-2*(v + 1)**4/3
Let j(z) be the second derivative of -z**4/42 - z**3/7 - 2*z**2/7 - 3*z. Let j(m) = 0. What is m?
-2, -1
Factor -2*z**4 + 5*z**5 + 2*z**5 + 2*z**2 - 7*z**5 + z - z**5.
-z*(z - 1)*(z + 1)**3
Let y be -6*8/84 - (-66)/91. Suppose -y*w + 0*w**2 + 2/13*w**3 + 0 = 0. What is w?
-1, 0, 1
Let v(b) be the second derivative of b**8/168 + b**7/35 + b**6/20 + b**5/30 + 2*b**2 + 4*b. Let y(o) be the first derivative of v(o). Solve y(p) = 0 for p.
-1, 0
Let l(q) be the first derivative of 0*q + 2/15*q**5 + 1/12*q**4 - 1/18*q**6 - 2 - 2/9*q**3 + 0*q**2. What is r in l(r) = 0?
-1, 0, 1, 2
Let d be 2/(((-39)/65)/((-9)/10)). Let x(k) be the first derivative of 3 - 2/21*k**d + 3/7*k**2 - 4/7*k. Factor x(z).
-2*(z - 2)*(z - 1)/7
Let r(v) be the second derivative of 3*v**5/160 - v**4/8 + 5*v**3/16 - 3*v**2/8 + 21*v. Suppose r(t) = 0. What is t?
1, 2
Suppose -5*d + 5*o - 10 = 0, -4*d + 2*d + o + 1 = 0. Determine q so that 3*q**3 - 20*q**3 - 4*q**4 - 3*q**d - 20*q - 33*q**2 - 4 = 0.
-2, -1/2
Let c(d) be the second derivative of -d**4/32 - d**3/4 - 3*d**2/4 + 15*d. What is j in c(j) = 0?
-2
Let b = -15/4 + 53/12. Factor 0 + 1/3*w**3 + b*w**2 + 0*w.
w**2*(w + 2)/3
Let d(f) be the first derivative of -3/10*f**2 + 3/5*f**5 - 9/20*f**4 + 0*f + 2/5*f**6 - 2 - f**3. Find h such that d(h) = 0.
-1, -1/4, 0, 1
Let f(b) be the second derivative of 0 + 11/18*b**4 + 7/45*b**6 - 2/9*b**3 - 3*b - 8/15*b**5 + 0*b**2. Factor f(r).
2*r*(r - 1)**2*(7*r - 2)/3
Suppose 3*u**2 + 3*u**4 - 3*u**3 - 6*u**2 - 3*u**3 + 3*u**3 + 3*u**5 = 0. Calculate u.
-1, 0, 1
Suppose -2*w - w = m + 6, 0 = 3*m - w - 12. Let k(r) be the second derivative of -r - 1/15*r**m + 0*r**2 + 1/50*r**5 + 0 + 0*r**4. Factor k(h).
2*h*(h - 1)*(h + 1)/5
Let t(g) = g**2 + g - 1. Let s(n) = -16*n**2 + 28*n - 88. Let f(i) = s(i) + 12*t(i). Determine h, given that f(h) = 0.
5
Let p(s) be the second derivative of 3/10*s**5 + 4*s - 1/2*s**4 + 3/10*s**6 + 0 + 1/14*s**7 - 3/2*s**3 - 3/2*s**2. Factor p(t).
3*(t - 1)*(t + 1)**4
Let n(v) be the third derivative of 1/24*v**4 + 3*v**2 - 1/60*v**5 + 0 + 0*v**3 + 0*v. Factor n(q).
-q*(q - 1)
Let x be (-8)/(-8) - -1*3. Suppose -5*l + 3*j + 0 - 12 = 0, -j = -3*l - x. Factor 1/4*m**5 + l + 1/4*m**2 - 1/4*m**3 + 0*m - 1/4*m**4.
m**2*(m - 1)**2*(m + 1)/4
Let o(m) be the first derivative of m**5/5 - 13*m**4/20 + 4*m**3/15 + 2*m**2/5 - 12. Find f, given that o(f) = 0.
-2/5, 0, 1, 2
Let i be (-144)/(-66) + -2 + (-20)/(-11). Find j such that 1/2*j**5 - 1/2*j**4 + 0 + 0*j + 0*j**i + 0*j**3 = 0.
0, 1
Factor 0 - 33/7*g**2 + 6/7*g.
-3*g*(11*g - 2)/7
Let q(v) be the second derivative of 3*v**5/20 + v**4/4 - 4*v. Factor q(b).
3*b**2*(b + 1)
Let v(g) = -5*g**2 + 4*g - 4. Let h(i) = -6*i**2 + 4*i - 4. Suppose 0 = o - 3*o - 24. Let j = o - -8. Let z(b) = j*h(b) + 5*v(b). Factor z(y).
