2/5*i**a.
2*i*(i - 1)*(i + 1)/5
Let v(c) be the third derivative of c**8/2184 - 22*c**7/273 + 70*c**6/13 - 6125*c**5/39 + 214375*c**4/156 - c**2 + 28*c - 1. Determine h, given that v(h) = 0.
0, 5, 35
Let d(z) be the first derivative of z**6/4 + 81*z**5/10 - 171*z**4/8 + 29*z**3/2 - 7766. Factor d(n).
3*n**2*(n - 1)**2*(n + 29)/2
Let d(v) be the first derivative of 5*v**3/12 - 111*v**2/4 + 22*v + 1764. Factor d(w).
(w - 44)*(5*w - 2)/4
Let t be 7/(((-1652)/(-2360))/(6/(-8) - (-115)/92)). Suppose 1/3*s**2 + 50/3 - t*s = 0. Calculate s.
5, 10
Let u be -1 - (-5)/((-30)/(-108)). Determine m so that -39*m + m**2 + u*m - 3*m**2 + 24 = 0.
-12, 1
Let m(l) be the first derivative of -211 - 4*l**3 + 7*l**4 - 38*l**2 + 56*l + 4/5*l**5. Factor m(z).
4*(z - 1)**2*(z + 2)*(z + 7)
Let z(i) be the first derivative of i**6/90 + i**5/3 + 25*i**4/6 - 8*i**3/3 - 65. Let x(f) be the third derivative of z(f). Factor x(s).
4*(s + 5)**2
Suppose -4*u - 3*i = 13 - 24, 0 = 5*u - 5*i - 5. Determine j, given that -4*j**u + 3*j**2 - 142 - 143 + 10*j + 269 = 0.
2, 8
Find u, given that 0 + 0*u - 28/3*u**2 + u**3 + 1/3*u**4 = 0.
-7, 0, 4
Factor 3379*j - 3619*j + 0*j**2 - 235 - 5*j**2.
-5*(j + 1)*(j + 47)
Let z = -130 - -135. What is q in -83 + 15 - 47 - z*q**2 - 106*q + 226*q = 0?
1, 23
Let p = 821960 - 821960. Solve 2/3*z**3 - 10/3*z**2 + p + 8/3*z = 0.
0, 1, 4
Factor -144/7*o**2 + 24*o + 0 + 6/7*o**4 + 18/7*o**3.
6*o*(o - 2)**2*(o + 7)/7
Determine b so that -21313*b - 31*b**2 - 8*b**3 + 21275*b - 15*b**2 = 0.
-19/4, -1, 0
Suppose 10*a - 5*a + 40 = 5*n, -26 = 4*a - n. Let w be 54/(-9)*a/66. Let 5/11*x + 1/11*x**5 - w*x**3 - 1/11*x**4 - 2/11*x**2 + 3/11 = 0. Calculate x.
-1, 1, 3
Let l(k) be the second derivative of 0*k**3 - 1/6*k**6 + 0*k**2 - 3/2*k**5 + k - 6 - 15/4*k**4. Determine q so that l(q) = 0.
-3, 0
Suppose -u = u - 4*x, -10 = -5*u + 5*x. Let s be (3/4*6/(-9))/(185/(-592)). Factor 0 + 4/5*v**u + s*v**2 + 0*v - 12/5*v**3.
4*v**2*(v - 2)*(v - 1)/5
Let n(q) = -11369*q + 136430. Let t be n(12). Let -22/9*h + h**t + 8/9 = 0. What is h?
4/9, 2
Suppose -5*h + 2*k + 8 + 9 = 0, 1 = h + 2*k. Suppose -2*m = 3*n - 20, 0 = -3*n - 918*m + 913*m + 41. Factor 1/4*w**n - 5/8*w - 3/4 + 1/8*w**h.
(w - 2)*(w + 1)*(w + 3)/8
Let n(u) = -5*u**3 + 515*u**2 - 14440*u + 137176. Let f(p) = 10*p**3 - 1020*p**2 + 28880*p - 274353. Let y(g) = -4*f(g) - 7*n(g). Factor y(h).
-5*(h - 38)**2*(h - 19)
Let v be (110/(-396))/(10/(-54)). What is n in -21/2*n**2 + v*n**4 + 6*n + 3*n**3 + 0 = 0?
-4, 0, 1
Let o = -27023 - -135131/5. Let v(t) be the first derivative of 4 - 14*t**2 - o*t**5 - 13*t**4 - 20*t**3 - 4*t. Solve v(y) = 0 for y.
-1, -1/4
Solve -192*k + 36*k**3 - 8*k**2 + 13*k**4 - 54*k**4 + 19*k**4 + 18*k**4 = 0 for k.
