- 2/5*q**2 + r + 0*q + 2/5*q**3 = 0.
-1, 0, 1
Suppose 3*o - 24 = -4*w + o, -5*w + 43 = -4*o. Let f be -2*(42/(-4))/w. Factor 8/3*p**4 - 14/3*p**f + 0 - 4/3*p**2 + 0*p.
2*p**2*(p - 2)*(4*p + 1)/3
Let p(h) be the third derivative of h**5/30 - h**4/12 - 13*h**2. Find u, given that p(u) = 0.
0, 1
Let b(j) be the second derivative of j**6/165 + j**5/110 - j**4/33 + 66*j. Suppose b(d) = 0. What is d?
-2, 0, 1
Find p such that 0 - 2/3*p**2 - 2/3*p + 2/3*p**3 + 2/3*p**4 = 0.
-1, 0, 1
Let k(b) = b**3 - 2*b**2 - b - 2. Let n be k(3). Let c be n/6 + 3/(-9). Factor 1/3*l**3 + c*l**4 - 1/3*l**2 + 0 - 1/3*l.
l*(l - 1)*(l + 1)**2/3
Suppose 1 = 5*t + 26. Let b(a) = a + 7. Let n be b(t). Let 6/7*x**n - 2/7*x**3 + 2/7 - 6/7*x = 0. What is x?
1
Let t(o) be the first derivative of -81*o**5/5 + 9*o**4 + 67*o**3 + 48*o**2 + 12*o + 4. Solve t(w) = 0.
-1, -1/3, -2/9, 2
Let o(v) = 4*v**2 - 1 + v**2 + 3 - v**3 + 0. Let n be o(5). Factor 9/5*m**n - 3*m + 6/5.
3*(m - 1)*(3*m - 2)/5
Let i(o) be the third derivative of -1/50*o**5 + 1/20*o**4 + 0*o - 3*o**2 + 1/300*o**6 + 0 - 1/15*o**3. Factor i(f).
2*(f - 1)**3/5
Let b = 1/410 + 163/410. Factor 18/5 + 12/5*t + b*t**2.
2*(t + 3)**2/5
Let z(k) = -k**2 + k - 1. Let o(b) = -75*b**2 + 70*b - 25. Let q(i) = o(i) - 15*z(i). Let q(w) = 0. Calculate w.
1/4, 2/3
Suppose -7*g - 10 = -38. Let v(x) be the third derivative of 0*x**3 - 1/60*x**g + 1/300*x**6 + 0*x + 0 + 1/525*x**7 - x**2 - 1/150*x**5. Factor v(c).
2*c*(c - 1)*(c + 1)**2/5
Let b(m) be the second derivative of -m**4/12 - m**3/2 - 5*m**2/2 - 4*m. Let z(q) = 4*q**2 + 12*q + 21. Let n(o) = 26*b(o) + 6*z(o). Factor n(u).
-2*(u + 1)*(u + 2)
Let k(a) = -12*a**5 - 23*a**4 + a**3 + 19*a**2 + 13*a + 2. Let o(r) = -r**3 + r**2. Let h(c) = -5*k(c) - 10*o(c). Determine u so that h(u) = 0.
-1, -2/3, -1/4, 1
Let f be (-14)/(-10) - (-1 + 1 + 1). Solve 0*l - 6/5*l**4 + 0 + f*l**2 + 4/5*l**3 = 0 for l.
-1/3, 0, 1
Factor -1/5*g**2 - 7/5*g + 0.
-g*(g + 7)/5
Let p(f) be the first derivative of -2 + 3/5*f**2 - 1/5*f**3 - 3/5*f. Let p(a) = 0. What is a?
1
Factor -6 - 3*o - 6*o**2 + 9*o**2 + 6*o.
3*(o - 1)*(o + 2)
Suppose 0 = -5*a + 4*r + 7 + 23, 3*r = -15. Solve 28*i - 24*i**a + 6*i**4 - 28*i**3 + 0*i**2 + 8 + 10*i**4 = 0 for i.
-1, -1/4, 1, 2
Let -100/3*n**4 - 84*n**3 + 0 - 4*n**5 - 36*n**2 + 72*n = 0. What is n?
-3, 0, 2/3
Solve 12/5*x**2 + 2*x**3 + 2/5*x**4 - 16/5 - 8/5*x = 0.
-2, 1
Factor -40 - 3*d**2 + 400*d - 444*d - d**2.
-4*(d + 1)*(d + 10)
Let p(g) = g**2 - 3*g + 5. Let i be p(2). Solve -3/5*l**i + 3/5*l + 0*l**2 + 0 = 0.
-1, 0, 1
Solve 16*b**3 - 65 - 4*b**5 - 8*b**2 - 4*b**4 + 4*b**4 + 73 - 12*b = 0 for b.
