 12*x**4 - 9*x**3 + 15*x**2 - 15*x - 9. Let v be (-3)/12 - 35/4. Let g(u) = u**5 + u**4 + u + 1. Let t(w) = v*g(w) - q(w). Factor t(b).
-3*b*(b - 1)**3*(b + 2)
Let h(c) be the second derivative of -7*c**7/18 - 112*c**6/45 - 361*c**5/60 - 127*c**4/18 - 38*c**3/9 - 4*c**2/3 - 13*c. Determine f, given that h(f) = 0.
-2, -1, -2/7
Let j be ((-4)/3)/(4/(-102)). Let a be -3*(-4 + j/9). Factor 0*u + 2/3*u**3 + 0 + a*u**2.
2*u**2*(u + 1)/3
Let h(s) be the first derivative of -1/3*s**3 - 5/24*s**4 - 1/20*s**5 - 2 - s**2 + 0*s. Let x(g) be the second derivative of h(g). Factor x(f).
-(f + 1)*(3*f + 2)
Factor -4/3*o**2 - 4/3*o**3 - 2/3 + 2*o**4 + 2*o - 2/3*o**5.
-2*(o - 1)**4*(o + 1)/3
Let t(s) be the second derivative of -2*s**7/105 + s**6/15 - 3*s**5/40 - 2*s**3/3 + s. Let f(q) be the second derivative of t(q). Suppose f(i) = 0. What is i?
0, 3/4
Let q(i) be the first derivative of i**6/60 - i**5/20 + i**3/6 - i**2/4 + i - 1. Let k(p) be the first derivative of q(p). Find n, given that k(n) = 0.
-1, 1
Let h(g) be the first derivative of 2*g**3/27 + 5*g**2/9 + 6. Factor h(o).
2*o*(o + 5)/9
Let j = 27/2 - 13. Let a(k) be the first derivative of 1 + 9/8*k**2 + 7/12*k**3 + j*k. Determine h so that a(h) = 0.
-1, -2/7
Suppose -3*z - 5*z - 4*z = 0. Suppose -2/7*y + 0 + z*y**2 + 2/7*y**3 = 0. Calculate y.
-1, 0, 1
Factor -20*i**4 + i**5 + 4*i**5 + 11*i**3 + 4*i**3.
5*i**3*(i - 3)*(i - 1)
Let p be -8 + 2/(1/1). Let z be p/33 + (-46)/(-11). Find l such that z*l**2 + 2 - 4*l - 6*l**2 + 0*l + 5*l**3 - l = 0.
-1, 2/5, 1
Suppose 4*d = -4*w + 28, -w = -3*d + 14 - 5. Solve -10/3*v**2 - 10*v**5 + 2/3*v**d + 0 + 62/9*v**3 + 4/9*v = 0 for v.
-1, 0, 1/3, 2/5
Let s be (-3 - -4)/(6/30). Factor -13/3*c**3 + 0*c + 0 + 2/3*c**2 - 3*c**s + 20/3*c**4.
-c**2*(c - 1)**2*(9*c - 2)/3
Suppose -9*t - 8 = -11*t. Factor 1/4*i**t - i + 3/4*i**2 - 1 + i**3.
(i - 1)*(i + 1)*(i + 2)**2/4
Let t(d) be the first derivative of d**6/21 + 2*d**5/35 - d**4/7 - 4*d**3/21 + d**2/7 + 2*d/7 + 18. Factor t(q).
2*(q - 1)**2*(q + 1)**3/7
Factor 59*q**2 - 19*q - 54*q**2 + 8*q - 19*q + 25.
5*(q - 5)*(q - 1)
Let g = -4 - 1. Let h(b) = -2*b**4 + 6*b**2. Let a(z) = 3*z**4 - z**3 - 7*z**2. Let p(f) = g*h(f) - 4*a(f). Solve p(q) = 0.
0, 1
Suppose 48 = -3*m - 3*q, -2*q + 7*q = 2*m + 32. Let w be m/(-7) - (-10)/(-35). Factor -1/2*p**w - 1/2 - p.
-(p + 1)**2/2
Find t, given that -8/7 + 18/7*t**2 - 24/7*t + 2*t**3 = 0.
-2, -2/7, 1
Let t(m) be the second derivative of -m**7/98 - m**6/14 - 3*m**5/35 - 8*m. Determine r, given that t(r) = 0.
-4, -1, 0
Let z(w) be the first derivative of -4*w**5/5 - w**4 - 3. Determine s so that z(s) = 0.
-1, 0
Find t such that -2*t**2 - 9 - 14*t**2 + 10*t + 9*t + 5*t = 0.
3/4
Solve -4/7*v + 26/7*v**2 + 0 - 40/7*v**3 = 0 for v.
0, 1/4, 2/5
Let k(j) be the first derivative of 8*j**3 - 7*j**2 + 2*j + 2. Factor k(u).
