 - 1/2*o + 1/4*o**5 - 1/4*o**4 + 5/4*o**2 - 3/4*o**3.
o*(o - 1)**3*(o + 2)/4
Suppose m + 373 = 21. Let j = 3172/9 + m. Find c such that -2/9 - 2/9*c**2 - j*c = 0.
-1
Let u be (-2)/((-8)/11) - 2. Let f(p) = p**3 + 6*p**2 - 6*p + 10. Let s be f(-7). Factor 0 - 1/4*x**4 + 1/4*x - 3/4*x**2 + u*x**s.
-x*(x - 1)**3/4
Find w such that 14*w**2 + 18/5*w - 8/5*w**3 + 0 = 0.
-1/4, 0, 9
Let w(d) be the first derivative of -d**6/8 + d**5/10 + d**4/16 - 39. Factor w(i).
-i**3*(i - 1)*(3*i + 1)/4
Find l such that 2/9*l**3 + 2/9*l**5 + 0 + 0*l + 0*l**2 - 4/9*l**4 = 0.
0, 1
Let t = 15 + -15. Let h(i) be the third derivative of -1/3*i**3 + 0*i - 1/15*i**5 + 1/4*i**4 + 4*i**2 + t. Factor h(v).
-2*(v - 1)*(2*v - 1)
Let q(j) be the second derivative of -1/30*j**6 + 7/12*j**3 + 1/12*j**7 - 2*j + 1/6*j**4 - 1/2*j**2 - 7/20*j**5 + 0. Determine c, given that q(c) = 0.
-1, 2/7, 1
Let b(k) be the first derivative of 6*k**3 + 0*k - 7/3*k**6 + 2 + 2*k**2 + 5/2*k**4 - 18/5*k**5. Find r, given that b(r) = 0.
-1, -2/7, 0, 1
Let g = 1 - -1. Determine n so that -2*n**2 - 8*n**g + 0*n - 2*n**2 - 2 + n**3 - 11*n + 4*n**4 = 0.
-1, -1/4, 2
Solve 0*n**3 + 17*n**2 - 2*n**3 - 19*n**2 = 0 for n.
-1, 0
Let s(h) = -h**4 + h**2. Suppose 10 - 2 = 4*d. Let j(p) = -2*p**3 + p**3 - p + d*p. Let v(y) = -j(y) + s(y). Let v(w) = 0. What is w?
-1, 0, 1
Let s(m) be the second derivative of m**6/80 + 9*m**5/40 + 27*m**4/16 + 27*m**3/4 + 3*m**2/2 + m. Let l(j) be the first derivative of s(j). Factor l(d).
3*(d + 3)**3/2
Let f(k) be the third derivative of k**6/36 - 11*k**5/45 + 2*k**4/9 + 7*k**2 + k. Determine q so that f(q) = 0.
0, 2/5, 4
Let k(q) = -3*q + 1. Let m be k(2). Let t be (-40)/(-32)*(-2)/m. What is j in 1/2*j + t*j**3 + 0 - j**2 = 0?
0, 1
Suppose -i = -2*i. Suppose 12 = 3*t - i*t. Factor 0*z**4 - 2*z**3 + 0*z**t + 2*z**4 + 0*z**3 + 2*z - 2*z**2.
2*z*(z - 1)**2*(z + 1)
Determine z, given that 12*z**2 + 15/4*z**3 - 21/4*z**4 + 3*z + 0 = 0.
-1, -2/7, 0, 2
Let o(k) = 7*k**3 - 3*k**2 - 5*k. Let i(a) = -8*a**3 + 4*a**2 + 6*a. Let p(w) = 5*i(w) + 6*o(w). Factor p(g).
2*g**2*(g + 1)
Let l be (-1)/(-3 - (-20)/6). Let f(p) = p**4 + 5*p**2. Let m(d) = -2*d**4 - 14*d**2. Let s(h) = l*m(h) - 8*f(h). Suppose s(z) = 0. Calculate z.
-1, 0, 1
Let i(q) be the second derivative of 1/2*q**2 + 1/4*q**4 - 1/60*q**5 + 0 + 3*q - 3/2*q**3. Let m(u) be the first derivative of i(u). Factor m(h).
-(h - 3)**2
Factor 0 - 14/9*s**2 - 2/9*s.
-2*s*(7*s + 1)/9
Let l(n) be the third derivative of n**5/80 - n**4/32 - n**3/4 - 31*n**2. Determine f, given that l(f) = 0.
-1, 2
Let n(m) = -2*m**4 - 6*m**3 + 16*m**2 - 14. Let j(w) = 2*w**4 + 5*w**3 - 15*w**2 + 13. Let s(k) = -6*j(k) - 5*n(k). Determine t, given that s(t) = 0.
