
-1, 0, 2
Let p(q) be the first derivative of -27/4*q**4 + 1 + 12*q - 24*q**2 + 21*q**3. Factor p(s).
-3*(s - 1)*(3*s - 2)**2
Let f = -25 - -25. Factor f*g**3 + 0*g - 1/2*g**4 + 0 + 0*g**2.
-g**4/2
What is q in -q**3 + 7*q + 2*q**3 - 8*q = 0?
-1, 0, 1
Factor -2/17*z**2 + 6/17*z**3 + 0 - 6/17*z + 2/17*z**4.
2*z*(z - 1)*(z + 1)*(z + 3)/17
Let n(p) be the second derivative of 5*p**4/48 - 5*p**3/12 + 5*p**2/8 - 11*p. Factor n(k).
5*(k - 1)**2/4
Let w(p) be the third derivative of 4*p**7/105 - 3*p**6/10 + 11*p**5/15 - 8*p**3/3 - 3*p**2. Suppose w(l) = 0. What is l?
-1/2, 1, 2
Let f(d) be the third derivative of d**8/23520 - d**7/2940 + d**6/840 - d**5/420 + d**4/12 - 4*d**2. Let y(t) be the second derivative of f(t). Factor y(a).
2*(a - 1)**3/7
Let p(j) = -21*j**4 - 47*j**3 - 39*j**2 - 6*j + 4. Let r(z) = 104*z**4 + 236*z**3 + 196*z**2 + 30*z - 20. Let q(g) = -14*p(g) - 3*r(g). Factor q(b).
-2*(b + 1)**3*(9*b - 2)
Factor -45*w**2 - 35 - 37*w**3 - 35*w**3 + 67*w**3 - 75*w.
-5*(w + 1)**2*(w + 7)
Let y(m) = m**3 + 10*m**2 + 2*m + 7. Let p be y(-7). Let l = -978/7 + p. What is t in 0 + 2/7*t + l*t**2 = 0?
-1, 0
Factor -2/3*a**2 + 0 + 1/6*a**3 - 5/6*a.
a*(a - 5)*(a + 1)/6
Let r(i) be the second derivative of i**4/14 - 3*i**2/7 - 6*i. Factor r(f).
6*(f - 1)*(f + 1)/7
Let g(l) be the third derivative of -1/60*l**5 + 1/6*l**3 + 0*l + 0*l**4 - 5*l**2 + 0. Determine j, given that g(j) = 0.
-1, 1
Let s(t) be the third derivative of t**7/210 - t**5/20 + t**4/12 - 20*t**2. Factor s(c).
c*(c - 1)**2*(c + 2)
Let f be -5 + 23*(-5)/40*-2. Factor -3/4*h**2 - f*h + 0.
-3*h*(h + 1)/4
Factor -1/5*v**4 + 0*v + 0 - 1/5*v**3 + 2/5*v**2.
-v**2*(v - 1)*(v + 2)/5
Let j(k) be the third derivative of -k**5/15 - k**4/2 - 4*k**3/3 - 3*k**2. Factor j(d).
-4*(d + 1)*(d + 2)
Let k(g) = 12*g**3 - 15*g**2 - 3. Let j(q) = -q - 31*q**2 + 0*q + 16*q**3 - 7 + 9*q**3. Let b(w) = 3*j(w) - 7*k(w). Factor b(s).
-3*s*(s - 1)*(3*s - 1)
Let i(k) be the second derivative of k**8/9240 - k**7/4620 + k**3/2 + 2*k. Let y(s) be the second derivative of i(s). Let y(u) = 0. Calculate u.
0, 1
Let v(b) be the third derivative of -b**8/3192 - b**7/665 + b**6/1140 + 11*b**5/570 + b**4/19 + 4*b**3/57 + 9*b**2. Solve v(x) = 0 for x.
-2, -1, 2
Let t be 14/(-91) + 340/182. Let k = 64/21 - t. Factor 0*b - k*b**4 + 0 - 2/3*b**5 - 2/3*b**3 + 0*b**2.
-2*b**3*(b + 1)**2/3
What is t in 18/5*t**2 - 4/5 - 14/5*t = 0?
-2/9, 1
Let f(c) = -2*c**3 - 8*c**2 + c + 4. Let r be f(-4). Determine y so that -1/6*y**3 - 1/2*y**5 + 0*y + r - 1/6*y**2 + 5/6*y**4 = 0.
-1/3, 0, 1
Let j(i) = 2*i**2 + i + 3. Let g(t) = -5*t**2 - 3*t - 8. Let z(k) = 3*g(k) + 8*j(k). Factor z(c).
c*(c - 1)
Let s = -12 + 16. Suppose 3*n + 3*f - 4 = -1, 4*f = -3*n + s. Factor n*y**3 - 1/2*y**4 + 0*y + 0 + 1/2*y**5 + 0*y**2.
y**4*(y - 1)/2
Let x = 3 + -1. Let -2*v + 4 + x*v**2 - 2*v - 2*v = 0. Calculate v.