-2, 0, 3, 8
Let c(x) = -2*x + 45. Let a be c(20). Suppose a*o - 6 = 4. Solve -8*b**3 - 3*b**o - 3*b**4 - 4*b**5 + b**2 - 4*b**4 - 3*b**4 = 0.
-1, -1/2, 0
Let s(q) be the second derivative of -q**5/70 - q**4/6 - 11*q**3/21 - 5*q**2/7 - q - 3081. What is v in s(v) = 0?
-5, -1
Let q(i) be the third derivative of -i**6/200 + 21*i**5/10 - 11433*i**4/40 + 21218*i**3/5 + 232*i**2 + 10*i. Factor q(b).
-3*(b - 103)**2*(b - 4)/5
Let f = -10141 - -10141. Let z(n) be the third derivative of 1/42*n**4 - 1/210*n**5 + 0 + 8/21*n**3 + f*n - 11*n**2. Factor z(s).
-2*(s - 4)*(s + 2)/7
Let s(f) be the first derivative of f**3/3 - 6*f**2 - 7*f + 66. Let n(p) = 2*p - 1. Let q(v) = -2*n(v) - s(v). Find i such that q(i) = 0.
-1, 9
Solve 8023 - 2*u**3 + 3*u**3 + 134*u**2 - 8023 = 0.
-134, 0
Suppose 5*t = 2*s + 18, 5*t + 4*s - 699 + 675 = 0. Let d(f) be the first derivative of 20*f**2 + 75/2*f**t - 60*f**3 - 42 + 0*f - 7*f**5. Solve d(j) = 0.
0, 2/7, 2
Let t be (-6)/(-27)*-1*-9. Factor -134*c**t + 70 + 69*c**2 - 45*c + 70*c**2.
5*(c - 7)*(c - 2)
Let p(u) be the first derivative of u**6/2 - 15*u**4/4 + 6*u**2 - 1029. Let p(w) = 0. What is w?
-2, -1, 0, 1, 2
Let r be 813/1809 + 124/(-279). Let u = 415/2613 - r. Factor -u*y**3 - 2/13*y**2 - 6/13 + 10/13*y.
-2*(y - 1)**2*(y + 3)/13
Let d = 1804455/7 - 257779. Find b such that 78/7*b - d*b**3 - 144/7 - 4/7*b**2 = 0.
-8, 3
Let v(z) = z**4 - 2*z**3 - z**2. Let y(s) = 4*s + 20*s**2 - 103*s**4 - 92*s**4 + 2*s**3 + 181*s**4. Let m(a) = 6*v(a) + y(a). Suppose m(w) = 0. What is w?
-2, -1/4, 0, 1
Let a = -436 - -438. Let q be -4 - (-7 + -2) - 9/a. Factor -500 - q*r**3 - 15*r**2 - 150*r.
-(r + 10)**3/2
Let c(y) = -2*y**2 - 31*y + 315. Let j be c(7). Let p(s) be the second derivative of 0*s**3 + 1/12*s**5 + j + 0*s**4 + 7*s + 0*s**2. Factor p(r).
5*r**3/3
Factor -10*q**2 + 0*q**5 + 155*q**4 - 145 - 295*q - 12602*q**3 + 12892*q**3 + 5*q**5.
5*(q - 1)*(q + 1)**3*(q + 29)
Let n(v) = -20*v**2 - 6*v. Let b(x) = -7*x**2 - 2*x. Let c be 16/(-6)*((-116)/16 + 2). Let p(k) = c*b(k) - 5*n(k). Factor p(m).
2*m*(m + 1)
Factor 5/2*u**2 - 145/2*u + 70.
5*(u - 28)*(u - 1)/2
Let l(s) = -35*s - 63. Let o be l(-2). Let x(r) be the first derivative of -o - r**4 + 14/45*r**5 - 1/27*r**6 + 0*r + 40/27*r**3 - 8/9*r**2. Factor x(g).
-2*g*(g - 2)**3*(g - 1)/9
Factor -135/2*z**2 - 5/2*z**3 - 145/2 + 285/2*z.
-5*(z - 1)**2*(z + 29)/2
Suppose 2*c - 462 = -9*c. Let a be (-9)/(-6) - 15/c. Solve 4/7*d**3 + 4/7*d**5 + a*d**4 + 0*d + 0 + 0*d**2 = 0 for d.
-1, 0
Let s(h) be the third derivative of 2*h**6/315 + h**5/70 + 65*h**3/6 + 43*h**2. Let o(f) be the first derivative of s(f). Solve o(n) = 0 for n.
