
0, 1, 3
Let x = 131/15 - 37/5. Factor -1 - 1/3*t**2 - x*t.
-(t + 1)*(t + 3)/3
Factor -2/7*s**2 + 0*s + 0*s**3 + 2/7*s**4 + 0.
2*s**2*(s - 1)*(s + 1)/7
Let i(g) be the third derivative of -g**7/105 + g**6/30 - g**5/30 - 4*g**2. Determine b, given that i(b) = 0.
0, 1
Suppose 0 = 5*u - 3*a - 29, -12 = -u + 3*a + 1. Suppose u = f - 1. Factor 6/7*y**f - 10/7*y**4 + 2/7*y**2 + 2/7*y**3 + 0 + 0*y.
2*y**2*(y - 1)**2*(3*y + 1)/7
Let h(j) be the second derivative of -j**5/2 - j**4 + 12*j**3/5 - 8*j**2/5 - 9*j. Factor h(b).
-2*(b + 2)*(5*b - 2)**2/5
Determine p, given that 288 + 7*p**2 - 14*p**2 - 48*p + 9*p**2 = 0.
12
Factor -2/17 + 2/17*x**5 - 6/17*x + 6/17*x**4 + 4/17*x**3 - 4/17*x**2.
2*(x - 1)*(x + 1)**4/17
Let t(s) = s**3 - 3*s**2 - s - 1. Let u(d) = -2*d**3 + 7*d**2 + 2*d + 3. Let v(p) = 5*t(p) + 2*u(p). Factor v(z).
(z - 1)**2*(z + 1)
Let o = 7 - 5. Factor 2*z**3 + 0*z**2 + 2*z**2 + 0*z**o.
2*z**2*(z + 1)
Suppose 18 = 4*s - 2. Let u(k) be the third derivative of 2*k**2 + 0*k + 1/21*k**3 + 1/210*k**s + 1/42*k**4 + 0. Let u(x) = 0. Calculate x.
-1
Let h(g) = -3*g - g - 4 + 5*g**2 + 2*g**2 - 4*g**2. Let b(s) = -2*s**2 + 3*s + 3. Let o(v) = 4*b(v) + 3*h(v). Factor o(n).
n**2
Let x = -5 + 7. Suppose 2/5*o + 4/5 - 2/5*o**x = 0. Calculate o.
-1, 2
What is i in 0 - 1/9*i**5 + 0*i - 8/9*i**3 - 4/9*i**2 - 5/9*i**4 = 0?
-2, -1, 0
Factor 3/5*t**4 + 6/5*t**3 + 3/5 - 6/5*t**2 - 3/5*t - 3/5*t**5.
-3*(t - 1)**3*(t + 1)**2/5
Let y(g) be the third derivative of -g**5/120 + g**4/48 + 8*g**2. Find m, given that y(m) = 0.
0, 1
Let k(g) = -g**5 + g**3 - g. Let j(y) = -11*y**5 + 21*y**3 + 10*y**2 - 6*y. Let i(s) = j(s) - 6*k(s). Let i(h) = 0. Calculate h.
-1, 0, 2
Factor 2*g + 4/15 + 18/5*g**2.
2*(3*g + 1)*(9*g + 2)/15
Let a be 25/(-10) + 3 + (-11)/66. Determine o so that a*o**2 + 1/3*o**3 + 0*o + 0 = 0.
-1, 0
Factor 5*q**3 - 77*q + 812*q + 625*q**2 - 520*q**2 + 1715.
5*(q + 7)**3
Find u such that 4*u + 0 - 20*u**4 - u + 22*u**2 + 0*u**4 + 21*u**5 - 24*u**3 - 2 = 0.
-1, -1/3, 2/7, 1
Let k(x) be the first derivative of -x**5/10 + 3*x**4/8 - x**3/2 + x**2/4 - 7. Find j such that k(j) = 0.
0, 1
Let r = -30 - -32. Factor -m**r + 0 + 2/3*m.
-m*(3*m - 2)/3
Suppose -2*q = -0 - 6. Let w(u) = -u**3 + u + 3. Let x be w(0). Factor -9*c**3 + q*c + 0*c - 3*c**x - 3*c**2 - 6*c**2.
-3*c*(c + 1)*(4*c - 1)
Suppose x - 3*x + 4 = 0. What is t in 136*t**x + 80*t - 9 - 55*t**3 + 3*t**3 - 37 + 14 - 104*t**4 - 28*t**5 = 0?
-2, -1, 2/7, 1
Suppose 5*w = 5*x - 20, 4*w - 3*x + 5 = -7. Suppose w*z = 2*z - 10. Determine p so that 3*p**3 + p**z - 6*p**4 - 6*p**5 + 8*p**5 = 0.