-(y - 2)**2
Let b(d) be the third derivative of 0*d + 5*d**2 - 1/15*d**5 + 0 + 1/12*d**4 + 1/60*d**6 + 0*d**3. What is k in b(k) = 0?
0, 1
Let h(b) = -b**3 - 3*b**2 - 4*b - 2. Let j be h(-2). Let s be (-2)/j*(-12)/20. Factor 3/5*q**4 + 6/5 - 9/5*q**2 - s*q + 3/5*q**3.
3*(q - 1)**2*(q + 1)*(q + 2)/5
Let h(v) = 3*v**5 - 2*v**4 - 3*v**3 - 2*v**2 + 4. Let p(t) = t**5 - t**3 - t**2 + 1. Let o(l) = -h(l) + 4*p(l). Factor o(r).
r**2*(r - 1)*(r + 1)*(r + 2)
Let m(b) = 136*b + 277. Let o be m(-2). Factor 0 + 0*l**3 - 2/9*l**o + 8/9*l**2 - 2/3*l**4 + 0*l.
-2*l**2*(l - 1)*(l + 2)**2/9
Let p be (-3)/(-6)*(4 + 0). Factor -6*y + 3*y**3 - 3*y**p - y**3 + 5*y**3 - 4*y**3.
3*y*(y - 2)*(y + 1)
Let i = -1 - -2. Let k be 1/i*(1 - -1). Factor -k*t + 9/2*t**4 - 11/2*t**2 + 3*t**3 + 2.
(t + 1)**2*(3*t - 2)**2/2
Let r be (-4)/(-12)*3/4. Factor -1 + m - r*m**2.
-(m - 2)**2/4
Let q(f) be the first derivative of -f**5/5 - 3*f**4/2 - 13*f**3/3 - 6*f**2 - 4*f + 12. Factor q(s).
-(s + 1)**2*(s + 2)**2
Let h(d) be the third derivative of 1/120*d**4 + 0*d + 0*d**3 + 1/100*d**6 + 1/1680*d**8 - d**2 + 0 - 1/75*d**5 - 2/525*d**7. Solve h(b) = 0 for b.
0, 1
Let -60*h**3 + 6 + 26 - 30*h**2 - 2*h**4 + 16*h + 44*h**3 = 0. What is h?
-4, -1, 1
Let v(k) = -2*k - 6. Let q be v(-5). What is g in 3*g**q - 3*g**3 + 0*g**4 + 15*g**2 - 6*g - 9*g**3 = 0?
0, 1, 2
Let j(m) be the first derivative of 1 + 0*m**4 + 0*m**3 + 0*m - 2/5*m**5 + 0*m**2. Factor j(n).
-2*n**4
Let t be (-17)/(-36) + 4/(-18). Let v be 30/56 + (-8)/28. Factor -v + 1/4*c**2 - 1/4*c**3 + t*c.
-(c - 1)**2*(c + 1)/4
Let g = -67/55 - -7/5. Determine k, given that -18/11 - 12/11*k - g*k**2 = 0.
-3
Let i(y) be the third derivative of -1/20*y**5 + 1/9*y**3 + 0*y + 7/72*y**4 + 0 + 2*y**2. Factor i(b).
-(b - 1)*(9*b + 2)/3
Solve 5*c**4 + 16*c**3 + 19*c**3 + 2*c - 43*c**3 + c**2 = 0.
-2/5, 0, 1
Let n be 4/6 + (-12)/(-9). Solve n*s - 1 - s - s**2 + 0*s - 3*s = 0 for s.
-1
Let h = 61/10 - 329/54. Let l(m) be the third derivative of 1/945*m**7 + h*m**6 + 1/27*m**3 + 0*m + 0 + 1/27*m**4 + 1/45*m**5 + m**2. Factor l(v).
2*(v + 1)**4/9
Let s = 100/153 + 2/153. Let p(k) be the first derivative of 1/2*k**4 - 2 - s*k**3 + 0*k + 0*k**2. Factor p(v).
2*v**2*(v - 1)
Let h(o) be the first derivative of -o**5/20 + 4*o**2 - 6. Let g(p) be the second derivative of h(p). Factor g(l).
-3*l**2
Let j(c) be the second derivative of c**5/5 - c**4/12 - 2*c**3/3 + c**2/2 + 11*c. Factor j(a).
(a - 1)*(a + 1)*(4*a - 1)
Let u = 1 + 1. Suppose 4*j**3 + 3*j**2 + 2*j - 6*j**3 - 3*j**u = 0. Calculate j.
-1, 0, 1
Let w(o) be the third derivative of -o**7/240 + 3*o**6/320 - o**5/240 + 3*o**2. Factor w(l).
-l**2*(l - 1)*(7*l - 2)/8
Let i be (13 - 5)/(-40)*10/(-4). What is c in -5/2*c + 24*c**3 - 4*c**2 + i = 0?
