b - 1)**4/7
Let d(s) be the first derivative of -s**4 - 4*s**3/3 - 51. Factor d(j).
-4*j**2*(j + 1)
Suppose 2*c - h - 3 = 2, 0 = 5*h - 25. Factor -5*s - c*s - 2*s**2 + 2*s + 8*s**3 + 2 + 0*s.
2*(s - 1)*(s + 1)*(4*s - 1)
Determine h so that 4/3*h**2 + 1/6*h**3 + 7/6*h + 0 = 0.
-7, -1, 0
Suppose 0 = 5*y - 3*t - 75, 3*y - 2*t = 3*t + 61. Suppose 5*h + 2 = y. Factor 4*n**h - 5*n + 5*n + 2*n**3 + 0*n**3.
2*n**2*(n + 2)
Let x(q) be the first derivative of -1/12*q**4 - 2 + 0*q + 0*q**3 + 0*q**2. Factor x(w).
-w**3/3
Let l(v) be the first derivative of v**6/45 - 8*v**5/75 + v**4/5 - 8*v**3/45 + v**2/15 + 8. Factor l(h).
2*h*(h - 1)**4/15
Let m(a) be the third derivative of a**7/4200 - a**6/1200 + 5*a**4/12 + 11*a**2. Let u(h) be the second derivative of m(h). Let u(v) = 0. Calculate v.
0, 1
Let w(l) be the third derivative of -2*l**7/735 - l**6/70 - l**5/35 - l**4/42 - 2*l**2. Factor w(d).
-4*d*(d + 1)**3/7
Let m(p) = p**3 + p**2 + p. Let r(i) = -5*i**3 - 9*i**2 - 11*i - 3. Let v(n) = -4*m(n) - r(n). Suppose v(z) = 0. Calculate z.
-3, -1
Let a(p) be the first derivative of p**7/1260 - p**6/135 + p**5/45 - p**3/3 - 3. Let u(j) be the third derivative of a(j). Solve u(o) = 0.
0, 2
Let z(t) be the second derivative of -t**6/150 + t**4/60 + 4*t. Solve z(v) = 0 for v.
-1, 0, 1
Let j(r) be the first derivative of 3*r**5/5 + 3*r**4 + 5*r**3 + 3*r**2 + 5. Determine o, given that j(o) = 0.
-2, -1, 0
Let f be 2 - (2 + (-6)/3). Suppose s + 2 = f*s. Factor 3*b**2 - 2*b + 4*b - b**s.
2*b*(b + 1)
What is g in 9/4 - 3*g + 3/4*g**2 = 0?
1, 3
Let k be 1/2 + (-12)/24. Solve k + 2/9*l**3 - 2/3*l**2 + 4/9*l = 0.
0, 1, 2
Let h(u) be the third derivative of -u**6/240 - u**5/20 - 5*u**4/48 + 38*u**2. Factor h(i).
-i*(i + 1)*(i + 5)/2
Let r be ((-90)/(-54))/((-1)/21). Let f be 10/25 + 4/r. Let 4/7 - f*n - 2/7*n**2 = 0. Calculate n.
-2, 1
Let i(v) = 11*v**3 + 29*v**2 - 23*v - 17. Let h(q) = 4*q**3 + 10*q**2 - 8*q - 6. Let n = 22 + -39. Let r(l) = n*h(l) + 6*i(l). Factor r(w).
-2*w*(w - 1)**2
Let g(t) = 4*t**4 + 5*t**3 + t - 1. Let p = 3 - 1. Let w = p + 0. Let f(k) = -3*k**4 - 4*k**3 + 1. Let q(r) = w*g(r) + 3*f(r). Let q(n) = 0. What is n?
-1, 1
Factor 12/13*g**5 + 0*g - 2/13*g**2 + 0 - 2*g**4 + 16/13*g**3.
2*g**2*(g - 1)**2*(6*g - 1)/13
Let v(k) be the first derivative of -k**5/30 + k**4/8 - k**3/18 - k**2/4 + k/3 - 23. What is w in v(w) = 0?
-1, 1, 2
Suppose 3/7*b**2 + 0 + 6/7*b - 9/7*b**3 = 0. Calculate b.
-2/3, 0, 1
Suppose 5 + 7 = 4*u. Suppose 3*p - 3 = 0, 7 = 3*y - u*p + p. Let 1/2 - 1/2*q**2 + 3/4*q**y - 3/4*q = 0. What is q?
-1, 2/3, 1
Suppose -24 = -3*o + 5*c, 2*o - 12 = -0*o + 2*c. Suppose -2/7*z**o + 2/7*z - 2/7*z**2 + 2/7 = 0. Calculate z.