-2, -1, 1
Factor -527 + 503 - 49*j - 15*j**2 - 17*j.
-3*(j + 4)*(5*j + 2)
Let m(d) be the second derivative of d**6/345 + 6*d**5/115 + 8*d**4/23 + 64*d**3/69 + 20*d. Determine c so that m(c) = 0.
-4, 0
Let q(l) be the first derivative of l**6/6 - l**4/2 + l**2/2 + 1. Factor q(u).
u*(u - 1)**2*(u + 1)**2
Let h(a) = -6*a**4 + 7*a**3 - a**2 + 5. Let q(y) = 5*y**4 - 6*y**3 + y**2 - 4. Let g = -8 - -4. Let u(f) = g*h(f) - 5*q(f). Determine c, given that u(c) = 0.
0, 1
Suppose 2*b - 2*n + 12 = 0, 0 = -0*b + 5*b + 3*n + 22. Let o = 9 + b. Factor 2/3*f**o + 0 + 0*f + 0*f**2 - 2/3*f**3.
2*f**3*(f - 1)/3
Suppose -x - 10*x + 9*x = 0. Factor 24/7*n**2 - 26/7*n**3 + x + 12/7*n**4 - 8/7*n - 2/7*n**5.
-2*n*(n - 2)**2*(n - 1)**2/7
Let p be 3 + ((-6)/(-9))/((-112)/456). Factor 0 - 2/7*c**2 + p*c.
-2*c*(c - 1)/7
Factor 0 + 0 + 2*p**3 - 33*p**2 + 29*p**2.
2*p**2*(p - 2)
Let j be (-35 + 36)/((8/(-1))/(-2)). Factor 1/2*f**2 - j*f**3 + 0*f + 0.
-f**2*(f - 2)/4
Let h(y) = -y**2 - 11*y + 24. Let z be h(-12). Suppose -z = -6*r + 2*r. Factor -1/4 + 3/4*x**2 + 0*x - 1/2*x**r.
-(x - 1)**2*(2*x + 1)/4
Let a be (12/(-21))/((-90)/35). Find o such that a*o**3 + 2/9*o**2 - 2/9 - 2/9*o = 0.
-1, 1
Let d(s) be the second derivative of -2*s + 0 + 1/12*s**4 + 1/12*s**3 + 0*s**2. Factor d(u).
u*(2*u + 1)/2
Let y(f) = -f**3 + 13*f**2 + 18*f + 2. Let q(p) = -3*p**3 + 51*p**2 + 72*p + 9. Let a(o) = 2*q(o) - 9*y(o). What is n in a(n) = 0?
-1, 0, 6
Factor 0 + 4/15*q**2 + 2/15*q - 2/5*q**3.
-2*q*(q - 1)*(3*q + 1)/15
Let x(k) be the second derivative of -k**5/90 - k**4/9 - 4*k**3/9 - k**2 - 3*k. Let l(u) be the first derivative of x(u). Determine d, given that l(d) = 0.
-2
Let d(z) be the first derivative of 8/3*z**3 + 0*z + 3*z**4 + 8 + 4/5*z**5 + 0*z**2. Suppose d(n) = 0. Calculate n.
-2, -1, 0
Let f(s) be the third derivative of s**5/180 - s**4/36 - 3*s**2. Factor f(w).
w*(w - 2)/3
Suppose 2/13*o**2 + 0*o + 0 = 0. Calculate o.
0
Let p(n) be the second derivative of -n**7/14 + 3*n**6/10 - 9*n**5/20 + n**4/4 - n. Suppose p(x) = 0. Calculate x.
0, 1
Let q = 4292291/137654 + 1/12514. Let z = q - 31. Factor 4/11*u + z*u**3 + 0 + 6/11*u**2.
2*u*(u + 1)*(u + 2)/11
Let n = 1 + -1. Suppose 21 = 3*p - 0*q - 3*q, n = p + 5*q + 17. Factor 2*s + 3*s**2 - 3*s**2 - s**5 - 4*s**p + 3*s**5.
2*s*(s - 1)**2*(s + 1)**2
Let b(z) = -4*z**3 + 16*z**2 - 4*z. Let u(x) = -x**3 + 5*x**2 - x. Let f(d) = -3*b(d) + 8*u(d). Find n, given that f(n) = 0.
0, 1
Let u = 764/15 + -151/3. Factor -1/5*g**2 - 2/5 - u*g.
-(g + 1)*(g + 2)/5
Let t(s) = -2 + 2 + 14*s + 6*s**2 - 17. Suppose -85 = 2*n - 7*n. Let v(w) = -2*w**2 - 5*w + 6. Let b(u) = n*v(u) + 6*t(u). What is d in b(d) = 0?
0, 1/2
Let p(c) be the third derivative of -1/840*c**7 + 3*c**2 - 1/40*c**5 + 1/120*c**6 + 1/24*c**4 + 0 - 1/24*c**3 + 0*c. Factor p(z).