0, 1
Let d(j) be the second derivative of -j**9/60480 - j**8/8960 - j**7/3360 - j**6/2880 - j**4/12 - j. Let h(q) be the third derivative of d(q). Factor h(y).
-y*(y + 1)**3/4
Let g = 321/424 - 7/53. Let z(v) be the third derivative of -v**3 + 0*v + g*v**4 + 0 + 4*v**2 + 1/40*v**6 - 1/5*v**5. Let z(d) = 0. Calculate d.
1, 2
Let x be ((-54)/(-30) + -2)*5/(-8). What is y in 0*y + 0 + 1/8*y**4 + x*y**2 - 1/4*y**3 = 0?
0, 1
Find y, given that 5/2*y**4 + 1/2*y**5 + 5*y**2 + 1/2 + 5/2*y + 5*y**3 = 0.
-1
Let y(q) = -26*q**2 + 26. Let w(z) = -416*z**2 + 416. Let j(p) = 4*w(p) - 65*y(p). Let r(s) = -5*s**2 + 5. Let k(m) = 2*j(m) + 11*r(m). Factor k(g).
-3*(g - 1)*(g + 1)
Let f(u) be the third derivative of u**6/540 - u**4/108 + 3*u**2. Factor f(b).
2*b*(b - 1)*(b + 1)/9
Let k(n) be the first derivative of 1/27*n**6 + 4/15*n**5 + 4/9*n**2 - 1 + 0*n + 8/9*n**3 + 13/18*n**4. Factor k(z).
2*z*(z + 1)**2*(z + 2)**2/9
Let m(v) be the third derivative of 0 + 0*v - 1/80*v**6 - 5*v**2 + 1/16*v**4 + 1/2*v**3 - 1/20*v**5. Factor m(l).
-3*(l - 1)*(l + 1)*(l + 2)/2
Let u(c) be the second derivative of -c**6/10 - 9*c**5/20 - 3*c**4/4 - c**3/2 + 8*c. What is k in u(k) = 0?
-1, 0
Let b = -4 - 29. Let p be -2*(b/(-18))/(-11). Factor -p*s**5 + 0*s - 1/3*s**3 + 0 - 2/3*s**4 + 0*s**2.
-s**3*(s + 1)**2/3
Factor -1 - l**4 + 2*l**3 + l + 0*l**3 + 2*l**4 - 3*l.
(l - 1)*(l + 1)**3
Find i, given that -2 - 14*i + 2*i**5 + 2 + 16*i - 4*i**3 = 0.
-1, 0, 1
Let r(d) be the first derivative of 2*d**3/39 - 2*d/13 - 60. What is l in r(l) = 0?
-1, 1
Let g(k) be the first derivative of k**3/6 + 3*k**2/2 + 5*k/2 + 26. What is l in g(l) = 0?
-5, -1
Let l(s) be the third derivative of s**6/48 + 13*s**5/120 + s**4/12 - s**3/3 - 12*s**2. Factor l(r).
(r + 1)*(r + 2)*(5*r - 2)/2
Let p(v) = -v**2 - 10*v - 20. Let d be p(-6). Let j(k) be the first derivative of 1 + 68*k**2 - 16*k - 50*k**5 + 275/2*k**d - 140*k**3. Let j(w) = 0. What is w?
2/5, 1
Let w(i) be the second derivative of 3*i**5/20 - i**3/2 + 12*i. Find z, given that w(z) = 0.
-1, 0, 1
Factor -5/6*n**2 - 5 - 35/6*n.
-5*(n + 1)*(n + 6)/6
Let f(o) be the first derivative of 3*o**3 + 6*o**2 + 3*o - 9. Determine h, given that f(h) = 0.
-1, -1/3
Find g, given that -16*g**2 - 65 - 32*g**3 - 4*g**5 - 20*g**4 + 65 = 0.
-2, -1, 0
Let v(i) = -i - 5. Let z be v(-7). Factor -z*f**3 - 5 + 2*f**2 + 0 + 5.
-2*f**2*(f - 1)
Let y(d) = 4*d - 6. Let g be y(2). Suppose -1/5*f - 1/5*f**g + 0 = 0. Calculate f.
-1, 0
Let b be (-45)/6*16/36 - -4. Find d such that b - d + 0*d**4 - 2/3*d**2 + 4/3*d**3 - 1/3*d**5 = 0.
-2, -1, 1
Factor 2*p**2 + 23 - 21 + 2*p + 2*p.
2*(p + 1)**2
Let s(u) be the second derivative of -u**2 - 1/21*u**3 - 1/42*u**4 + 2*u + 0 - 1/210*u**5. Let i(b) be the first derivative of s(b). Solve i(l) = 0 for l.
-1
Let c be -3 + (-287)/96 - -6. Let k(w) be the third derivative of 1/480*w**6 + 0 + 0*w + 0*w**3 + w**2 + 0*w**5 - c*w**4. What is g in k(g) = 0?