-3/4, 0
Let c(v) = 3*v**3 + 25*v**2 - 112*v + 76. Let b(a) = -35*a**3 - 300*a**2 + 1345*a - 910. Let r(m) = 2*b(m) + 25*c(m). Factor r(f).
5*(f - 2)*(f - 1)*(f + 8)
Let w(q) be the third derivative of 0 - 11/270*q**5 + 46*q**2 - 5/108*q**4 - 1/945*q**7 + 0*q**3 - 7/540*q**6 + 4*q. Factor w(j).
-2*j*(j + 1)**2*(j + 5)/9
Let u(w) be the third derivative of w**8/112 + 24*w**7/35 - 99*w**6/40 + 5*w**5/2 + 270*w**2 + 2. What is d in u(d) = 0?
-50, 0, 1
Let t(d) be the second derivative of -d**6/105 + 31*d**5/70 - 577*d. Factor t(a).
-2*a**3*(a - 31)/7
Let i(b) be the first derivative of 2*b**3/3 + 69*b**2 + 396*b - 583. Factor i(k).
2*(k + 3)*(k + 66)
Factor -2/5*f**2 - 3174/5*f - 3172/5.
-2*(f + 1)*(f + 1586)/5
Let r(u) be the second derivative of u**6/30 - 123*u**5/20 - 94*u**4/3 - 42*u**3 + 1791*u. Solve r(l) = 0 for l.
-2, -1, 0, 126
Let t(q) be the second derivative of q**7/21 + 3*q**6/5 - 3*q**5/2 - 325*q**4/6 - 250*q**3 + 4151*q. Factor t(h).
2*h*(h - 6)*(h + 5)**3
Let p(q) = 2*q - 28. Let x be p(0). Let b = -26 - x. Let -7*n**b + n**2 - 2*n**4 - 3*n - 6*n**3 - n + 2*n = 0. What is n?
-1, 0
Let u(k) be the first derivative of k**5/20 + k**4/2 + 2*k**3 - 5*k**2/2 + 5*k + 31. Let x(t) be the second derivative of u(t). Factor x(i).
3*(i + 2)**2
Let g(q) be the third derivative of -q**8/112 + 183*q**7/35 + q**6/40 - 183*q**5/10 + 4159*q**2. Determine b so that g(b) = 0.
-1, 0, 1, 366
Let h = -284225 - -284225. Factor 4/7*p**3 - 2/7 + h*p**2 + 2/7*p**4 - 4/7*p.
2*(p - 1)*(p + 1)**3/7
Suppose 29*o - 4*t = 24*o, 4*t = 0. Suppose 5*g - 4*k - 36 = o, -29*g + k = -30*g. Factor 1/3*z**g + 0 + 0*z - 1/3*z**3 + 0*z**2.
z**3*(z - 1)/3
Suppose 0 - 2/9*d**2 - 868/3*d = 0. What is d?
-1302, 0
Suppose 27 = 242*a - 240*a - 3*m, 5*a + 5*m + 20 = 0. Factor 2020/3*y**a - 1600/3*y - 560/3*y**4 - 256/3 + 49/3*y**5 - 1840/3*y**2.
(y - 4)**3*(7*y + 2)**2/3
Let z(m) be the first derivative of -m**5/20 - 11*m**4/8 + 6*m**3 + m**2/2 + 5*m + 13. Let j(o) be the second derivative of z(o). Suppose j(y) = 0. What is y?
-12, 1
Let g(a) be the second derivative of -a**5/4 + 61*a**4/8 - 9*a**3/2 - 189*a - 9. Factor g(f).
-f*(f - 18)*(10*f - 3)/2
Let y(z) be the first derivative of -66/5*z**5 + 26 - 363/2*z**4 - 1/3*z**6 - 2662/3*z**3 + 0*z + 0*z**2. Find s, given that y(s) = 0.
-11, 0
Let k = 583/5 - 195863/1680. Let w(t) be the third derivative of 0*t**6 - 1/3*t**5 + 0*t**4 + 9*t**2 + 0 + 0*t**3 + k*t**8 + 1/14*t**7 + 0*t. Solve w(o) = 0.
-2, 0, 1
Let h(a) = -a**2 - 20*a - 23. Let y be h(-19). Let q be -1 + 1 + y + (-42)/(-10). What is v in 3/5*v**2 - q + 2/5*v = 0?
-1, 1/3
Let w(l) be the second derivative of -l**6/150 + l**5/25 + l**4/3 + 34*l**2 - 19*l. Let y(o) be the first derivative of w(o). Factor y(f).
-4*f*(f - 5)*(f + 2)/5
Let v be 34/(-153)*264/(-28). Let x = -16/21 + v. Factor 2*i**4 - 2*i - 2/3 + x*i**3 + 2/3*i**5 - 4/3*i*