-(z - 1)**4/4
Let a be ((-2)/16)/((-26)/8 - -3). Find m, given that -3/4*m + 1/2*m**2 - a = 0.
-1/2, 2
Suppose -a - 5*l + 58 = 2*a, -l = -a + 14. Let n be 1*(0 + 4)/a. Solve 0 - 1/4*i + n*i**2 = 0.
0, 1
Let z be ((-9)/396)/((-3)/8). Let o = 29/66 + z. Find t, given that 1/2*t**2 - 1/2 - 1/2*t**3 + o*t = 0.
-1, 1
Let p be (-2)/(0 - (-20)/(-15)). Factor -5/4*t + p*t**2 + 1/4.
(2*t - 1)*(3*t - 1)/4
Let q be 2/(-4) + (-99)/(-154). Let g = 5/14 + q. Find d such that d + 0 + g*d**3 - 3/2*d**2 = 0.
0, 1, 2
Let n be (-4)/(-12) + (-57)/9. Let a(r) = -2*r**2 - 3*r - 5. Let p(z) = -z**2 - z - 2. Let w(f) = n*a(f) + 15*p(f). Let w(g) = 0. What is g?
0, 1
Let q(s) = -s**3 + 9*s. Let u be q(-3). Factor -2/3*g - 2/3*g**2 + u.
-2*g*(g + 1)/3
Let r(i) be the first derivative of -3*i**5 - 21*i**4/4 - 2*i**3 - 7. Factor r(f).
-3*f**2*(f + 1)*(5*f + 2)
Let r(n) be the third derivative of n**7/140 + n**6/30 + n**5/30 - 3*n**2. Factor r(f).
f**2*(f + 2)*(3*f + 2)/2
Let i(t) be the third derivative of t**5/60 - 5*t**4/24 + 18*t**2. Suppose i(d) = 0. Calculate d.
0, 5
Let w(u) be the second derivative of -u**6/30 - u**5/10 + 27*u. Factor w(a).
-a**3*(a + 2)
Let p(x) be the second derivative of -x**8/13440 + x**7/2520 + x**4/2 - 2*x. Let a(l) be the third derivative of p(l). Factor a(k).
-k**2*(k - 2)/2
Let y = 14 - 9. Suppose 15 = y*w, 5*r - r - 4*w = -12. Factor -2*b**5 + 0*b**2 + 4/3*b**3 + 0*b + r - 2/3*b**4.
-2*b**3*(b + 1)*(3*b - 2)/3
Let f(u) be the first derivative of -15*u**4/4 + 18*u**3 - 18*u**2 - 24*u + 8. Find m such that f(m) = 0.
-2/5, 2
Suppose -3*c + 2 = -7. Let j = 8 + -8. What is t in -1/4*t**4 + j*t + 1/4*t**2 + 0*t**c + 0 = 0?
-1, 0, 1
Let p(l) = l**3 - 3*l + 2. Let n be p(2). Suppose r = 3*r - n. Determine g so that 5/3*g**4 + 10/3*g**r + 1/3*g**5 + 5/3*g + 10/3*g**3 + 1/3 = 0.
-1
Factor 0 + 2/13*m**3 - 6/13*m**2 + 4/13*m.
2*m*(m - 2)*(m - 1)/13
Let p be 250/15*(-2)/4. Let z = p + 10. Factor -4/3*j + z*j**4 + 2/3*j**5 - 4/3*j**2 + 2/3*j**3 - 1/3.
(j - 1)*(j + 1)**3*(2*j + 1)/3
Let m(g) be the second derivative of g**4/84 - g**3/21 + g**2/14 - g. Suppose m(u) = 0. What is u?
1
Let v(j) be the first derivative of -7*j**6/900 + j**5/25 + j**4/15 + j**3 - 3. Let g(k) be the third derivative of v(k). What is w in g(w) = 0?
-2/7, 2
Suppose -2*v = 5*f - 8, -2*f - 5*v + 1 - 2 = 0. Determine q so that 1/2*q**f + 0 - 1/2*q**3 + q = 0.
-1, 0, 2
Let p(a) be the second derivative of -a**7/210 - a**6/150 + a**5/100 + a**4/60 - 40*a. Suppose p(s) = 0. Calculate s.
-1, 0, 1
Factor u**2 - 187*u - 205*u + 3*u**2 + 344*u.
4*u*(u - 12)
Find s such that -20/7*s**2 - 68/7*s - 24/7 = 0.
-3, -2/5
Let s(p) be the first derivative of 1/10*p**2 - 1/15*p**3 + 2/5*p - 5. Factor s(d).
-(d - 2)*(d + 1)/5
Determine y, given that 4/11*y + 2/11*y**2 + 2/11 = 0.
-1
Let s be -5 + -2 + 