-1, 1
Let v(d) be the second derivative of 3/20*d**5 - 5*d + 0*d**2 + 0 + 0*d**4 - 1/2*d**3. Factor v(m).
3*m*(m - 1)*(m + 1)
Solve 0 + 4/11*f + 8/11*f**3 + 2/11*f**4 + 10/11*f**2 = 0 for f.
-2, -1, 0
Let q(u) be the first derivative of -4 + 1/5*u**2 + 0*u - 2/15*u**3. Factor q(c).
-2*c*(c - 1)/5
Suppose 19*q = 14*q. Let h(n) be the third derivative of q*n + 0*n**3 + 7/60*n**5 + n**2 - 1/24*n**6 - 1/12*n**4 + 0. Factor h(v).
-v*(v - 1)*(5*v - 2)
Factor 4*q - 2 + 1/2*q**3 - 5/2*q**2.
(q - 2)**2*(q - 1)/2
Let r(i) be the third derivative of -i**9/12096 - i**8/6720 - 7*i**3/6 + i**2. Let b(d) be the first derivative of r(d). Factor b(q).
-q**4*(q + 1)/4
Let t(p) be the second derivative of 7*p**6/30 + 3*p**5/5 - 25*p**4/12 + p**3 + 4*p. Factor t(n).
n*(n - 1)*(n + 3)*(7*n - 2)
Let m(n) be the third derivative of 4/3*n**3 - 6*n**2 + 1/15*n**5 + 1/2*n**4 + 0 + 0*n. What is q in m(q) = 0?
-2, -1
Let f(i) be the second derivative of -i**7/525 + i**6/75 - 3*i**5/100 + i**4/30 - i**3/6 + 7*i. Let j(c) be the second derivative of f(c). Solve j(w) = 0.
1/2, 2
Suppose 11*g + 443 = 476. Factor 1/4 + 3/4*j**4 - 1/2*j**g + 1/2*j - j**2.
(j - 1)**2*(j + 1)*(3*j + 1)/4
Factor 0 + 2/3*i**3 + 0*i - 4/3*i**2.
2*i**2*(i - 2)/3
Suppose 0 = -2*r + s - 2*s + 25, 5*r = 2*s + 49. Factor -3*l + 14*l - 4*l**4 + 8*l**3 - r*l.
-4*l**3*(l - 2)
Let y be 2/6*(3 - 3). Let l(n) be the first derivative of -2 + 1/10*n**4 + 4/15*n**3 + 1/5*n**2 + y*n. Factor l(m).
2*m*(m + 1)**2/5
Let g(i) be the first derivative of -5*i**3/3 + 25*i**2/2 - 20*i + 9. Let g(u) = 0. Calculate u.
1, 4
Let s(u) be the first derivative of -u**3/12 + 3*u**2/8 - u/2 + 5. Factor s(d).
-(d - 2)*(d - 1)/4
Factor 24*b**2 - 40*b**2 - 3*b**5 + 3*b**4 + 16*b**2.
-3*b**4*(b - 1)
Suppose m + 2 = 4. Let g(z) be the first derivative of 2*z**2 + 1/8*z**4 + 2 + 5/6*z**3 + m*z. Factor g(c).
(c + 1)*(c + 2)**2/2
Find q such that 15/7 + 18/7*q + 3/7*q**2 = 0.
-5, -1
Let p(i) be the first derivative of i**3/21 + 2*i**2/7 + 10. Factor p(v).
v*(v + 4)/7
Let y(s) be the third derivative of -2*s**5/15 + 5*s**4/6 + 2*s**3 + 4*s**2. Determine n so that y(n) = 0.
-1/2, 3
Let c(s) be the first derivative of 4/3*s**3 + 2/3*s - 3/2*s**2 + 3 - 5/12*s**4. Factor c(r).
-(r - 1)**2*(5*r - 2)/3
Let a(w) be the first derivative of w**9/7560 + w**8/1400 + w**7/700 + w**6/900 + 2*w**3/3 + 1. Let t(y) be the third derivative of a(y). What is i in t(i) = 0?
-1, 0
Let a(g) be the third derivative of 2*g**7/15 + 19*g**6/30 + 13*g**5/20 - g**4/6 - 2*g**3/3 - g**2 - 50. Factor a(p).
(p + 2)*(2*p + 1)**2*(7*p - 2)
Suppose -2*l + 6 = 2. Find h, given that -h**5 + 3*h**4 - 1 - 4*h**4 + 0*h**2 + l*h**3 + 2*h**2 - h = 0.
-1, 1
Solve -4/3*c - 2/3 - 2/3*c**2 = 0.
-1
Solve 33/2*n**2 + 3/2*n**4 + 15/2*n + 0 + 21/2*n**3 = 0 for n.
