j**3/21 + j**2/7 + 3*j. Factor b(m).
2*(m + 1)**2/7
Let 28*d**3 + 60*d**2 + 108/7 - 468/7*d = 0. What is d?
-3, 3/7
Let x = 16 - 10. Let u(o) be the third derivative of 1/12*o**5 + 2/3*o**3 + 0 + 3*o**2 + 0*o + 1/3*o**4 + 1/120*o**x. Factor u(n).
(n + 1)*(n + 2)**2
Let a = 3 + 0. Solve 3*c**3 + 3*c - 3 + 3*c**2 + c**a + 4 - 3*c**3 = 0.
-1
Let x(q) = 49*q**3 + 31*q**2 - 104*q + 20. Let y(j) = -97*j**3 - 63*j**2 + 207*j - 40. Let n(a) = -7*x(a) - 4*y(a). Solve n(p) = 0 for p.
-2, 2/9, 1
Suppose 4*u + 1 = -3. Let b be 1 - u - (-6)/(-9). Solve -13/3*j**4 - 2/3*j**2 + 11/3*j**3 + b*j**5 + 0*j + 0 = 0.
0, 1/4, 1, 2
Factor 2*j - 16/9 - 2/9*j**2.
-2*(j - 8)*(j - 1)/9
Factor 20*z**2 - 5*z**3 - 12*z - 90 + 10*z**3 - 3*z.
5*(z - 2)*(z + 3)**2
What is h in 0 + 14/15*h - 2/15*h**2 = 0?
0, 7
Let w be (8/6)/(6/9). Let t be 4 + -3 + w + -1. Factor 1/5*y + 1/5*y**t + 0.
y*(y + 1)/5
Let g(i) be the third derivative of i**6/40 - i**5/20 - 4*i**2. Factor g(p).
3*p**2*(p - 1)
Let b(z) = 6*z**5 + 13*z**4 - 13*z**3 - 13*z**2. Let a(u) = -4*u**5 - 9*u**4 + 9*u**3 + 9*u**2. Let s(t) = 7*a(t) + 5*b(t). Factor s(v).
2*v**2*(v - 1)*(v + 1)**2
Let h(k) be the third derivative of k**8/840 - 2*k**7/525 - k**6/300 + k**5/75 + 31*k**2. Determine v, given that h(v) = 0.
-1, 0, 1, 2
Let b(x) be the third derivative of -1/24*x**4 + 0*x + 2*x**2 - 1/120*x**5 + 0 + 0*x**3. Determine j, given that b(j) = 0.
-2, 0
Let x(w) be the second derivative of w**5/150 + w**4/9 + 28*w**3/45 + 8*w**2/5 - 10*w. Suppose x(n) = 0. What is n?
-6, -2
Let i be (8/(-168))/(-1 + 0). Let q(z) be the second derivative of -1/35*z**5 - 1/7*z**2 + 1/35*z**6 + 0 + 2*z - i*z**4 + 1/7*z**3 - 1/147*z**7. Factor q(l).
-2*(l - 1)**4*(l + 1)/7
Suppose -5*k = -2*s - 16, 4*s + 4*k + 0*k = 24. Let p(g) be the first derivative of 2 - 1/2*g**4 + 0*g**s - 1/5*g**5 - 1/3*g**3 + 0*g. Factor p(l).
-l**2*(l + 1)**2
Let t(i) be the second derivative of i**7/7560 - i**6/1080 - i**5/120 - i**4/3 - 5*i. Let z(f) be the third derivative of t(f). Let z(d) = 0. Calculate d.
-1, 3
Factor -2/7*z**4 + 6/7*z - 6/7*z**3 + 0 + 2/7*z**2.
-2*z*(z - 1)*(z + 1)*(z + 3)/7
Let u(x) be the first derivative of -x**4/24 + 2*x**3/9 - 5*x**2/12 + x/3 + 4. Factor u(q).
-(q - 2)*(q - 1)**2/6
Let a(n) be the second derivative of 0 - 3*n + 0*n**5 - 1/120*n**6 + 0*n**3 + 0*n**2 + 1/48*n**4. Factor a(p).
-p**2*(p - 1)*(p + 1)/4
Let f = -55 + 221/4. Determine s so that 0*s - f + 1/4*s**2 = 0.
-1, 1
Let i(h) be the second derivative of -20*h**7/21 + 62*h**6/15 - 26*h**5/5 - h**4/3 + 4*h**3 - 19*h. Solve i(w) = 0 for w.
-2/5, 0, 1, 3/2
Let a = -3/91 + 100/273. Let v = 34 + -101/3. Factor 1/3 - v*t**2 + 1/3*t - a*t**3.
-(t - 1)*(t + 1)**2/3
Let n = 9 + -4. Determine r, given that -4*r**4 + 4*r**2 + 12*r**4 - 10*r**3 - 2*r**5 + 0*r**n = 0.
