 = 0. Let u = y - -20. Let g(m) = u*a(m) + l(m). Solve g(q) = 0 for q.
-3, -1
Let l(h) be the second derivative of 40*h**4/3 - 5*h**3/12 + 155*h. Determine u, given that l(u) = 0.
0, 1/64
Let m = -359/78 + 62/13. Let t(x) be the first derivative of -m*x**4 + 0*x**2 - 1/6*x**3 + 9 + 0*x - 1/30*x**5. Factor t(a).
-a**2*(a + 1)*(a + 3)/6
Let c(h) be the third derivative of -1/120*h**6 - 6*h**2 - 1/24*h**4 + 1/30*h**5 + 0*h + 0*h**3 + 0. Factor c(z).
-z*(z - 1)**2
Suppose 4*p + 5*t = -12, 6 = -4*p - t + 10. Let q be 2/(p + (-20)/14). Factor -1/2*u**4 - 9*u**2 - 4 + q*u**3 + 10*u.
-(u - 2)**3*(u - 1)/2
Let d = -61 - -123. Let x = d - 44. Let s**3 - 3 + 5 - 2*s - 20*s**2 + x*s**2 + s**3 = 0. Calculate s.
-1, 1
Let c(h) be the first derivative of -2*h**5/5 - h**4/7 + 2*h**3/3 + 2*h**2/7 + 11. Determine d, given that c(d) = 0.
-1, -2/7, 0, 1
Let v be 3/(-2) - (-154)/84. Factor -v*b - 1/3*b**2 + 0.
-b*(b + 1)/3
Let d = 17 + -12. Let t(o) = 7*o**5 - 5*o**4 - 7*o**3 - 5*o + 5. Let x(k) = -4*k**5 + 3*k**4 + 4*k**3 + 3*k - 3. Let q(w) = d*x(w) + 3*t(w). Factor q(c).
c**3*(c - 1)*(c + 1)
Suppose 44 = -a + 3*a. Suppose -5*l + a + 3 = 0. Factor 6*q**4 - 3*q**2 + 3*q - 3*q**2 - 3*q**l + 0*q**5 + 0*q**2.
-3*q*(q - 1)**3*(q + 1)
Suppose 5*v - 13 = f, 0 = 4*v + f - 2*f - 11. Factor 13*p**3 + 14*p**3 + p + v*p - 30*p**3.
-3*p*(p - 1)*(p + 1)
Solve 800/7 + 2/7*t**2 - 80/7*t = 0.
20
Let c be 181/2*10/(-35). Let a = 26 + c. Factor 0 + 1/7*b**3 - a*b + 0*b**2.
b*(b - 1)*(b + 1)/7
Factor 17/2*h**4 + 63/2*h**3 + 0 - 81/2*h**2 + 0*h + 1/2*h**5.
h**2*(h - 1)*(h + 9)**2/2
Suppose 3*c = 3*k, 5*c - 2*k - 5 = 4. Suppose -2*d - 6 = -12. Factor d*f**4 - 3*f**c - f**2 + 0*f**4 + f**2.
3*f**3*(f - 1)
Suppose -45 = -3*o + 66. Determine z so that 2*z**4 - o*z**3 + 34*z**4 + 4 - 27*z**3 - 32*z + 88*z**2 - 32*z**3 = 0.
1/3, 1
Suppose 24 = 5*h + c, -2*h = -0*h - 2*c. Find a such that -35/3*a**5 + 0 + 35/3*a**3 + 0*a - 10/3*a**2 + 10/3*a**h = 0.
-1, 0, 2/7, 1
Suppose 194*m - 178*m - 48 = 0. Let m*k**3 - 27/5*k**5 + 9*k**2 + 0*k - 9*k**4 - 12/5 = 0. What is k?
-1, 2/3
Let a = -5/2731 - -185753/24579. What is f in -320/9*f + 256/9 + a*f**2 - 4/9*f**3 = 0?
1, 8
Let u(x) be the second derivative of 7/3*x**3 - 7/10*x**5 + 0 + 2/3*x**4 + 9*x - 4*x**2. Suppose u(c) = 0. What is c?
-1, 4/7, 1
Factor -10*y**4 + 18*y**3 - y**2 + 68*y**5 - 131*y**5 - 13*y**2 + 65*y**5 + 4*y.
2*y*(y - 2)*(y - 1)**3
Let r(w) be the third derivative of -w**6/540 + 7*w**5/270 - 7*w**4/108 - 5*w**3/9 + 25*w**2. Find s such that r(s) = 0.