2*(3*u - 1)*(4*u - 1)
Factor 0*v + 2/19*v**2 - 2/19*v**4 + 0*v**3 + 0.
-2*v**2*(v - 1)*(v + 1)/19
Let p be ((-2)/(-4))/(1/4). Solve 5*r - 4*r**3 + 2 + 0*r + r**2 - 5*r**3 - 7*r**p = 0 for r.
-1, -1/3, 2/3
Determine k so that 0 - 14/17*k**2 + 10/17*k**3 + 4/17*k = 0.
0, 2/5, 1
Suppose 0 = -12*j - 61 + 85. Find s, given that -11/6*s - 3/2*s**j - 1/3 = 0.
-1, -2/9
Suppose 5*j + 0*j - 30 = 0. Factor 27*f**3 + 57*f**4 + 35*f**3 + 12*f**4 + j*f + 21*f**5 + 39*f**2 + 19*f**3.
3*f*(f + 1)**3*(7*f + 2)
Suppose -3*q + 2 = -4. Let w(r) be the first derivative of -2/9*r**3 + 1/6*r**q + 0*r - 2. Find p such that w(p) = 0.
0, 1/2
Suppose -2*n + k = -0*n - 12, 4*n = -4*k. Factor -2*q**4 + 3*q**5 - 14*q + 8*q + 10*q**4 + q**n - 9*q**2 + 3*q**3.
3*q*(q - 1)*(q + 1)**2*(q + 2)
Suppose 0 = -2*x + 5*x - 72. Factor 2*o**5 + 2*o + 16*o**2 + 12*o**4 + x*o**3 + 0*o**4 - 2*o.
2*o**2*(o + 2)**3
Let x(j) = -8*j**2 + 2*j - 11. Let u(l) = 4*l**2 - l + 6. Suppose -5*d - 5*t - 30 = 0, -3*d - 2*t = 8 + 15. Let c(r) = d*u(r) - 6*x(r). Solve c(b) = 0.
0, 1/4
Let j(f) = -f**2 - 6*f - 5. Let t(r) = 4*r**2 + 19*r + 15. Let b(c) = 11*j(c) + 4*t(c). Factor b(z).
5*(z + 1)**2
Suppose -4*k + 3*f - 15 = 0, f - 9 = 4*f. Let b be (-9)/k*2/1. Suppose -2*h**4 + h**2 + 4*h + 0*h**3 - h**3 - b*h + h**4 = 0. Calculate h.
-1, 0, 1
Let u be (-9)/2*(-4)/6. Factor v**3 + v**3 + u*v**2 - v**4 - 3 - 4*v - 1.
-(v - 2)**2*(v + 1)**2
Factor -b**3 + 12*b**3 - 2*b**3 - 12*b - 4*b**4 + 4*b**2 + 3*b**3.
-4*b*(b - 3)*(b - 1)*(b + 1)
Let d(b) = -3*b + 2*b + 2*b - 1 + 0*b. Let p be d(4). Let -t**5 - 10*t**p - 2 - 5*t - 2 + 5 + 10*t**2 + 5*t**4 = 0. Calculate t.
1
Let f(z) be the second derivative of -z**4/4 + z**3 - 15*z. Factor f(x).
-3*x*(x - 2)
Let u = -1333/3 + 449. Factor 0 + 2*c**4 - 2/3*c - u*c**3 + 10/3*c**2.
2*c*(c - 1)**2*(3*c - 1)/3
Determine s so that 0*s - 1/6*s**2 - 1/6*s**4 + 1/3*s**3 + 0 = 0.
0, 1
Factor -1/3*z**3 - z**2 + 4/3 + 0*z.
-(z - 1)*(z + 2)**2/3
Let x(r) = -r**2 - 1. Let j(m) = -5*m**2 - 24*m - 37. Let b(l) = -j(l) + x(l). Determine f so that b(f) = 0.
-3
Let s be 3*2/(-10)*(-3 - 2). Find p such that -2/7*p**s + 4/7*p**2 - 2/7*p + 0 = 0.
0, 1
Let -1/4*q + 1/8 + 1/8*q**2 = 0. Calculate q.
1
Let b = -522/67 - -28801/1005. Let c = b + -91/5. Suppose 8/3*t**5 + 0 + 2/3*t**2 + 0*t - c*t**3 - 2/3*t**4 = 0. What is t?
-1, 0, 1/4, 1
Let b be 1 + 15/(-10)*(-4)/6. Let w(h) be the third derivative of 1/72*h**4 + 1/360*h**6 - 1/90*h**5 + 0*h**3 + 0*h + 0 - h**b. Factor w(v).
v*(v - 1)**2/3
Let b(p) = 7*p**4 - 8*p**3 - 4*p**2 + 24*p + 18. Let a(c) = -4*c**4 + 4*c**3 + 2*c**2 - 12*c - 9. Let m(n) = 5*a(n) + 3*b(n). Solve m(j) = 0 for j.