-2, -1, 1, 2
Let r be 2/12 - 15/(-180)*22. Factor 1/4*m**3 + 1/4*m**5 + 1/2*m**4 + 0*m + 0 + 0*m**r.
m**3*(m + 1)**2/4
Determine n so that 3*n - 1/3*n**4 - 19/3*n**2 + 11/3*n**3 + 0 = 0.
0, 1, 9
Let k(o) = 9*o**2 + 35*o + 105. Let v(d) = 4*d**2 + 18*d + 52. Let w(a) = 2*k(a) - 5*v(a). Factor w(n).
-2*(n + 5)**2
Let o be (46/(-345))/((-1)/3). Let a(m) be the first derivative of o*m**2 - 6/5*m**3 + 2 + 18/25*m**5 - 2/3*m**6 + 4/5*m**4 + 0*m. Determine y so that a(y) = 0.
-1, 0, 2/5, 1/2, 1
Let n = 5/3 + -13/9. Solve n*h**2 - 2/9*h - 4/9 = 0.
-1, 2
Let i(d) = 26*d**4 - 53*d**3 + 28*d**2 - d. Let u(b) = 25*b**4 - 52*b**3 + 29*b**2 - 2*b. Suppose 5*w - 3*w = -10. Let c(v) = w*u(v) + 4*i(v). Factor c(k).
-3*k*(k - 1)**2*(7*k - 2)
Let c be (-1)/36*(-1 - 2). Let i(v) be the third derivative of 0 - 1/60*v**5 + 0*v - 1/6*v**3 + v**2 - c*v**4. Factor i(f).
-(f + 1)**2
Let q(r) = 5*r**4 + 10*r**2 + 4*r + 5. Suppose 0 = 3*l - 0*l + 12. Let u(a) = 6*a**4 - a**3 + 11*a**2 + 4*a + 6. Let s(p) = l*u(p) + 5*q(p). Factor s(t).
(t + 1)**4
Let k(m) be the first derivative of -m**5/60 + m**3/6 - m**2 + 2. Let a(v) be the second derivative of k(v). Factor a(g).
-(g - 1)*(g + 1)
Let j(b) be the second derivative of -b**7/42 - b**6/15 + b**4/6 + b**3/6 + 4*b. Find o such that j(o) = 0.
-1, 0, 1
Suppose 4*c - 3 = 3*c. Let -6*a**4 - 3*a**2 - a**c + 9*a**4 + a**3 = 0. What is a?
-1, 0, 1
Determine r so that 7*r - 7*r**4 + 16*r**3 - 5*r + 3*r**4 - 20*r**2 + 6*r = 0.
0, 1, 2
Let o(r) = -10*r**3 - 65*r**2 - 105*r - 50. Let n(p) = 5*p**3 + 33*p**2 + 53*p + 25. Let b(v) = 5*n(v) + 2*o(v). Factor b(c).
5*(c + 1)**2*(c + 5)
Solve -9/2*r + 5 - 1/2*r**2 = 0.
-10, 1
Let a(g) = g**2 + g + 2. Let v be a(-2). Suppose -4*r + 7*r + 9 = -3*l, 2*r = -l - 8. Find u such that 3/2 + 0*u**l - 3*u**3 - 3/2*u**v + 3*u = 0.
-1, 1
Let x(o) be the first derivative of -2/33*o**3 + 0*o + 1/11*o**2 - 3. Factor x(p).
-2*p*(p - 1)/11
Suppose -26 = 5*c - 2*d - d, c + 14 = 5*d. Let f be ((-2)/c)/(2/8). Solve 0*j**3 + f*j**3 - 2*j**4 + 2 - 2 + 2*j**2 - 2*j = 0 for j.
-1, 0, 1
Let w(r) = -8*r**3 + 8*r**2 - 5*r + 5. Let k(z) = -39*z**3 + 39*z**2 - 24*z + 24. Let s(a) = 5*k(a) - 24*w(a). Factor s(u).
-3*u**2*(u - 1)
Factor 2/9*t**4 + 2/3*t**5 + 0*t - 4/9*t**3 + 0 + 0*t**2.
2*t**3*(t + 1)*(3*t - 2)/9
Let w(z) be the third derivative of -z**8/28 + 26*z**7/105 - 8*z**6/15 + 4*z**5/15 + 24*z**2. Let w(y) = 0. Calculate y.
0, 1/3, 2
Let t(z) be the third derivative of -z**6/120 - z**5/20 - z**4/12 - 6*z**2. Factor t(m).
-m*(m + 1)*(m + 2)
Let i(p) be the first derivative of 0*p - 1/10*p**4 + 2/15*p**6 + 0*p**2 + 2/25*p**5 + 0*p**3 - 7. Solve i(a) = 0.
-1, 0, 1/2
Let m = 13668/5 + -983791/360. Let z = m + -5/8. Factor -4/9*v**3 - 2/9*v**2 + 0 + 0*v - z*v**4.
