he third derivative of a**7/735 + a**6/630 - 13*a**3/6 + 12*a**2. Let i(g) be the first derivative of n(g). Factor i(h).
4*h**2*(2*h + 1)/7
Let a(y) = -y**3 + 10*y**2 + 26*y - 22. Let z be a(12). Factor -z*f**2 - 4/11*f + 0.
-2*f*(11*f + 2)/11
Let 16/3*v + 4 + v**2 - 1/3*v**3 = 0. Calculate v.
-2, -1, 6
Suppose 257*n - 4*n**3 - 96*n**2 - 5*n**3 - 2048 - 1025*n + 5*n**3 = 0. Calculate n.
-8
Let f = -67 - -69. Factor u**2 - 3*u**f + 8*u + 66 - 56.
-2*(u - 5)*(u + 1)
Find a such that -119/9*a**2 + 0 + 2/3*a**4 + 8/3*a + 139/9*a**3 = 0.
-24, 0, 1/3, 1/2
Suppose -4*z = -2*z - 8. What is l in 7*l**z + 5*l**3 - 2*l**3 + 2*l**3 - 2*l**4 = 0?
-1, 0
Let a(i) be the first derivative of 0*i - 7/10*i**5 - 2*i**2 + 1/4*i**4 + 14/3*i**3 + 5. Suppose a(r) = 0. Calculate r.
-2, 0, 2/7, 2
Let q(d) = d**2 - 35*d + 104. Let k be q(32). Determine r, given that -k*r**2 - 2*r + 0 - 7/2*r**3 = 0.
-2, -2/7, 0
Suppose -4*o + 25 = x, 2*x - 38 = -7*o + 2*o. Suppose -5*v + x = 9. Factor 1/4*f**3 - f**2 + f + v.
f*(f - 2)**2/4
Factor -44/7*a**3 + 0 - 2/7*a**4 - 242/7*a**2 + 0*a.
-2*a**2*(a + 11)**2/7
Factor h - 1/2*h**2 + 3/2.
-(h - 3)*(h + 1)/2
Let u be (-34 - -28)*(6/4 + (-11)/6). Factor 0 + 4/3*f + 2/3*f**5 + 10/3*f**4 + 14/3*f**u + 6*f**3.
2*f*(f + 1)**3*(f + 2)/3
Let p(w) = 5*w**2 - 3 - 5*w**2 - 6*w**2 + 5 + w**3. Let b be p(6). Factor 3*m**3 - b*m**2 + m**3 - m - 7*m**3 + 2*m**3.
-m*(m + 1)**2
Find u, given that 0 + 3*u**4 + 14/3*u**3 + 0*u + 0*u**2 + 1/3*u**5 = 0.
-7, -2, 0
Let k(h) be the first derivative of 2*h**7/105 + h**6/90 - 2*h**5/15 - h**4/6 - 14*h**3/3 + 14. Let q(y) be the third derivative of k(y). Factor q(z).
4*(z - 1)*(z + 1)*(4*z + 1)
Suppose 0 = -3*v + 27*t - 25*t + 13, -3*v + 4*t = -23. Factor -19/2*x + v - 21/2*x**2.
-(x + 1)*(21*x - 2)/2
Let n(s) be the first derivative of s**3/12 - 13*s**2/2 - 287. Factor n(v).
v*(v - 52)/4
Let i(x) be the first derivative of x**4/4 + 4*x**3/3 + x**2/2 - 6*x - 1. Factor i(h).
(h - 1)*(h + 2)*(h + 3)
Let z(u) = -60*u**4 - 4*u**3 + 52*u**2 - 28*u - 40. Let q(m) = 19*m**4 + m**3 - 17*m**2 + 9*m + 13. Let k(a) = -16*q(a) - 5*z(a). Factor k(y).
-4*(y - 2)*(y - 1)*(y + 1)**2
Let j = -77 + 79. Suppose 152 - 3*a**3 - 3*a**2 - 9*a + 2*a**3 - 157 + j*a**3 = 0. What is a?
-1, 5
Suppose -4*k + 7 + 12 = -m, 1 = -2*k - 3*m. Factor -9*h**3 - 8*h**4 + 5*h**2 - 31*h**3 + 79*h**k + 9*h**4.
5*h**2*(4*h - 1)**2
Factor -3/7*l**2 + 1/7*l**4 - 1/7*l + 1/7*l**3 + 2/7.
(l - 1)**2*(l + 1)*(l + 2)/7
Let f be 5/(-3) + (-90)/(-54). Let u(k) be the third derivative of -3*k**2 + 1/240*k**5 - 1/480*k**6 + f*k + 0*k**3 + 0 + 0*k**4. Find q, given that u(q) = 0.
