c.
-2, -1
Factor 12*b + 11*b**3 - 47/2*b**2 + 0 + 1/2*b**4.
b*(b - 1)**2*(b + 24)/2
Suppose 5*s + z - 20 = 0, -3*s - 4*z + 39 = 10. Let d = 30 + s. Determine u, given that 19*u**2 + 3*u**3 - 4*u**2 + d*u + 15 + 6*u**2 = 0.
-5, -1
Let t = -140/1067 - -28722/7469. Factor -2/7*x + t + 2/7*x**3 - 26/7*x**2.
2*(x - 13)*(x - 1)*(x + 1)/7
Let 152/5*r - 438/5 - 2/5*r**2 = 0. What is r?
3, 73
Suppose 0 + 0*z - 24/25*z**2 + 2/25*z**3 - 2/25*z**5 + 24/25*z**4 = 0. What is z?
-1, 0, 1, 12
Let h(y) = 2*y**5 + 26*y**4 + 22*y**3 - 2*y**2. Let m(b) = -4*b**5 - 49*b**4 - 42*b**3 + 3*b**2. Let x(g) = -11*h(g) - 6*m(g). Factor x(f).
2*f**2*(f + 1)**2*(f + 2)
Let k(h) be the second derivative of 4*h**2 + 1/36*h**4 - h - 5/9*h**3 + 0. Factor k(w).
(w - 6)*(w - 4)/3
Let w(z) be the second derivative of -z**4/12 - 97*z**3/6 - 48*z**2 - 10201*z. Factor w(u).
-(u + 1)*(u + 96)
Let t(p) be the third derivative of p**7/840 + p**6/1080 + 23*p**3/3 - 3*p**2. Let r(g) be the first derivative of t(g). Factor r(j).
j**2*(3*j + 1)/3
Suppose 75*r + 151*r = -104*r + 990. Solve 1/4*p**5 + 5/4*p**r - p**4 + 0*p + 0 - 1/2*p**2 = 0 for p.
0, 1, 2
Let r(n) be the first derivative of 16*n - 99 + 4/3*n**3 - 10*n**2. Factor r(m).
4*(m - 4)*(m - 1)
Let y be 12*2/3*(5763/(-340) + 17). Solve -4/5*u**4 + 0*u + 4/5*u**2 + 2/5*u**3 - y*u**5 + 0 = 0 for u.
-2, -1, 0, 1
Let a(f) be the first derivative of -f**6/216 - f**5/18 - 5*f**4/18 - f**3 + f**2 - 90. Let y(i) be the third derivative of a(i). Factor y(b).
-5*(b + 2)**2/3
Let v(y) be the third derivative of -y**5/20 + 49*y**4/8 - 272*y**3 + 496*y**2. Solve v(a) = 0.
17, 32
Factor 3/5*v**4 + 72/5 + 36/5*v**3 + 27*v**2 + 174/5*v.
3*(v + 1)**2*(v + 4)*(v + 6)/5
Let t be ((-21)/(-18) - 2)/((-100)/(-10) - (-16415)/(-1617)). Factor -1/2*s**3 + 6*s**2 - t*s + 0.
-s*(s - 11)*(s - 1)/2
Suppose -113 = -21*z - 71. Factor -3*x**2 + 80 + 16*x**2 + 4*x**3 - 9*x**z - 64*x.
4*(x - 2)**2*(x + 5)
Let z be 882/1176*(-16)/(-6). Let n(j) be the second derivative of 27/26*j**4 + 0 + 4/13*j**z + 17*j + 12/13*j**3. Factor n(a).
2*(9*a + 2)**2/13
Let v be (-1058)/6877*(-26)/228. Let j(y) be the third derivative of 0*y - 1/570*y**5 + 6*y**2 - 1/19*y**3 + v*y**4 + 0. Factor j(d).
-2*(d - 3)*(d - 1)/19
Let w = -849 + 902. Suppose -w = 18*p - 53. Factor 1/5*f**2 - 1/5*f + p.
f*(f - 1)/5
Let r(x) be the third derivative of -x**6/40 + 39*x**5/50 + 54*x**4/5 + 16*x**3 + x**2 + 60*x. Let r(o) = 0. What is o?
-4, -2/5, 20
Let j(h) be the third derivative of -1/100*h**6 + 9/50*h**5 + 0 + 54/5*h**3 + 0*h + 9/4*h**4 + 43*h**2 - 1/525*h**7. Let j(a) = 0. Calculate a.
-3, 6
Suppose -2 = -i + 2, -780 = 4*j + 5*i. Let c be (-1*6/8)/(30/j). Solve 0*t**2 + 0 + 0*t**4 - 2/7*t**3 + 1/7*t**c + 1/7*t = 0 for t.
-1, 0, 1
Suppose w = 3*a + 2*a - 423, -263 = -3*a - 4*w. Factor -14*g**3 - 30 + 72*g**3 - 5*g**4 - 85*g**2 - 23*g**3 + a*g.
-5*(g - 3)*(g - 2)*(g - 1)**2
Let o(h) be the first derivative of -h**5/5 + h**4 - 4*h**3/3 + 44*h - 48. Let d(u) be the first derivative of o(u). Factor d(w).
-4*w*(w - 2)*(w - 1)
Let c(g) be the third derivative of 0*g**3 + 2/45*g**5 + 4/135*g**7 + 0*g - 13/180*g**6 - 1/108*g**4 - g**2 - 24. Solve c(f) = 0 for f.
0, 1/7, 1/4, 1
Let g(m) be the third derivative of -5*m**8/336 + m**7/14 + 7*m**6/24 - 11*m**5/12 - 5*m**4/4 + 20*m**3/3 + 273*m**2 + 2*m. Determine x, given that g(x) = 0.
-2, -1, 1, 4
Let g = -2520 - -2518. Let p be 31 + -13 - 1/(g/(-3)). Factor 0 + 9*j**4 + p*j**3 - 3/2*j + 6*j**2.
3*j*(j + 1)**2*(6*j - 1)/2
Let l(y) = 228685*y - 228692*y + 33 + 3*y**3 - 11*y**2 - 4*y**3. Let j be l(-10). Factor 1/5*x**j - x**2 + 7/5*x - 3/5.
(x - 3)*(x - 1)**2/5
Let b(h) = -8*h - 5*h**3 + 6 + 3*h**3 + h**2 + 5*h**3. Suppose -2281 + 2271 = 10*v. Let f(l) = l - 1. Let s(t) = v*b(t) - 6*f(t). Suppose s(x) = 0. Calculate x.
-1, 0, 2/3
Let 395/3*j**2 - 166*j + 200/3 - 1/3*j**4 - 32*j**3 = 0. What is j?
-100, 1, 2
Suppose -492*v + 493*v - 656 = 0. Let m = v + -654. Suppose 0 + 38/3*x**4 + 2/3*x**m + 14/3*x**5 + 10*x**3 - 4/3*x = 0.