0, 1, 2
Let a(g) = -g + 13. Let o be a(9). Let o*j**4 - 7*j**5 - 2*j**4 + 9*j**5 - 2*j**2 - 2*j**3 = 0. Calculate j.
-1, 0, 1
Let o(r) be the third derivative of -r**9/60480 + r**8/10080 - r**5/30 - 2*r**2. Let t(w) be the third derivative of o(w). What is m in t(m) = 0?
0, 2
Let q = 66 - 62. Suppose -c = -t, 2*t - 10 = -3*c - 0*c. Let -6/5*d + 4/5 - 2/5*d**c - 2/5*d**q + 6/5*d**3 = 0. Calculate d.
-1, 1, 2
Let j(w) = -w**2 - 5*w - 3. Let b be j(-3). Let h(o) = o - 6. Let s be h(10). Factor 0*z**2 + 2*z**b - 2*z**4 + s*z**4 - 2*z**2 - 2*z**5.
-2*z**2*(z - 1)**2*(z + 1)
Let u be -3 + (0/(-3))/(-3). Let j be 4 - (6*-1)/u. Let 0*z + 0 + 2/11*z**j = 0. Calculate z.
0
Let l(x) = -3*x + 2. Let b be l(-2). Suppose 0 = -b*d + 6*d. Determine j so that -1/4*j**2 + d + 0*j = 0.
0
Let z(s) = -s**3 - 8*s**2 - 8*s - 7. Let k be z(-4). Let a = 119/3 + k. Factor -6 - 4*j - a*j**2.
-2*(j + 3)**2/3
Let j be 0/(39/45 + 22/165). Let y = 21 + -83/4. Factor j*t**2 - 1/4*t**3 + y*t + 0.
-t*(t - 1)*(t + 1)/4
Let x be (-469)/(-91) + -1 - 4/26. Let s(p) be the first derivative of 0*p**x - 1/5*p - 2 + 0*p**2 - 1/25*p**5 + 2/15*p**3. Determine l, given that s(l) = 0.
-1, 1
Let r(f) = -2*f**2 - 37*f - 18. Let m be r(-18). Factor m + 1/4*k - 1/4*k**2.
-k*(k - 1)/4
Suppose 0 = 2*o + r + 26, -51 = 3*o - 2*r - 12. Let m be 12/(-30) + o/(-20). Factor 1/2 + 1/4*t - m*t**2.
-(t - 2)*(t + 1)/4
Let h(m) be the second derivative of -m**7/27 + 19*m**6/135 + 2*m**5/9 - 40*m**4/27 + 32*m**3/27 + 16*m**2/9 - 15*m. Solve h(y) = 0.
-2, -2/7, 1, 2
Let v(f) be the first derivative of -16/7*f + 8/7*f**2 + 3 - 4/21*f**3. Factor v(u).
-4*(u - 2)**2/7
Let i(c) be the third derivative of c**8/1680 + 2*c**7/525 + c**6/120 + c**5/150 - 9*c**2. Suppose i(m) = 0. What is m?
-2, -1, 0
Let i = 1438/165 + -90/11. Let b = i + -1/5. Factor 1/3 + t**2 - b*t**3 - t.
-(t - 1)**3/3
Let m = 5 + -5. Let o be ((-3)/9)/(8/(-6)). Factor -1/4*b**3 + m + o*b**2 + 0*b.
-b**2*(b - 1)/4
Factor 0 + 17/2*l**2 + 3*l + 5/2*l**3.
l*(l + 3)*(5*l + 2)/2
Suppose 0 = -0*b + 3*b. Let r(z) be the third derivative of -2/3*z**3 + 0 - 1/60*z**5 + 1/6*z**4 + b*z + z**2. Suppose r(l) = 0. Calculate l.
2
Let i(o) be the first derivative of -3*o**4/4 - 16*o**3/3 - 15*o**2/2 + 18*o + 31. Determine a so that i(a) = 0.
-3, 2/3
Suppose 5*q + 2 = -8. Let b = q + 2. Factor 6/5*l + b*l**2 - 2/5*l**3 - 4/5.
-2*(l - 1)**2*(l + 2)/5
Let f be (4/(-6))/((-10)/12). Let h(x) be the first derivative of 0*x**3 - 2 - 1/10*x**4 - f*x + 3/5*x**2. Factor h(t).
-2*(t - 1)**2*(t + 2)/5
Suppose 4 = 2*p, 0 = 2*f - 4*f - 4*p + 16. Let c(t) be the first derivative of 0*t**3 + 1/12*t**f + 0*t + 0*t**2 + 3. Factor c(n).
n**3/3
Let a = 50 - 16. Let p be a/(-51)*(-9)/2. Let 2/11*c**4 + 0 - 4/11*c**2 + 0*c + 2/11*c**p = 0. Calculate c.
