i - i**2 = 0.
0, 1
Factor 3*x - 8*x**2 - 6*x**4 - 33*x**3 - 2 + 5 + 18*x**3 - x**2.
-3*(x + 1)**3*(2*x - 1)
What is t in -3/4*t**4 + 1/4*t**3 - 1 - 1/4*t**5 + 0*t + 7/4*t**2 = 0?
-2, -1, 1
Factor -2/9*d**2 + 0*d + 0.
-2*d**2/9
Suppose 4*s = 2*g - 4 + 26, 5*s + 2*g - 23 = 0. Factor 4*j + 5*j**2 + 2*j**3 - 7 + 3 + s.
(j + 1)**2*(2*j + 1)
Let k = 646/7 - 92. Suppose -4/7 + 2/7*o**2 - k*o = 0. Calculate o.
-1, 2
Let u = 100 + -98. Let b(s) = -s - 3. Let h be b(-6). Solve -2/3*k**u + 2/3 - 5/3*k + 5/3*k**h = 0.
-1, 2/5, 1
Let h(d) be the third derivative of d**8/84 - d**6/15 + d**4/6 - 6*d**2. Solve h(k) = 0 for k.
-1, 0, 1
Let v(h) be the second derivative of -5*h**4/6 + 2*h**3 - 9*h**2/5 + 10*h. Factor v(p).
-2*(5*p - 3)**2/5
Suppose 4 + 3 = k. Factor -3*o**2 - o**2 - 2*o**3 + 2*o + k*o**4 - 3*o**4 - o**4 + 1.
(o - 1)**2*(o + 1)*(3*o + 1)
Let p = -194 + 395/2. Find k such that p*k**3 + 6*k**2 - 1 + 3/2*k = 0.
-1, 2/7
Let l(c) be the second derivative of -c**5/100 - 2*c**4/15 - 13*c**3/30 - 3*c**2/5 + 13*c. Determine k, given that l(k) = 0.
-6, -1
Let l be (2 - 28/12)*-15. Let h(o) be the second derivative of 0*o**4 + 1/10*o**l + 0*o**3 - 1/21*o**7 - o + 0*o**6 + 0*o**2 + 0. Let h(n) = 0. What is n?
-1, 0, 1
Let b(x) = -2*x - 17. Let n be b(-12). Suppose -v = -n + 2. Factor 0*z**2 + 0*z**4 + 0 - 1/3*z**v + 1/3*z**3 + 0*z.
-z**3*(z - 1)*(z + 1)/3
Let o(v) = -6*v. Let a(u) = -13*u + 1. Let l(p) = -2*a(p) + 5*o(p). Let c be l(-1). Factor 0 + 0*q - 3/7*q**c.
-3*q**2/7
Let f be (-7)/(14/(-6)) + -3. Factor f - 1/4*w + 1/4*w**2.
w*(w - 1)/4
Factor -1/3*f**2 + 1/3 - 1/3*f + 1/3*f**3.
(f - 1)**2*(f + 1)/3
Let q(k) be the third derivative of -k**7/1260 + k**6/180 - k**5/60 - 5*k**4/24 + k**2. Let i(u) be the second derivative of q(u). Factor i(p).
-2*(p - 1)**2
Let s(h) be the third derivative of -1/20*h**6 + 0*h**7 + 6*h**2 + 0*h**3 + 0*h**5 + 0*h + 0 + 1/8*h**4 + 1/112*h**8. Suppose s(g) = 0. What is g?
-1, 0, 1
Let c(r) be the third derivative of r**5/60 - 7*r**4/24 + r**3 + 14*r**2. What is w in c(w) = 0?
1, 6
Let c(a) be the third derivative of a**8/560 - a**6/100 + a**4/40 + 7*a**2. Factor c(p).
3*p*(p - 1)**2*(p + 1)**2/5
Let a(l) = 195*l**3 + 21*l**2 + 5*l - 5. Let z(t) = -97*t**3 - 11*t**2 - 3*t + 3. Let p(n) = -3*a(n) - 5*z(n). Let p(o) = 0. Calculate o.
-2/25, 0
Let p(k) be the third derivative of -k**8/3360 - k**7/420 - k**6/120 - k**5/60 - k**4/4 + 3*k**2. Let l(j) be the second derivative of p(j). Factor l(w).
-2*(w + 1)**3
Factor 20 - 5*o**2 - 78*o + 78*o.
-5*(o - 2)*(o + 2)
Suppose 5*l - 46 = -18*l. Factor 4/5*n**3 - 3*n**l + 3/5 + 8/5*n.
(n - 3)*(n - 1)*(4*n + 1)/5
Let t(r) = 7*r**2 - r + 2. Suppose 3*x = -3*o + 12, -2*x + 4 = 3*o - 1. Let d(a) = 0 + 3 + 10*a**2 - a + 0*a. Let s(n) = x*t(n) - 5*d(n). Factor s(b).