-1, 0, 1
Find a, given that -5*a**4 + 3*a**5 + 12*a - 3 - 10*a**4 + 16*a + 30*a**3 - 13*a - 30*a**2 = 0.
1
Let q(m) = -m**2 + 17*m + 19. Let v be q(17). Suppose -4*t = 2*y - 3 - v, -2*y + 2*t = 2. Factor 2/3*x**y - 2/3 + 2*x - 2*x**2.
2*(x - 1)**3/3
Let l be -4 - -2 - (-8)/2. Factor -2*y**4 + l*y**3 + 0*y**2 + 7*y**5 + 2*y**2 + 0*y**2 - 9*y**5.
-2*y**2*(y - 1)*(y + 1)**2
Suppose 14/9*n**2 - 14/9*n**4 + 8/3*n**5 + 0 - 2/9*n - 22/9*n**3 = 0. What is n?
-1, 0, 1/4, 1/3, 1
Let i(y) be the third derivative of y**5/270 + y**4/12 + y**2 + 65*y. Factor i(m).
2*m*(m + 9)/9
Suppose -8*p + 72 = 56. Determine b, given that 4/3 - 2/3*b**3 + 0*b**p + 2*b = 0.
-1, 2
Suppose 0 = 5*r - 20, -2*w + 2 = 4*r - 18. Let p be 5/w - (-6)/12. Factor 6 - 3*x**2 - x**p - 5 + 3.
-(x - 1)*(x + 2)**2
Let r be (-14)/28*(0 - 0). Let z(k) be the second derivative of -2*k - 1/20*k**5 + 0*k**2 + 0*k**3 + 0*k**4 + r + 1/30*k**6. Factor z(f).
f**3*(f - 1)
Let o(k) be the second derivative of k**7/42 + k**6/10 + k**5/10 - k**4/6 - k**3/2 - k**2/2 - 11*k. Factor o(v).
(v - 1)*(v + 1)**4
Let u(y) be the second derivative of y**6/135 - y**4/54 + 10*y. Factor u(l).
2*l**2*(l - 1)*(l + 1)/9
Let k(m) be the first derivative of -m**6/6 + m**5 - 3*m**4/2 - 4*m**3/3 + 4*m**2 + 10. Determine v, given that k(v) = 0.
-1, 0, 2
Let d(y) be the third derivative of y**7/360 + y**6/80 + y**5/60 - y**4/24 - 2*y**2. Let q(u) be the second derivative of d(u). Factor q(m).
(m + 1)*(7*m + 2)
Solve 4 + 15*g + 15*g**2 + 80*g**3 + 5*g**2 - 70*g**3 - g**5 = 0 for g.
-1, 4
Factor 4/3*k**2 + 0 + 5/3*k**4 + 1/3*k**5 + 8/3*k**3 + 0*k.
k**2*(k + 1)*(k + 2)**2/3
Let r be 28/(-5)*(-13 + 474/42). Factor -r*k**2 - 33/5*k - 21/5*k**3 - 6/5.
-3*(k + 1)**2*(7*k + 2)/5
Suppose 6*y + 0*y = 18. Let i(m) be the third derivative of -1/210*m**7 + 0*m**4 - 1/180*m**6 + 0*m + 2*m**2 + 0*m**5 + 0 + 0*m**y. Factor i(x).
-x**3*(3*x + 2)/3
Let i(l) = l**2. Let p(d) be the third derivative of d**6/40 - d**5/12 - d**4/8 + 5*d**2. Let y(k) = 5*i(k) + p(k). Solve y(c) = 0 for c.
-1, 0, 1
Find c such that -32/15*c + 2/15*c**2 + 128/15 = 0.
8
Suppose -5*q = d - 14, 0*d + 2*q = -d + 8. Suppose d*z + z = 0. Let -6*i - 3*i**2 + 3*i - i**3 + z - 1 = 0. What is i?
-1
Let b be 2*1*(-3)/(-3). Factor -n - 9*n**b - 6*n**4 + n + 3*n + 9*n**3 + 3*n**4.
-3*n*(n - 1)**3
Find o such that 5*o + 4*o**4 + 0*o**2 + 20*o**3 + 32*o**2 + 11*o = 0.
-2, -1, 0
Let p(b) be the third derivative of 2*b**7/105 - 2*b**6/45 + 7*b**5/180 - b**4/72 - 15*b**2 + 3*b. Factor p(j).
j*(2*j - 1)**2*(3*j - 1)/3
Let d be -1 - -3 - (-4 - (-44)/8). Factor 1/2*n**3 - d*n + 1/2*n**2 - 1/2.
(n - 1)*(n + 1)**2/2
Let v(i) be the first derivative of 0*i**4 + 4/3*i**3 - 2/5*i**5 + 2 - 2*i + 0*i**2. Factor v(h).