*(k - 1)**3*(k + 1)**2
Let f be (-8)/(-36) + (-20)/9. Let y be (f + 1 + 1)/2. Factor 8/5*g**2 + 0 + y*g + 2/5*g**4 + 8/5*g**3.
2*g**2*(g + 2)**2/5
Find h, given that 2/5 + 3/5*h**2 - h + 1/5*h**3 - 1/5*h**4 = 0.
-2, 1
Let d(w) be the second derivative of 0 + 14/3*w**3 + 3*w - 7/5*w**5 + 2/3*w**4 - 4*w**2. Factor d(h).
-4*(h - 1)*(h + 1)*(7*h - 2)
Let r be 0 - (-3)/2*2 - 1. Let o(s) be the second derivative of 0*s**r + 0 + 0*s**4 - 2*s + 0*s**3 - 1/50*s**6 - 3/100*s**5. Solve o(p) = 0.
-1, 0
Find m such that 3/7*m + 9/7*m**2 - 3/7*m**4 - 3/7*m**3 - 6/7 = 0.
-2, -1, 1
Let z(q) be the first derivative of -q**6/20 + 3*q**4/8 - q**3/2 - 3*q - 8. Let c(u) be the first derivative of z(u). Factor c(o).
-3*o*(o - 1)**2*(o + 2)/2
Let u(g) be the second derivative of 2/5*g**6 - 1/12*g**3 + 7*g + 0 - 4/21*g**7 - 1/40*g**5 + 0*g**2 - 1/4*g**4. Let u(c) = 0. Calculate c.
-1/4, 0, 1
Let j(f) be the third derivative of 0 + 1/60*f**6 + 0*f + 0*f**3 + f**2 + 1/210*f**7 + 1/60*f**5 + 0*f**4. Factor j(o).
o**2*(o + 1)**2
Let l be (-7)/(-5) + 9/15. Solve -3*q**2 + 1 - 4 + l*q**2 + 1 + 3*q = 0.
1, 2
Factor 4*a - 2 + 0*a**2 + 3*a**2 - 2*a**2 - 3*a.
(a - 1)*(a + 2)
Let i(u) = 0*u + 1 - u - u + u. Let f(c) = -c**2 + c - 1. Let q(g) = -3*f(g) - 3*i(g). Factor q(o).
3*o**2
Solve 31*k**4 + 2*k**3 - 24*k**2 - 6 + 4*k**3 - 25*k**4 + 21*k - 3*k**5 = 0 for k.
-2, 1
Suppose 4*w + 18 = 5*m, 9*m - 2 = 4*m - 4*w. Factor 5 - 1 - q**2 - 3*q**2 - m*q**3 + 2*q.
-2*(q - 1)*(q + 1)*(q + 2)
Let z(f) be the third derivative of f**11/332640 + f**10/151200 - f**5/60 + 3*f**2. Let t(d) be the third derivative of z(d). Suppose t(m) = 0. Calculate m.
-1, 0
Let f(g) be the second derivative of g**5/60 - g**4/72 - g**3/12 + 25*g. Factor f(k).
k*(k + 1)*(2*k - 3)/6
Factor y**2 + 7*y**2 - 3*y**3 + 4*y - 4 - 3*y**2.
-(y - 2)*(y + 1)*(3*y - 2)
Let k(j) be the second derivative of -j**6/10 - 4*j**5/15 - 5*j**4/36 + j**3/9 + 12*j. Factor k(s).
-s*(s + 1)**2*(9*s - 2)/3
Let n(f) = f**3 - f**2 + f - 1. Let v(a) = 2*a**4 + 10*a**3 + 4*a**2 + 5*a - 3. Let g(i) = -3*n(i) + v(i). Suppose g(d) = 0. Calculate d.
-2, -1, -1/2, 0
Factor 0*x**2 + 2/11*x**3 + 0*x + 0 + 2/11*x**5 + 4/11*x**4.
2*x**3*(x + 1)**2/11
Find f such that -5*f**4 + 2*f - 44*f**2 - 2*f + 49*f**2 = 0.
-1, 0, 1
Let i be (-6)/4*1*3/(-135). Let l(u) be the third derivative of i*u**5 + 0 + 0*u + 0*u**4 + 0*u**3 + 3*u**2. Factor l(r).
2*r**2
Determine l, given that 75*l**3 - 6 - 48*l**4 - l**5 + l + 13*l**5 + 3 - 57*l**2 + 20*l = 0.
1/2, 1
Let 72*v + 15*v**5 - 48 - 10*v**5 - 69*v**3 + 21*v**2 - 8*v**5 + 27*v**4 = 0. What is v?
-1, 1, 4
Let p = -319 - -7657/24. Let o(k) be the third derivative of 0 + 0*k + 1/120*k**6 - 1/30*k**5 + 2*k**2 + 0*k**3 + 1/105*k**7 - p*k**4. Solve o(b) = 0 for b.