-1/3, 1/4
Let m(y) = 9*y**2 - 3*y + 2. Let g be m(1). Factor 3*l + l**3 - 3*l**2 - g*l**2 - 25*l**3 + 5*l**2.
-3*l*(2*l + 1)*(4*l - 1)
Solve 4*z**2 + 26*z + 0*z**2 - 9 - 4 - 77*z = 0.
-1/4, 13
Let x = 66 + -31. Let w = -33 + x. Factor -243/5*f**3 - 12/5 - 24*f - 351/5*f**w.
-3*(f + 1)*(9*f + 2)**2/5
Let z(w) be the first derivative of -w**4/6 + 3*w - 1. Let f(n) be the first derivative of z(n). Factor f(v).
-2*v**2
Factor -2/9 - 2/3*q - 2/3*q**2 - 2/9*q**3.
-2*(q + 1)**3/9
Let b(z) be the third derivative of 1/40*z**6 + 6*z**2 - 27/2*z**3 + 0 + 0*z - 9/20*z**5 + 27/8*z**4. Find t such that b(t) = 0.
3
Find k, given that -9/5*k - 1/5*k**2 - 2/5 + 3/5*k**4 - 4/5*k**5 + 13/5*k**3 = 0.
-1, -1/4, 1, 2
Let r be (-4)/6*(-19)/38. Factor 0 - 1/3*p**2 - r*p.
-p*(p + 1)/3
Suppose -4 = 3*c + c, -2*c = -3*s + 5. Let z = 1 + s. Suppose -5*g**z + 3*g**2 + g**2 + 2*g**2 = 0. Calculate g.
0
Let y(a) = a**3 + 5*a**2 + 4*a + 3. Let t be y(-4). Suppose -3*o = 5*q - 20, -q - 16 = t*o - 5*q. Factor 4*s**2 - 1 - 2*s + o - 5*s**2.
-(s + 1)**2
Let h(f) = 5*f**3 + 2*f**2 - 5*f - 8. Let b(u) = -60*u**3 - 25*u**2 + 60*u + 95. Let o(n) = 3*b(n) + 35*h(n). Factor o(p).
-5*(p - 1)*(p + 1)**2
Let a(l) be the third derivative of -l**5/20 + 13*l**4/4 - 169*l**3/2 + 33*l**2. Suppose a(h) = 0. What is h?
13
Let c(a) = 1. Let i(y) = y**2 - 6*y - 6. Let b be i(7). Let l(s) = 2*s**2 - 2*s. Let z(v) = b*l(v) - 4*c(v). Factor z(o).
2*(o - 2)*(o + 1)
Determine z so that 91*z - 5*z**2 - 88*z + 4*z**2 - 2 = 0.
1, 2
Let h(n) be the third derivative of n**5/510 - 2*n**4/17 + 48*n**3/17 - 30*n**2. Factor h(v).
2*(v - 12)**2/17
Suppose 25 = -7*g + 6*g - 5*k, g + k + 5 = 0. Find h such that 4/3*h + g + 2/3*h**2 = 0.
-2, 0
Let x be -4 + 9/(-24) + 35/8. Let p(d) = d**3 - 8*d**2 + 3. Let g be p(8). Solve 1/3*f + x + 2/3*f**2 + 1/3*f**g = 0.
-1, 0
Let a = 15 + -11. Suppose a = 3*p - p. Factor 1 - 2*y**p + 1 + 0*y**2.
-2*(y - 1)*(y + 1)
Let s be ((-84)/21)/((-4)/30). Factor -s*x**4 - 8/3*x**2 + 0*x + 0 - 16*x**3 - 50/3*x**5.
-2*x**2*(x + 1)*(5*x + 2)**2/3
Let v(o) = o**5 - 8*o**4 + 17*o**3 - o**2 + 9*o + 9. Let d(s) = 2*s**4 - 4*s**3 - 2*s - 2. Let q(p) = 18*d(p) + 4*v(p). Factor q(x).
4*x**2*(x - 1)*(x + 1)**2
Let x = 55 + -55. Factor 2/9*v**5 + 0*v**4 + 0 + 0*v**2 - 2/9*v**3 + x*v.
2*v**3*(v - 1)*(v + 1)/9
Let v(g) be the third derivative of -g**6/900 - g**5/300 - g**3/6 + 2*g**2. Let h(o) be the first derivative of v(o). Find z, given that h(z) = 0.
-1, 0
Let q = -31 - -37. Let p(x) be the second derivative of -3*x + 11/20*x**5 - 1/6*x**4 + 0*x**3 + 1/6*x**7 + 0*x**2 - 8/15*x**q + 0. Factor p(y).
y**2*(y - 1)**2*(7*y - 2)
Let q be (23/((-644)/(-16)))/(10/7). Factor -q*w