-2*v**2*(v + 1)**2/9
Let z(s) = s**3 + 4*s**2 - 2*s - 6. Let r = 9 + -13. Let n be z(r). Factor -2/5*v + 2/5*v**3 + 0*v**n + 0.
2*v*(v - 1)*(v + 1)/5
Let b be 4/8 - 33/(-6). Let f be 3 + 1 - 2/2. Factor -10*x**4 - b*x**2 - 2*x - 3*x**5 + 4*x - f*x - 12*x**3.
-x*(x + 1)**3*(3*x + 1)
Factor 0*b + 1/5*b**2 - 1/5.
(b - 1)*(b + 1)/5
Suppose -3*s - 5*u = 25, 15 = s - 5*u - 10. Suppose r + s = 3. Find v such that 0*v + 4/7*v**r + 0 + 2/7*v**2 + 2/7*v**4 = 0.
-1, 0
Let f = 7/22 - -1/22. What is t in -8/11*t**3 + 2/11*t + 6/11*t**5 + 0 - 4/11*t**2 + f*t**4 = 0?
-1, 0, 1/3, 1
Let o(l) = l**2 + l - 2. Let c(r) = 6*r**2 + 5*r - 13. Let f(v) = -6*c(v) + 39*o(v). Factor f(i).
3*i*(i + 3)
Let -4*t**2 - 7*t - 4*t + 3*t = 0. Calculate t.
-2, 0
Suppose 12 = -4*k, -2*r + 5*r = 3*k + 3. Let u = 2 - r. Solve -3*y**4 + 3*y**3 + y**4 - u*y**2 + 3*y**3 = 0.
0, 1, 2
Let t be (-5)/2 + (-2)/4. Let z = t - -5. Factor -z + a**2 + a + 2.
a*(a + 1)
Let o(q) be the third derivative of -2*q**7/105 + 7*q**6/30 - 61*q**5/60 + 7*q**4/4 - 3*q**3/2 + 15*q**2. Determine d, given that o(d) = 0.
1/2, 3
Suppose 0 = n - x, -x + 18 = 5*n + 3*x. Factor 75*s**n + 3*s**5 + 16*s**4 + 33*s**3 + 24*s**3 + 12 + 5*s**4 + 48*s.
3*(s + 1)**3*(s + 2)**2
Let n(f) be the second derivative of 0*f**4 + 1/120*f**5 - 2*f - 1/240*f**6 + 0*f**3 + 0 - f**2. Let b(o) be the first derivative of n(o). Factor b(a).
-a**2*(a - 1)/2
Let p(y) = -3*y**2 + 5*y + 3. Suppose 0 = 3*l + 9. Let m(f) = -7*f**2 + 9*f + 5. Let i(g) = l*m(g) + 5*p(g). Factor i(n).
2*n*(3*n - 1)
Let u = 26 + -24. Let r(n) be the second derivative of 0*n**3 + 3*n + 0 + 1/54*n**4 + 0*n**u. Let r(m) = 0. Calculate m.
0
Let w(o) = -o**2 - o - 5. Let g(v) = -v**2 - v - 7. Let k(q) = 5*g(q) - 7*w(q). What is b in k(b) = 0?
-1, 0
Solve -2*d**5 + 20*d**3 - d**5 - 8*d**4 + 24*d**2 - d**5 = 0 for d.
-3, -1, 0, 2
Let -2/3*v**2 + 4/3*v - 2/3 = 0. Calculate v.
1
Let n(d) be the third derivative of -d**11/498960 + d**10/113400 - d**9/90720 - d**5/30 + 4*d**2. Let u(q) be the third derivative of n(q). Factor u(l).
-2*l**3*(l - 1)**2/3
Let l be (2 - 1)/(5/10). Factor -2*m**2 + m**2 + m**4 - m**2 + 3*m**2 - l*m**3.
m**2*(m - 1)**2
Let c = 4 + -3. Suppose -2*l = -3*u + c, -4*l + 5 = -2*u + 3*u. Suppose -a + 2*a + 1 - l - a**4 + 3*a**3 - 3*a**2 = 0. Calculate a.
0, 1
Let c(d) be the third derivative of -d**9/181440 - d**8/60480 + d**5/12 + 2*d**2. Let v(b) be the third derivative of c(b). Factor v(t).
-t**2*(t + 1)/3
Let s = -6 + 8. Find u, given that 2*u**2 + 3*u + 2 - s*u + 3*u = 0.
-1
Let g = 283/215 - 5/43. Factor 4/5*k + g*k**2 + 2/5*k**3 + 0.
2*k*(k + 1)*(k + 2)/5
Suppose 252 = 5*c - c. Let a = 5 - 2. Let 0 - 4*l - c*l**a + 30*l**2 + 49/2*l**4 = 0. Calculate l.
0, 2/7, 2
Let m = 6 + -6. Determine h so that h**4 - h**5 - h**2 