0, 1
Let h(v) be the third derivative of v**8/168 + 23*v**7/315 + 61*v**6/180 + 61*v**5/90 + 2*v**4/9 - 4*v**3/3 - 7*v**2 + 13*v. Let h(p) = 0. What is p?
-3, -2, -1, 1/3
What is g in 86/3*g**2 + 6*g**4 - 31/3*g - 71/3*g**3 - 2/3 = 0?
-1/18, 1, 2
Let a(s) be the third derivative of -s**5/270 - s**4/12 + 52*s**3/27 - 11*s**2 + 11*s. Factor a(m).
-2*(m - 4)*(m + 13)/9
Let q be -4 - (-598)/22 - (-70)/(-14). Factor -40/11*j - q - 2/11*j**2.
-2*(j + 10)**2/11
Let m be 3/(-6)*(0 + 0 + -4). Let s = 8 - 6. What is p in -2*p**2 - p**s + 2*p**m - 2*p**2 = 0?
0
Let l be 32/9 + 536/(-603). Find w, given that 0 - 2/3*w**3 + 0*w**2 + l*w = 0.
-2, 0, 2
Let n be (48/(-882))/((-20)/35). Let x(v) be the third derivative of -1/210*v**5 - n*v**3 + 0 + 0*v + 1/28*v**4 + 12*v**2. Determine g so that x(g) = 0.
1, 2
Factor -666*b + 24*b**3 + 349*b - 44*b**2 + 341*b - 4*b**4.
-4*b*(b - 3)*(b - 2)*(b - 1)
Let m(n) be the second derivative of n**4/30 + 12*n**3/5 + 68*n**2/5 + 696*n. What is q in m(q) = 0?
-34, -2
Suppose 0*j - 2*f + 14 = 3*j, 0 = 4*j + 4*f - 20. Suppose 5*u - 7 = -2*l + 4*u, 4*u = 12. Find x, given that -8/3*x + 0 - 34/3*x**3 + 10/3*x**j + 32/3*x**l = 0.
0, 2/5, 1, 2
Let z(s) be the second derivative of s**5/180 - s**4/36 + s**3/18 - 19*s**2/2 - 10*s. Let a(q) be the first derivative of z(q). Find b such that a(b) = 0.
1
Let -24/5*x + 21/5 + 3/5*x**2 = 0. What is x?
1, 7
Let x be (11/2)/(44/(-28) + 1). Let s = 10 + x. Suppose 0*g - s*g**2 + 0 = 0. What is g?
0
Let u(j) be the second derivative of -j**6/180 - j**5/10 - 3*j**4/4 + 5*j**3/6 + 5*j. Let z(i) be the second derivative of u(i). Factor z(q).
-2*(q + 3)**2
Factor -57/2 - 30*n - 3/2*n**2.
-3*(n + 1)*(n + 19)/2
Let h = 2952 - 2952. Determine c, given that -1/2*c**3 - 1/2*c**2 + c + h = 0.
-2, 0, 1
Let b(f) be the third derivative of 0*f - 36*f**2 + 1/4*f**3 + 9/80*f**5 + 0 - 11/32*f**4. Factor b(z).
3*(z - 1)*(9*z - 2)/4
Suppose -3*f + 2*g - 6 = 0, -16*g + 21*g - 38 = -4*f. Determine b so that -20/3*b**3 + 5/3*b**4 + 0*b**f + 0 + 0*b = 0.
0, 4
Let z(u) be the third derivative of u**8/84 - 8*u**7/105 + u**6/5 - 4*u**5/15 + u**4/6 - 3*u**2 - 17. Factor z(y).
4*y*(y - 1)**4
Suppose -5*x**5 + 118*x**3 + 45*x**2 - 171*x**3 + 108*x**3 - 45*x**4 - 50*x = 0. Calculate x.
-10, -1, 0, 1
Let x be (125/625)/((-16)/(-15)). Let l(u) be the first derivative of x*u**4 - 3/20*u**5 + 0*u - 3/8*u**2 - 14 + 1/4*u**3. Find h, given that l(h) = 0.
-1, 0, 1
Determine c so that 594 - 3690/11*c**2 + 1026*c - 4/11*c**4 - 254/11*c**3 = 0.
-33, -1/2, 3
Let z(j) be the second derivative of j**5/15 - j**4/3 - 14*j**2 - 23*j. Let q(s) be the first derivative of z(s). Factor q(c).
4*c*(c - 2)
Suppose -g = -5*g - 20, 0 = -5*t - 2*g + 30. Suppose 5*p = -t*x + 3*x + 10, -4*x - 4 = 0. Suppose -33/5*z**2 + 4*z**p + 3*z - 2/5 = 0. What is z?