1, 2
Suppose 2*b + 5*c - 24 = 0, 26 = -b + 5*c + 8. Let -3*n + 5*n**b + 5*n - 3*n**2 - n**2 = 0. What is n?
-2, 0
Suppose -5*w - 3*q + 6 + 16 = 0, 0 = -5*w + 2*q + 27. Factor 9*l**4 + 3*l**5 + 2*l**3 + w*l**3 - l**3.
3*l**3*(l + 1)*(l + 2)
Let 4/7*j**4 + 0*j + 0 - 8/7*j**2 - 4/7*j**3 = 0. Calculate j.
-1, 0, 2
Let d(m) = m**2 + m + 2. Let k be d(-2). Let h(t) be the third derivative of 0 + 0*t**k + 1/240*t**5 + 0*t + 2*t**2 + 0*t**3. Factor h(y).
y**2/4
Let a(w) be the first derivative of -w**3/3 - w**2/2 - 2*w - 2. Let n(x) = -2*x**2 - 2*x - 5. Let y = -50 - -48. Let m(p) = y*n(p) + 5*a(p). Solve m(h) = 0.
-1, 0
Let p be (-45)/(-10)*6/9. Let s(d) be the first derivative of -2/7*d - 1 - 2/21*d**p - 2/7*d**2. Factor s(c).
-2*(c + 1)**2/7
Let i(h) be the first derivative of 1/8*h**2 + 0*h + 1/6*h**3 - 2 + 1/16*h**4. Factor i(r).
r*(r + 1)**2/4
Let s(b) = -b + 11. Suppose -2*q = -5*q + 24. Let z be s(q). Find x such that -2/3*x**2 - 1/3*x**z + 0 - 1/3*x = 0.
-1, 0
Let q = 260 + -258. Find l such that 2/7*l + 2/7*l**5 + 4/7*l**q - 2/7*l**4 - 4/7*l**3 - 2/7 = 0.
-1, 1
Let x = 205/3 - 407/6. Solve -1/2*h + 1/3 + 7/6*h**3 - x*h**4 - 1/2*h**2 = 0.
-2/3, 1
Let i be 4/((-8)/3)*32/(-24). Find x, given that -3 - 1/3*x**i + 2*x = 0.
3
Let a(w) be the first derivative of -2*w**5/5 - w**4 - 2*w**3/3 + 7. Find d, given that a(d) = 0.
-1, 0
Let w(k) = 4*k**5 - 7*k**4 - 20*k**3 - 9*k**2 + 5*k - 5. Let r(p) = -p**5 + p**3 - p + 1. Let v(z) = -5*r(z) - w(z). Suppose v(t) = 0. What is t?
-3, -1, 0
Let f be (-2 + 2)/(4/(-2)). Suppose f + 0*x - 2/9*x**2 = 0. Calculate x.
0
Let l(s) be the first derivative of 9*s**7/7 + 9*s**6/5 - 2*s**4/3 - 3*s + 2. Let n(u) be the first derivative of l(u). Let n(r) = 0. Calculate r.
-2/3, 0, 1/3
Let k(l) be the third derivative of -1/200*l**6 + 0*l**4 + 0 + 0*l**3 + 0*l - 1/350*l**7 + 1/50*l**5 - l**2. What is g in k(g) = 0?
-2, 0, 1
Find b such that -11*b**5 + 0*b**5 - 8*b**2 + 245*b**4 + b**5 - 32*b**3 - 279*b**4 = 0.
-2, -1, -2/5, 0
Let t(s) be the third derivative of s**9/6048 - s**8/3360 - s**7/1680 + s**6/720 + s**3/6 - 3*s**2. Let o(y) be the first derivative of t(y). Factor o(w).
w**2*(w - 1)**2*(w + 1)/2
Let v = -280 - -2803/10. Let d(i) be the first derivative of v*i**2 - 1/5*i**3 + 3/25*i**5 + 0*i - 1 - 3/20*i**4. Factor d(w).
3*w*(w - 1)**2*(w + 1)/5
Let s(p) = -2*p**3 - p**2 - p. Let d be s(-1). Suppose 3*r + 2 + 2*r - 4*r + r**3 - d*r**3 - 2*r**2 = 0. Calculate r.
-2, -1, 1
Let l be (-16)/6*(-7 + (-1140)/(-168)). What is n in l*n**2 + 2/7*n**3 + 0 + 0*n = 0?
-2, 0
Let v(s) be the third derivative of s**9/15120 - s**8/10080 - s**7/2520 - s**5/15 - 4*s**2. Let p(j) be the third derivative of v(j). Factor p(o).