-2, 0, 1
Let j(a) be the second derivative of -a**5/90 + 2*a**4/27 - 11*a. Factor j(m).
-2*m**2*(m - 4)/9
Let o = -5 + 7. Factor -4 + 2*k**3 - 2*k + 5 + k**4 - o.
(k - 1)*(k + 1)**3
Let q(w) = w**2 + 2*w. Suppose 4 = -3*m - 2. Let x be q(m). Suppose x - 2 + 6*v**2 - 4*v**2 = 0. Calculate v.
-1, 1
Let r(g) = 2*g + 4. Let l be r(0). Let q(n) be the third derivative of -2*n**2 + 1/2*n**5 - 4/3*n**3 + 0*n + 0 + n**l + 1/15*n**6. Determine f so that q(f) = 0.
-2, 1/4
Let u(h) be the first derivative of -8*h**3/15 + 2*h**2 - 8*h/5 + 14. Factor u(m).
-4*(m - 2)*(2*m - 1)/5
Let m(i) = i**3 - 3*i + 4. Let k be 0 + -7 + (-1 - -2). Let r(j) = -j**2 + j. Let g(f) = k*r(f) - 2*m(f). Let g(s) = 0. What is s?
-1, 2
Let r(w) be the first derivative of 4/5*w - 1/10*w**4 + 1/5*w**2 - 4/15*w**3 - 9. Factor r(s).
-2*(s - 1)*(s + 1)*(s + 2)/5
Let f(l) be the first derivative of 3 - 2/3*l**2 + 1/9*l**3 + 4/3*l. Factor f(t).
(t - 2)**2/3
Let p(y) = -8*y**4 - 6*y**3 + 4*y**2 - 6*y - 2. Let g(m) = 6*m + m**3 - 2*m + 0*m**4 + m**4 - 3*m. Let l(o) = 6*g(o) + p(o). Factor l(r).
-2*(r - 1)**2*(r + 1)**2
Let z(t) be the third derivative of t**7/210 - t**5/60 - 13*t**2. Determine k, given that z(k) = 0.
-1, 0, 1
Let v = 38 - 113/3. Let q(n) be the second derivative of 4*n + 1/12*n**4 + 0 + v*n**3 + 1/2*n**2. Factor q(c).
(c + 1)**2
Let v be ((-2)/(-10))/(6/10)*1. Let 4/3*d**2 + v - 5/3*d = 0. What is d?
1/4, 1
Let z(a) be the second derivative of a**7/21 + 2*a**6/15 - a**5/10 - a**4/3 + 2*a. Solve z(f) = 0 for f.
-2, -1, 0, 1
Let w(v) = 2*v**2 + 6*v - 3. Let s(l) = -9*l**2 - 24*l + 12. Let f(r) = 5*s(r) + 21*w(r). Let f(u) = 0. What is u?
1
Let o be 26/20*(92 - -6). Let a = -127 + o. Suppose -1/5*y**2 - 3/5*y**3 - 1/5*y**4 + a + 3/5*y = 0. What is y?
-2, -1, 1
Let a(j) be the first derivative of 35*j**4/24 - 5*j**3/9 + 16. Factor a(t).
5*t**2*(7*t - 2)/6
Let g = 1681/48 - 35. Let t(i) be the second derivative of -1/168*i**7 + 1/80*i**5 + 0*i**3 + g*i**4 + 0*i**2 - 2*i + 0 - 1/120*i**6. Factor t(k).
-k**2*(k - 1)*(k + 1)**2/4
Factor 2/13*y + 2/13 - 4/13*y**4 - 10/13*y**3 - 6/13*y**2.
-2*(y + 1)**3*(2*y - 1)/13
Factor 1/4*y**2 + 1/2*y**4 + 3/4*y**3 + 0 + 0*y.
y**2*(y + 1)*(2*y + 1)/4
Suppose 11*g - 26 + 4 = 0. Suppose 0 - 1/5*d**g + 1/5*d = 0. What is d?
0, 1
Let l(j) be the third derivative of j**5/60 - j**3/6 - 7*j**2 - 2. Factor l(g).
(g - 1)*(g + 1)
Factor 0*i + 0 - 1/10*i**2.
-i**2/10
Let z(j) be the third derivative of 1/15*j**5 + 0*j - 1/24*j**4 - 3/112*j**8 + 1/60*j**6 + 0 - 2/35*j**7 + 3*j**2 + 0*j**3. Factor z(f).
-f*(f + 1)**2*(3*f - 1)**2
Suppose 20 = c + 4*c. Let p(w) be the second derivative of 2*w - 1/9*w**3 + 1/6*w**c + 0*w