1/4, 2/5, 1
Let x = -1984 + 1987. Let m(c) be the first derivative of 0*c - 1/6*c**2 - 3 + 1/9*c**x. Factor m(a).
a*(a - 1)/3
Let q(v) be the first derivative of v**7/525 - v**5/150 + 3*v**2/2 - 18. Let h(f) be the second derivative of q(f). Factor h(x).
2*x**2*(x - 1)*(x + 1)/5
Suppose -a = 2*a - 12. Factor -260*m + 260*m - a*m**4.
-4*m**4
Factor 2/15*c**5 + 32/5*c - 112/15*c**2 - 6/5*c**4 - 32/15 + 64/15*c**3.
2*(c - 2)**4*(c - 1)/15
Let z(h) be the third derivative of -23*h**5/90 - 71*h**4/108 - 2*h**3/27 - 39*h**2. Factor z(f).
-2*(f + 1)*(69*f + 2)/9
Let b be (-171)/(-27) - (-6)/(-1). Let k(t) be the second derivative of 7*t + 0 + 4/3*t**3 + b*t**4 + 2*t**2. Suppose k(d) = 0. What is d?
-1
Suppose 14*q**2 - 38*q**2 - 3*q**3 - 2*q**4 - 10*q**3 - 3*q**3 = 0. What is q?
-6, -2, 0
Let b(u) be the first derivative of 30 - 3/14*u**2 - 1/7*u**3 + 6/7*u. Let b(v) = 0. What is v?
-2, 1
Suppose -11/8*j**2 + 3/8*j**4 - 3/2*j + 1/8*j**5 - 1/8*j**3 - 1/2 = 0. Calculate j.
-2, -1, 2
Suppose 0 - 30 = -2*v. Let y be (-6)/(-2*12/v) + -2. Factor -y*l**2 + 1/2 + 5/4*l.
-(l - 1)*(7*l + 2)/4
Let b(p) = -6*p**2 - 393*p - 37646. Let o(n) = -5*n**2 - 392*n - 37644. Let h(y) = 4*b(y) - 5*o(y). Determine i, given that h(i) = 0.
-194
Solve -208/5 - 4/5*q**4 + 72/5*q**3 - 292/5*q**2 + 432/5*q = 0 for q.
1, 2, 13
Let f(m) be the second derivative of 0*m**2 + 2*m + 0*m**5 + 0*m**3 + 0 - 1/120*m**6 + 1/48*m**4. Factor f(v).
-v**2*(v - 1)*(v + 1)/4
What is t in -12/17 - 14/17*t**5 - 12/17*t**4 + 28/17*t**3 - 14/17*t + 24/17*t**2 = 0?
-1, -6/7, 1
Suppose 10*t = -838 + 858. Find b such that -3/5*b**t + 6/5*b + 0 = 0.
0, 2
Factor 14/3*u**3 + 40/3*u + 16/3 + 2/3*u**4 + 12*u**2.
2*(u + 1)*(u + 2)**3/3
Suppose 28*h + 25*h = -27*h + 160. Let p be 17 - -2 - (1 - -1). Find g such that -p*g**4 + 23/7*g**h - 4/7 - 7*g**5 + 16/7*g - 67/7*g**3 = 0.
-1, 2/7
Let r(p) = 4*p**2 + 14*p - 14. Let f be r(1). Let h(x) be the third derivative of 0*x + 0*x**3 - x**2 - 1/60*x**6 + 1/10*x**5 + 0 - 1/6*x**f. Factor h(l).
-2*l*(l - 2)*(l - 1)
Let x(h) be the third derivative of -h**7/525 + h**6/100 + 3*h**5/50 + h**4/12 - 2*h**2 + 32. Find i, given that x(i) = 0.
-1, 0, 5
Let v(t) be the third derivative of t**7/42 - t**6/8 - t**5/2 + 5*t**4/3 + 3*t**2 + 64. Factor v(u).
5*u*(u - 4)*(u - 1)*(u + 2)
Suppose -4*r + 306 = -r + 3*m, -183 = -2*r + 5*m. Let h be (4/3)/(22/r). Determine p, given that h*p**3 + 0 - 3/4*p + 3/2*p**2 = 0.
-1/2, 0, 1/4
Let n = 9/20 - -3/20. Suppose 0 = 11*b + 1507 - 1529. Factor n*h**b + 12/5*h + 9/5.
3*(h + 1)*(h + 3)/5
Suppose 2*t - 230 + 24 = -2*i, 2*i = 3*t - 299. Let c = t + -97. Factor -6/7*s**2 - 1/7 + 4/7*s**3 + 4/7*s - 1/7*s**c.
-(s - 1)**4/7
Suppose 2048/3 + 2/3*y**4 - 2816/3*y + 280*y**2 - 74/3*y**3 = 0. What is y?
1, 4, 16
Let v(q) = 3*q - 5. Let z be v(3). 