-1, -1/2, 0, 1
Let u(p) be the third derivative of 0*p**3 + 0*p**4 + 0*p - 1/300*p**6 - 3*p**2 + 0*p**5 + 0. Factor u(y).
-2*y**3/5
Solve -10*x + 2*x + 5*x**2 - 15 + 18*x = 0.
-3, 1
Let q(x) be the first derivative of 5*x**3/3 - 5*x**2/2 + 7. Solve q(u) = 0 for u.
0, 1
Let g(r) be the first derivative of 3 - 2*r - 1/3*r**3 - 3/2*r**2. Determine n so that g(n) = 0.
-2, -1
Let r(n) = n**2 - 2*n + 1. Let i be r(3). Factor -k - 2 + 5*k**3 - k**2 - 4*k + k**3 + 3*k**i - k**3.
(k - 1)*(k + 1)**2*(3*k + 2)
Let l(g) = -g**2 - 7*g - 10. Let q be l(-4). Factor -3/7*h**q - 1/7 + 1/7*h**3 + 3/7*h.
(h - 1)**3/7
Solve 2/7*d**2 - 4/7 - 2/7*d = 0 for d.
-1, 2
Let r = -10 - -7. Let l = 6 + r. Factor -4 + s**2 - 2*s**l + s**3 + 3 + s.
-(s - 1)**2*(s + 1)
Factor 2/13*m**4 - 2/13*m**2 + 2/13*m + 0 - 2/13*m**3.
2*m*(m - 1)**2*(m + 1)/13
Let g(n) be the second derivative of 0*n**4 + 0*n**2 + n + 0 - 1/10*n**3 + 3/100*n**5. Factor g(v).
3*v*(v - 1)*(v + 1)/5
Solve 0 - 2/7*q**3 + 4/7*q**2 - 2/7*q = 0.
0, 1
Suppose -3*r = -2*g - 86, g = -4*r + 6*r - 58. Determine m, given that -23/3*m**2 - 5/3*m + 47/3*m**3 + 2/3 - r*m**5 + 23*m**4 = 0.
-1/2, -2/5, 1/3, 1
Solve -14 - 15 + 2*s**2 - 2*s**3 + 29 = 0.
0, 1
Let i = 46/11 - 151/44. Suppose 3/4*p**2 - 1/4*p + 1/4*p**4 + 0 - i*p**3 = 0. Calculate p.
0, 1
Suppose 5*p - 22 + 1 = a, -a = 2*p - 7. Suppose k**5 - 4*k**3 + 10*k**4 - 2*k**5 - 14*k**p = 0. What is k?
-2, 0
Let n be ((-8)/10)/(7/(-5)). Factor 0*d - 6/7*d**5 - n*d**3 - 10/7*d**4 + 0*d**2 + 0.
-2*d**3*(d + 1)*(3*d + 2)/7
Let n be -2*(9/(-6) - 0). Suppose -2*x + 5*f + 19 = -x, -3*x + n*f + 21 = 0. Factor 5 + l**4 - 2*l**3 + 6*l**2 - x*l**3 - 4 - 4*l + 2*l**3.
(l - 1)**4
Let d(x) be the third derivative of x**5/140 + 3*x**4/56 + 11*x**2. Factor d(j).
3*j*(j + 3)/7
Let t(j) be the third derivative of j**7/3780 - j**6/540 + j**5/180 - j**4/4 - 5*j**2. Let w(n) be the second derivative of t(n). Suppose w(c) = 0. What is c?
1
Suppose 1 = j - 1. Let u(r) be the first derivative of 2/5*r**5 + 1/2*r**4 + 2/9*r**3 + 2 + 0*r**j + 1/9*r**6 + 0*r. Factor u(d).
2*d**2*(d + 1)**3/3
Let z(m) = -m - 3. Let i be z(-4). Let k(n) = -n**2 + n + 1. Let g(j) = -2*j**2 + 2*j. Let w(f) = i*g(f) - 4*k(f). Factor w(v).
2*(v - 2)*(v + 1)
Let j(v) = -v**4 - v**3 - 6*v. Let f(c) = -c**4 - c**3 - 7*c. Suppose -g - 9 = -2*o - 2*g, -o = -5*g - 21. Let x(d) = o*f(d) - 7*j(d). Factor x(s).
s**3*(s + 1)
Let p(y) be the first derivative of y**3/5 + 6*y**2/5 + 12*y/5 - 11. Factor p(l).
3*(l + 2)**2/5
Let d(n) be the second derivative of -8*n**7/21 + 34*n**6/15 - 28*n**5/5 + 22*n**4/3 - 16*n**3/3 + 2*n**2 - 26*n. Solve d(a) = 0 for a.