-5, -1, 0
Suppose 4 - 22 = -3*x. Let o(m) be the second derivative of -1/30*m**x - 3/20*m**5 - 2*m + 0 + 0*m**2 - 1/4*m**4 - 1/6*m**3. Factor o(z).
-z*(z + 1)**3
Let v(x) be the third derivative of x**5/75 + x**4/24 + x**3/30 + 5*x**2. Solve v(l) = 0 for l.
-1, -1/4
Suppose -3*n + 33 = 3*t, 2*t = -n - 0*t + 13. Suppose -5*m + 2*z + 35 = -3*z, -n = m + 3*z. Find y, given that 0*y**m + 0 - 2/9*y**2 + 0*y + 2/9*y**4 = 0.
-1, 0, 1
Let x(d) be the second derivative of d**6/40 - d**4/8 + 3*d**2/8 - 7*d. Factor x(v).
3*(v - 1)**2*(v + 1)**2/4
Suppose -4*q + 6*q = 10. Let k(u) be the second derivative of 3/40*u**q + 1/84*u**7 + 0*u**3 + 0*u**2 + 0 + 1/20*u**6 - u + 1/24*u**4. Factor k(n).
n**2*(n + 1)**3/2
Let z(f) = -f**3 + 4*f**2 - 5*f + 5. Let q be z(4). Let x = 15 + q. Factor 2/5*b - 2/5*b**4 + x - 6/5*b**2 + 6/5*b**3.
-2*b*(b - 1)**3/5
Let k(b) be the second derivative of b**10/15120 + b**9/3780 + b**8/3360 - b**4/4 + 3*b. Let v(m) be the third derivative of k(m). Find o such that v(o) = 0.
-1, 0
Solve 5*s**2 + s**3 - 7*s**2 - s**2 = 0.
0, 3
Let m be (-2 + 44/16)*122/3. Let b(y) be the first derivative of m*y**4 + 4*y**3 - 16*y**6 + 3 - 16/5*y**5 - 13*y**2 + 4*y. Let b(j) = 0. Calculate j.
-1, -2/3, 1/4, 1
Let i = 25 - 22. Determine c so that 0*c**2 + 0*c + 1/3*c**i + 0 = 0.
0
Let w(r) be the second derivative of -r**6/15 + 7*r**5/10 - 5*r**4/2 + 3*r**3 - 18*r. What is k in w(k) = 0?
0, 1, 3
Let m(s) be the second derivative of 0 + 2*s - 1/3*s**6 - 3/2*s**4 + 1/3*s**3 - 13/10*s**5 + 2*s**2. Solve m(f) = 0 for f.
-1, 2/5
Let t be ((3 - 6) + 2 - -4) + 1. Factor 0 - 2/11*h**2 + 0*h - 2/11*h**t + 4/11*h**3.
-2*h**2*(h - 1)**2/11
Suppose 0*l**3 + 2/7*l - 2/7*l**5 - 4/7*l**4 + 0 + 4/7*l**2 = 0. Calculate l.
-1, 0, 1
Let b(s) be the third derivative of s**7/1260 - s**5/60 + s**4/24 + 2*s**2. Let c(x) be the second derivative of b(x). Factor c(q).
2*(q - 1)*(q + 1)
Let h(c) be the first derivative of -2*c**3/9 + 4*c**2/3 + 6. Let h(j) = 0. What is j?
0, 4
Let r(f) be the second derivative of f**5/70 + 5*f**4/42 + f**3/3 + 3*f**2/7 + 5*f. Factor r(i).
2*(i + 1)**2*(i + 3)/7
Let u(z) be the first derivative of z**2 + 0*z - 2/3*z**3 - 4. Factor u(o).
-2*o*(o - 1)
Let c(d) = -d**3 - 6*d**2 + 2*d + 6. Let h be c(-6). Let i(k) = -k**3 + 9*k**2 - 3*k + 7. Let o(w) = -w**2 - 1. Let p(b) = h*o(b) - i(b). Factor p(f).
(f - 1)**3
Determine c so that -1 + 0 + 2*c + 0*c**2 - c**2 = 0.
1
Let a(o) = 3*o**2 + 13*o - 48. Let k(z) = -4*z**2 - 20*z + 72. Let y(r) = 8*a(r) + 5*k(r). Factor y(g).
4*(g - 2)*(g + 3)
Let n be (6/(-21))/((-2)/28). Let w(a) be the third derivative of -2*a**2 + 0*a + 0 + 1/15*a**5 + 1/6*a**3 + 5/24*a**n. Factor w(c).
(c + 1)*(4*c + 1)
Let z = 17 + -12. Let b(f) = f + 11. Let m be b(-8). Factor 1/4*a + 0*a**2 + 1