-(b + 1)**2
Let u(y) = -10*y**2 - 15*y + 15. Let l(p) = -p**2 - p + 1. Let b(d) = -44*l(d) + 4*u(d). Factor b(n).
4*(n - 2)**2
Let u be 12*((-8)/12 + 1). Determine t so that -t**u + 6*t**3 - t - 2*t**4 - 3*t**2 + t = 0.
0, 1
Let i(o) = o**2 + 3*o. Let q be i(-2). Let s = -1 - -2. Let a(f) = f - 1. Let b(w) = -2*w**2 + 4*w + 2. Let j(p) = q*a(p) + s*b(p). Factor j(l).
-2*(l - 2)*(l + 1)
Let m be ((-290)/30 + 3)*1/(-36). Let r(k) be the second derivative of 1/45*k**6 - 2/9*k**2 + 1/18*k**5 - 1/54*k**4 + 0 - m*k**3 + 2*k. Solve r(f) = 0.
-1, -2/3, 1
Let l = -2/235 - -1424/1645. Factor -10/7*w**2 - l - 2/7*w**3 - 2*w.
-2*(w + 1)**2*(w + 3)/7
Find c such that 2 + 5583*c**4 - 6 - 5576*c**4 - 21*c**2 + 2*c**3 - 20*c = 0.
-1, -2/7, 2
Let i be (-3)/(-9) - 6/9*-4. Suppose 4/9*w + 0 - 2/3*w**2 + 2/9*w**i = 0. What is w?
0, 1, 2
Let t(v) be the first derivative of 0*v - 1/20*v**5 + 0*v**2 - 10 + 1/16*v**4 + 0*v**3. Factor t(i).
-i**3*(i - 1)/4
Let n(a) be the third derivative of a**6/240 - a**5/120 - 6*a**2. Suppose n(w) = 0. What is w?
0, 1
Determine s, given that 6*s**4 - 2*s**5 - 6*s**2 + 4*s**2 - 4*s**2 - 8*s**2 + 8 + 2*s**3 = 0.
-1, 1, 2
Factor 2/3*x**3 + 1/3*x**4 - 2/3*x + 0*x**2 - 1/3.
(x - 1)*(x + 1)**3/3
Factor 1/3 + 13/3*c**4 + 22/3*c**3 + 6*c**2 + 7/3*c + c**5.
(c + 1)**4*(3*c + 1)/3
Find l such that 75*l**2 - 117*l + 65 - 18*l - 4*l**3 - l**3 = 0.
1, 13
Suppose 3 = -5*z + 38. Let l(q) = -8*q**3 + 2*q**2 + 4*q + 6. Let b(r) = -9*r**3 + 3*r**2 + 5*r + 7. Let i(x) = z*l(x) - 6*b(x). What is j in i(j) = 0?
-1, 0
Let v(r) be the first derivative of -r**3/2 - 9*r**2/4 - 36. Determine z so that v(z) = 0.
-3, 0
Let w = 2341/6 - 390. Solve -1/3*v - 1/6 - w*v**2 = 0.
-1
Let y(m) be the second derivative of -m**4/6 - 10*m**3/3 - 25*m**2 - 5*m. Factor y(z).
-2*(z + 5)**2
Let g(o) = 2*o**4 + 7*o**3 - 2*o**2 + 5*o + 6. Let t be ((-12)/(-18))/(1/9). Let q(n) = n**4 + n**3 - n**2 + n + 1. Let h(w) = t*q(w) - g(w). Factor h(z).
z*(z - 1)*(z + 1)*(4*z - 1)
Suppose z - 13 = -20. Let j(c) = c**3 + 8*c**2 + 6*c - 7. Let a be j(z). Suppose 1/5*n**2 + 1/5*n + a = 0. Calculate n.
-1, 0
Let j(o) be the first derivative of 3*o**5/5 - o**3 - 4. Factor j(n).
3*n**2*(n - 1)*(n + 1)
Let x(o) be the second derivative of -o**7/2520 - o**6/90 - 2*o**5/15 - o**4/2 + 4*o. Let h(u) be the third derivative of x(u). Factor h(g).
-(g + 4)**2
Let j(v) be the first derivative of -v**4/36 - v**3/18 - 4*v + 4. Let r(q) be the first derivative of j(q). Let r(a) = 0. What is a?
-1, 0
Suppose 0 + 2/5*r**4 - 2/5*r**2 + 2/5*r**5 - 2/5*r**3 + 0*r = 0. What is r?
-1, 0, 1
Let n(l) be the third derivative of -l**7/1050 - l**6/300 + l**5/100 + 2*l**2. Factor n(p).