1/4, 1
Let a(h) be the first derivative of 3*h**5/20 - h**3/2 - 5*h - 6. Let k(o) be the first derivative of a(o). Factor k(x).
3*x*(x - 1)*(x + 1)
Let u(a) be the third derivative of a**7/1050 - a**6/600 - a**5/150 + 5*a**2. Factor u(d).
d**2*(d - 2)*(d + 1)/5
Let c = 19 + -15. Suppose -k = -c*k. Find y such that -1/3*y**5 + 0*y**2 + 1/3*y**3 + 0*y + k*y**4 + 0 = 0.
-1, 0, 1
Let 4/5*h**4 + 2/5*h**2 - h**3 - 1/5*h**5 + 0 + 0*h = 0. What is h?
0, 1, 2
Let d(b) be the first derivative of b**6/30 - 2*b**5/25 + 2*b**3/15 - b**2/10 + 29. Factor d(a).
a*(a - 1)**3*(a + 1)/5
Let l be (-10)/(-4) - 1/(-2). Suppose 5*m - 8 = l*m. Find o, given that -2*o**2 - 2*o**m + 3*o - 4*o**2 - o + 6*o**3 = 0.
0, 1
Let n(v) be the first derivative of -6*v + v**3 - 3/2*v**2 + 2. Determine q, given that n(q) = 0.
-1, 2
Let c be (56/63)/((-6)/9 + 2). Solve -1/3*l**2 - 1/3*l**4 + 0 - c*l**3 + 0*l = 0.
-1, 0
Solve 4*t - 4/3*t**2 + 0 = 0.
0, 3
Find f such that 18*f**5 + 3*f**4 + 16*f**3 - 15*f**3 + 3*f - 3*f**2 - 22*f**3 = 0.
-1, -1/2, 0, 1/3, 1
Let z(q) be the first derivative of 0*q**2 + 2*q - 1/30*q**5 + 2/9*q**3 + 4 - 1/18*q**4. Let v(j) be the first derivative of z(j). Find i such that v(i) = 0.
-2, 0, 1
Let w(p) = -4*p**4 + 5*p**3 - 2*p**2 - 5*p - 4. Let a(o) = -3*o**4 + 4*o**3 - 2*o**2 - 4*o - 3. Let l(b) = -5*a(b) + 4*w(b). Determine m so that l(m) = 0.
-1, 1
Let f(c) = -c**2 - 10*c + 2. Let p be f(-10). Let w(z) = z**3 - 10*z**2 - 10*z - 6. Let r be w(11). Factor -2*m - r*m + 4*m + 3*m**p.
3*m*(m - 1)
Factor 6*s**2 + 18*s - 30*s + 18*s + 2 + 2*s**3.
2*(s + 1)**3
Let x = -9 + 18. Determine g so that x*g**4 - 3 + 6*g**3 - 7*g**4 - 6*g + 12*g**2 - 11*g**4 = 0.
-1, -1/3, 1
Let k(q) be the second derivative of -q**6/1260 - q**5/105 - q**4/21 + q**3/6 - 2*q. Let j(l) be the second derivative of k(l). Factor j(i).
-2*(i + 2)**2/7
Let v(c) be the first derivative of 6/7*c**3 - 6/7*c**2 + 2/7*c - 1 - 2/7*c**4. Solve v(d) = 0.
1/4, 1
Let a(c) = 3*c**2 + 2*c + 3. Let t(i) = -13*i**2 - 8*i - 13. Let s(d) = -9*a(d) - 2*t(d). Factor s(l).
-(l + 1)**2
Let f = -17/195 + 2/13. Let j(c) be the first derivative of f*c**3 - 2/5*c**2 + 1 + 4/5*c. Factor j(o).
(o - 2)**2/5
Let w(o) be the first derivative of -5*o**6/2 - 2*o**5 + 15*o**4/4 + 10*o**3/3 + 10. Let w(c) = 0. What is c?
-1, -2/3, 0, 1
Let s(l) be the second derivative of -l**6/900 + l**4/60 - l**3/3 + 3*l. Let r(i) be the second derivative of s(i). Factor r(d).
-2*(d - 1)*(d + 1)/5
Let r(i) be the first derivative of 1 + 0*i**2 + 0*i + 1/6*i**4 + 0*i**3 + 0*i**5 - 1/9*i**6. Factor r(o).
-2*o**3*(o - 1)*(o + 1)/3
Let f(t) = 2*t**2 - 4*t + 3. Let c be f(2). Let g = -12 + 13. Determine n, given that 2 - g + 1 - c*n**2 + n**2 = 0.
-1, 1
Let b(f) be the second derivative of -f**4/54 + f**3/9 + 2*f. Determine q so that b(q) = 0.
0, 3
Let h(w) be the third derivative of 2/105