-1, 3, 5
Let d(s) = 4*s**2 - 9*s + 7. Let o be (-39)/(-13)*(10/3 - 2). Let q(z) = 4*z**2 - 8*z + 8. Let i(t) = o*q(t) - 5*d(t). Find x, given that i(x) = 0.
1/4, 3
Let z(v) be the first derivative of -2*v**3/21 + v**2 + 155. Solve z(w) = 0 for w.
0, 7
Find m such that -144*m - 4/5*m**4 + 0 - 68/5*m**3 - 384/5*m**2 = 0.
-6, -5, 0
Let a(k) be the third derivative of -6*k**2 - 1/1575*k**7 + 0*k**3 - 1/300*k**6 - 1/180*k**4 - 1/150*k**5 + 0 + 0*k. Factor a(l).
-2*l*(l + 1)**3/15
Let b(f) be the first derivative of -f**4/18 + 4*f**3/9 + 3*f + 11. Let p(o) be the first derivative of b(o). Solve p(d) = 0.
0, 4
Let p(w) be the second derivative of 2*w**6/9 - 395*w**5/12 + 7205*w**4/4 - 78045*w**3/2 - 59895*w**2/2 - 25*w + 4. Factor p(d).
5*(d - 33)**3*(4*d + 1)/3
Let i(h) be the first derivative of -1/10*h**4 - 1/15*h**2 + 0*h + 12 + 8/45*h**3. Suppose i(s) = 0. What is s?
0, 1/3, 1
Factor -32/5 - 16*r**2 - 1/5*r**5 - 2*r**4 - 8*r**3 - 16*r.
-(r + 2)**5/5
Factor -64/3 - 1/3*w**4 - 20*w**2 + 112/3*w + 13/3*w**3.
-(w - 4)**3*(w - 1)/3
Let p be 21 + -9 - (-435)/(-116). Factor 9/4*k**3 - p*k - 15/4*k**2 - 9/4.
3*(k - 3)*(k + 1)*(3*k + 1)/4
Factor -11*n**2 - 3*n + 0*n - 42*n**2 - 7*n + 5*n**2.
-2*n*(24*n + 5)
Let n(o) be the third derivative of o**10/10080 - o**9/6048 - o**8/4032 - 13*o**5/60 - 6*o**2. Let q(a) be the third derivative of n(a). Factor q(j).
5*j**2*(j - 1)*(3*j + 1)
Let x(i) = i**2 + 9*i + 2. Let q be x(-9). Factor 6*d**3 + 6*d**q - 4*d**3 - 3*d - 5*d**3.
-3*d*(d - 1)**2
Factor -27*k + 4*k**3 + 35*k**2 - 27*k**2 - 48 - 15*k - 2*k.
4*(k - 3)*(k + 1)*(k + 4)
Let r(q) be the third derivative of -1/168*q**4 + 1/420*q**5 + 0*q - 1/42*q**3 + 8*q**2 + 1/840*q**6 + 0. Factor r(j).
(j - 1)*(j + 1)**2/7
Let s = -352837/243 - -1452. Let y = 2921/1215 + s. Factor -8/5*l - 8/5*l**3 + 2/5*l**4 + y*l**2 + 2/5.
2*(l - 1)**4/5
Factor 1/2*u**4 - 4*u**3 + 11*u**2 - 12*u + 9/2.
(u - 3)**2*(u - 1)**2/2
Let v(r) = 5*r**3 - 82*r**2 + 53*r. Let n(t) = 55*t**3 - 900*t**2 + 585*t. Let i(y) = 6*n(y) - 65*v(y). Suppose i(w) = 0. What is w?
0, 1, 13
Let p(q) be the second derivative of -q**6/6 + 3*q**5/4 - 10*q**3/3 + 2*q + 28. Solve p(g) = 0.
-1, 0, 2
Suppose 0 = 4*f - 6*f + 20. Suppose 3*d = 3*r, 2*d - 3*d = 4*r - f. Solve 3*h**r - 5*h**2 - 2*h**4 - 6*h**2 + 8*h**3 = 0.
0, 2
Let o = 165 - 161. Let n(l) = l**3 + 7*l**2 + 5*l - 3. Let x be n(-6). Determine u so that 1/2 - u**2 - o*u**x + u - u**5 - 7/2*u**4 = 0.
-1, 1/2
Let t = 2069/33 - 187/3. Factor t*n**2 + 16/11*n**4 + 14/11*n**3 + 6/11*n**5 + 0 + 0*n.