2*o*(o - 1)*(2*o + 1)
Factor 3/2*w**3 + 0*w**2 - 3/2*w + 0.
3*w*(w - 1)*(w + 1)/2
Let k(q) = -q**2 + 5*q + 3. Let r be k(4). Suppose 0*z**3 + 3*z**3 - r*z + z**2 + 2*z**2 + z = 0. Calculate z.
-2, 0, 1
Let y(f) be the second derivative of -f**5/25 + 7*f**4/15 - 22*f**3/15 + 2*f**2 + 7*f. Solve y(j) = 0 for j.
1, 5
Let y(v) be the first derivative of -v**6/10 + 3*v**4/20 - 6. Suppose y(w) = 0. What is w?
-1, 0, 1
Let j(c) be the third derivative of -2*c**7/105 - c**6/30 + 9*c**2. Solve j(b) = 0 for b.
-1, 0
Suppose -l - l = 0. Let g(c) be the first derivative of 0*c**3 + 1/4*c**4 - 1/5*c**5 + 0*c**2 - 1 + l*c. Factor g(a).
-a**3*(a - 1)
Let x(y) be the first derivative of 2/3*y + y**2 - 3 + 2/3*y**3 + 1/6*y**4. Suppose x(w) = 0. What is w?
-1
Let c(b) be the third derivative of -1/600*b**6 + 0 + 0*b**4 + 1/350*b**7 + 0*b**3 + 0*b + 0*b**5 + 3*b**2. Let c(t) = 0. Calculate t.
0, 1/3
Let b(l) be the second derivative of -3*l**5/20 - 2*l**4/3 - 2*l**3/3 - 3*l. Factor b(d).
-d*(d + 2)*(3*d + 2)
Factor 5 + w**2 + 0*w**2 - 1 - 21*w + 25*w.
(w + 2)**2
Factor 1/6*z + 0 - 1/6*z**2 + 1/6*z**4 - 1/6*z**3.
z*(z - 1)**2*(z + 1)/6
Let c(d) be the third derivative of -d**6/12 + 7*d**5/12 - 5*d**4/3 + 5*d**3/2 - 3*d**2. Determine h, given that c(h) = 0.
1, 3/2
Suppose -2*g + 72 = -0*g. Let k be 2/9 - 8/g. Factor -2*d**2 + 4/3*d + 2/3*d**3 + k.
2*d*(d - 2)*(d - 1)/3
Let t be (-9)/6*(-4)/12. Determine d so that 0*d - 1/4 - 1/4*d**4 + t*d**2 + 0*d**3 = 0.
-1, 1
Let g(h) be the first derivative of -2*h**4/9 - 10*h**3/27 - h**2/9 + 37. Factor g(y).
-2*y*(y + 1)*(4*y + 1)/9
Let m be (-16)/(-54)*(-60)/(-16). Find v, given that -8/3*v**4 + 0 + m*v**5 - 2/9*v**3 + 8/3*v**2 - 8/9*v = 0.
-1, 0, 2/5, 1, 2
Find h such that h**2 - 7/8*h - 1/4*h**3 + 1/8*h**5 + 1/4 - 1/4*h**4 = 0.
-2, 1
Let b = -77 + 79. Solve 80/3*l**b - 34/3*l + 4/3 - 32/3*l**3 = 0 for l.
1/4, 2
Suppose -7*u - 72 = -3*u. Let d(a) = a**2 + 2*a + 2. Let o(k) = 5*k**2 + 9*k + 9. Let x(b) = u*d(b) + 4*o(b). Find q such that x(q) = 0.
0
Let z = 53/3 - 262/15. Factor 0*k + 0*k**2 + 0 + 0*k**3 - z*k**5 + 1/5*k**4.
-k**4*(k - 1)/5
Let q = 1 + 3. Suppose 4*c - 3*y = 4, -2*c + 0*c + 3*y - q = 0. Suppose h + h - 2*h**2 + c*h**2 = 0. What is h?
-1, 0
Let -3*u**2 + 9*u**3 - 5*u**5 - 2*u**3 + 9*u**4 - 6*u**4 - 2*u = 0. Calculate u.
-1, -2/5, 0, 1
Let a = -11 - 13. Let t be (a/(-9))/((-6)/(-9)). Factor -4/5*j**2 + 2/5*j**t + 0*j + 0 - 2/5*j**3.
2*j**2*(j - 2)*(j + 1)/5
Let s(a) be the third derivative of 3*a**7/35 - 13*a**6/80 + a**5/30 + a**4/12 + 8*a**2. Factor s(n).
n*(3*n - 2)**2*(4*n + 1)/2
Let b(p) be the third derivative of p**6/540 - p**5/120 + p**4/72 - 2*p**3/3 + 2*p**2. Let y(c) be the f