-p**2*(p - 1)*(p + 3)/5
Let q(b) = b**2 - b - 2. Let v(i) = -11*i**2 + 6*i + 15. Let k(l) = -21*l**2 + 12*l + 30. Let d(g) = 5*k(g) - 9*v(g). Let m(p) = 2*d(p) + 15*q(p). Factor m(c).
3*c*(c - 1)
Let d(w) be the first derivative of 4*w**5/11 + w**4/22 - 4*w**3/33 + 9. Determine v so that d(v) = 0.
-1/2, 0, 2/5
Let s(l) be the first derivative of l**6/3 - 2*l**5/5 - 3*l**4/2 + 2*l**3/3 + 2*l**2 - 1. Find v such that s(v) = 0.
-1, 0, 1, 2
Let b(q) be the third derivative of q**7/945 + q**6/135 + q**5/54 + q**4/54 + 13*q**2. Factor b(p).
2*p*(p + 1)**2*(p + 2)/9
Let o(c) be the third derivative of c**8/110880 + c**7/27720 - 7*c**5/60 + 10*c**2. Let f(r) be the third derivative of o(r). Factor f(h).
2*h*(h + 1)/11
Let o(z) be the first derivative of -z**4/28 - 5*z**3/7 - 75*z**2/14 - 125*z/7 - 27. Factor o(s).
-(s + 5)**3/7
Let t(w) be the first derivative of -8*w**5/25 - w**4/5 + 6*w**3/5 - 11*w**2/10 + 2*w/5 - 5. Solve t(r) = 0 for r.
-2, 1/2
Let x be (-1 + 5/3)*(25 - 22). Determine j, given that 0 + 0*j + 2/5*j**x = 0.
0
Suppose -22*l + 6 + 55/2*l**2 - 13*l**3 + 3/2*l**4 = 0. Calculate l.
2/3, 1, 6
Let o(v) be the third derivative of v**6/30 - 4*v**5/15 + v**4/2 - 21*v**2. Find g, given that o(g) = 0.
0, 1, 3
Factor 0*o + 12/7*o**3 - 9/7*o**2 - 3/7*o**4 + 0.
-3*o**2*(o - 3)*(o - 1)/7
Let l(v) be the first derivative of -5*v**3/3 + 15*v**2 - 25*v + 8. Factor l(z).
-5*(z - 5)*(z - 1)
Let k = -31 + 33. Factor -4/7 - 6/7*b - 2/7*b**k.
-2*(b + 1)*(b + 2)/7
Let u(m) be the first derivative of m**4/8 + m**3/6 - m**2/4 - m/2 + 23. Factor u(w).
(w - 1)*(w + 1)**2/2
Suppose -h - 2*h + 6 = 0. Find o such that -1/3 + 2/3*o - 2/3*o**3 + 1/3*o**4 + 0*o**h = 0.
-1, 1
Let q(m) = -5*m**3 + 10*m**2 + 3*m - 6. Let h(b) = -4*b**3 + 9*b**2 + 3*b - 5. Let u(c) = 6*h(c) - 5*q(c). Factor u(r).
r*(r + 1)*(r + 3)
Let f = 107 + -107. Factor -2/5*n**5 - 6/5*n**4 + f*n - 2/5*n**2 - 6/5*n**3 + 0.
-2*n**2*(n + 1)**3/5
Suppose -5*s = -16 - 9. Factor s*j - 2*j**2 + 2*j - 6*j + j**3.
j*(j - 1)**2
Let z(f) be the first derivative of 2 + 1/20*f**5 - f**2 - 1/6*f**3 - 2*f + 1/6*f**4. Let u(g) be the first derivative of z(g). Factor u(l).
(l - 1)*(l + 1)*(l + 2)
Let w(m) be the first derivative of 3/2*m**2 - 5 - 9/2*m - 1/6*m**3. Factor w(a).
-(a - 3)**2/2
Let f be (-9 + 497/56)*4*-1. Factor 1/4*r**4 - 1/4 - f*r**3 + 0*r**2 + 1/2*r.
(r - 1)**3*(r + 1)/4
Let r(c) = 2*c**2 - 15*c + 9. Let f be r(7). Determine k, given that -3/4*k + 3/4*k**f + 0 = 0.
0, 1
Let v(u) be the first derivative of 5*u**4/4 + 35*u**3/3 + 40*u**2 + 60*u - 31. Factor v(c).
5*(c + 2)**2*(c + 3)
Factor -4/5*a**2 + 6/5 + 1/5*a**3 + 1/5*a.
(a - 3)*(a - 2)*(a + 1)/5
Let y = -643 - -3231/5. Let z = 53/15 - y. Solve -2/3*j**2 + z*j + 1/3 = 0 for j.
-1/2, 1
Suppose 2*v = -3*v - 20. Let z(u) = 