-1, 3
Let v(g) be the first derivative of g**3/15 + 2*g**2/5 + 4*g/5 + 5. Suppose v(o) = 0. What is o?
-2
Let y = 1 + 1. Suppose 0 = -g + 2*g, 2*k = y*g + 2. Factor 0*c**2 - c**3 + 2*c**2 - c**2 - k + c.
-(c - 1)**2*(c + 1)
Let c(p) be the first derivative of 2/15*p**3 + 4 + 0*p**2 + 0*p. Determine m so that c(m) = 0.
0
Let f(n) = -n**3 - 5*n + 2. Let k(r) be the third derivative of r**6/120 + r**4/24 + 5*r**2. Let w(x) = -3*f(x) - 6*k(x). What is j in w(j) = 0?
-2, 1
Let u(o) be the second derivative of 5*o**5/14 - 15*o**4/14 + 8*o**3/7 - 4*o**2/7 - 17*o. Factor u(a).
2*(a - 1)*(5*a - 2)**2/7
Let x be (4 - -1) + (1 + -2 - 2). Factor 2/7*k**x + 8/7 - 8/7*k.
2*(k - 2)**2/7
Let s be 3 + 24 - 0/1. Let q be -6*-1*3/s. Factor -q + 2/3*o**2 + 0*o.
2*(o - 1)*(o + 1)/3
Let d = 1163/120 - 99/10. Let y = d + 7/8. Factor -y*s**2 + 1/3 + 1/3*s.
-(s - 1)*(2*s + 1)/3
Let w be 625/260 + 2*5/(-65). Factor -7/8*f + w*f**2 - 11/4*f**3 + 1/8 - 3/8*f**5 + 13/8*f**4.
-(f - 1)**4*(3*f - 1)/8
Suppose 21 = 3*f - 21. Suppose 3*z = -2*z + c + f, 4*c + 8 = 4*z. Factor -d**4 + d**z - d**2 + 3*d**2 - 2*d**2.
-d**3*(d - 1)
Suppose 5/3*q**4 + 1/3*q - 13/3*q**3 + 3*q**2 - 2/3 = 0. Calculate q.
-2/5, 1
Suppose -7*o + 1 = -13. Factor 2/5*c**o - 2/5*c + 0.
2*c*(c - 1)/5
Let u(x) = -x**4 - x**3 + x. Let g(p) = 20*p**4 + 5*p**3 + 5*p**2 - 15*p. Let v(k) = g(k) + 15*u(k). Factor v(n).
5*n**2*(n - 1)**2
Let i(z) be the first derivative of -z**5/5 + 3*z**4/2 - 4*z**3 + 4*z**2 + 1. What is w in i(w) = 0?
0, 2
Suppose -68/3*a**2 + 40/3*a**3 + 32/3*a + 0 - 4/3*a**4 = 0. Calculate a.
0, 1, 8
Determine p so that 14/9*p**3 - 26/9*p**2 - 2/3*p + 4 - 2/9*p**4 = 0.
-1, 2, 3
Suppose -4*i + 14 = 2*r, -2*i - 4*r = 5 - 27. Let c be i - ((-44)/12 - -4). Factor -2/3*b**4 + 0 + 2/3*b**2 - c*b**3 + 2/3*b.
-2*b*(b - 1)*(b + 1)**2/3
Suppose 0 + 2 = x. Suppose 4 - 7 + p**x + 4 + 3*p - p = 0. Calculate p.
-1
Let r(m) be the second derivative of -m**4/6 + 4*m**2 - 17*m. Factor r(l).
-2*(l - 2)*(l + 2)
Let l be (0 - 1/1)*0/(-2). Let n(j) be the first derivative of l*j - 1/9*j**3 - 1 + 1/6*j**2. Factor n(f).
-f*(f - 1)/3
Factor -1/3*r**2 + 4/3*r - 4/3.
-(r - 2)**2/3
Suppose a + 4*a = 70. What is j in -10*j**2 - 14*j**3 + 4*j**2 - 4 + 10*j**4 + a*j + 0*j = 0?
-1, 2/5, 1
Suppose -19 + 11 = -2*h. Let n(c) be the second derivative of 4/27*c**3 + 1/9*c**2 - 2/5*c**5 - 1/5*c**6 - 1/9*c**h + 0 - 3*c. Solve n(m) = 0.
-1, -1/3, 1/3
Let v(d) = -3*d**4 + 5*d**3 + 3*d**2 - 9*d. Let z(j) = -8*j**4 + 15*j**3 + 9*j**2 - 27*j. Let w(c) = -11*v(c) + 4*z(c). Suppose w(u) = 0. Calculate u.
-3, 0, 1
Let p(s) be the third derivative of -s**9/34020 + s**8/10080 - s**6/3240 + 7*s**4/24 + s**2. Let n(m) be the second derivative of p(m). Solve n(x) = 0.
-1/2, 0, 1
Let u(n) be the