2*n**2*(n + 1)**2*(3*n + 2)/11
Factor 0 - 12/5*x**2 + 4/5*x - 6/5*x**4 + 1/5*x**5 + 13/5*x**3.
x*(x - 2)**2*(x - 1)**2/5
Let v(i) = i**3 - 5*i**2 - 7*i + 8. Let r be v(6). Factor 2*l**2 + r*l**4 + 6*l**3 - 6*l**4 - 2*l**4 - 2*l**4.
-2*l**2*(l - 1)*(4*l + 1)
Let d(o) = -11*o**3 + 5*o**2 - 6. Let w(q) = 100*q**3 - 45*q**2 + 55. Let y = 133 - 188. Let z(u) = y*d(u) - 6*w(u). Factor z(c).
5*c**2*(c - 1)
Let a(d) be the second derivative of -3*d**5/20 + 2*d**4 - 5*d**3/2 - 75*d**2 - 3*d. Solve a(n) = 0 for n.
-2, 5
Suppose 12122*x - 12139*x = -51. Solve -14/5*n - 2*n**2 - 6/5 - 2/5*n**x = 0 for n.
-3, -1
Let i(q) be the second derivative of -q**7/294 + q**6/105 + q**5/35 - q**4/42 - q**3/14 - 53*q. Find n, given that i(n) = 0.
-1, 0, 1, 3
Let s(d) = 3*d**4 + 6*d**3 - d**2 - 3*d + 5. Let m(g) = 6 + 6*g**4 - 4*g - 221*g**3 + 227*g**3 - 2*g**4. Let i(c) = -5*m(c) + 6*s(c). Factor i(y).
-2*y*(y - 1)**3
Let b(r) = -r**3. Let a(q) = -4*q**3 + 3*q**2 + 24*q - 36. Let v(y) = a(y) - b(y). Factor v(s).
-3*(s - 2)**2*(s + 3)
Suppose 5*m - 68 = -13. Factor -20*g + m*g**3 - 40*g + 10*g**2 + 40 + 4*g**3 - 5*g**4.
-5*(g - 2)**2*(g - 1)*(g + 2)
Suppose -2/7*l**3 + 4/7 + 0*l**2 + 6/7*l = 0. Calculate l.
-1, 2
Let g = 13 + -9. Let t(z) = -8*z**4 - 11 - 675*z + 675*z + 4*z**3 - z**3. Let c(u) = 3*u**4 - u**3 + 4. Let b(n) = g*t(n) + 11*c(n). Factor b(j).
j**3*(j + 1)
Let h(o) = o**2 + o. Let k(b) = 32*b**2 + 86*b - 96. Let g(c) = -68*h(c) + 2*k(c). Factor g(n).
-4*(n - 24)*(n - 2)
Factor 57 - 2610*z**2 - 97 - 405*z**3 - 1100*z - 80.
-5*(z + 6)*(9*z + 2)**2
Let f be -6 + 2 + 158/39. Let h(i) be the first derivative of 1/13*i**2 + 0*i - 4 - f*i**3. Find c, given that h(c) = 0.
0, 1
Factor -15/2*s**3 - 63*s**2 + 0 - 24*s.
-3*s*(s + 8)*(5*s + 2)/2
Let u(p) be the third derivative of -p**8/160 + p**7/420 - p**6/2520 + 29*p**5/60 + 6*p**2. Let f(d) be the third derivative of u(d). Factor f(y).
-2*(21*y - 1)**2/7
Let l(y) = 4*y**2 - 3*y + 3. Let a(p) = p**2 - p + 1. Let j be (-4)/14 + 120/(-21). Let z(q) = j*a(q) + 2*l(q). Factor z(g).
2*g**2
Let s = -20 - -11. Let v(n) = -n - 7. Let t be v(s). Factor 2*w**t + 2 + 3*w**2 - 4*w**2 + 0*w**2 - 3*w.
(w - 2)*(w - 1)
Suppose -8 = -i + 2*t, 10 = -5*i + 5*t + 60. Factor -119*c - i*c**2 - c**3 + 3*c**3 + 129*c.
2*c*(c - 5)*(c - 1)
Let 1/3*g**4 + 20/3*g**2 + 0 - 8/3*g**3 - 16/3*g = 0. Calculate g.
0, 2, 4
Suppose -8*p - 11 - 1 - 6*p**2 + p**3 - 8*p + 12 = 0. What is p?
-2, 0, 8
Let w(f) be the third derivative of 91/20*f**5 - 5*f**2 - 9/16*f**8 + 9/2*f**4 + 2 + 0*f + 27/40*f**6 - 19/14*f**7 + 2*f**3. Determine r so that w(r) = 0.
-1, -2/7, -2/9, 1
Let g be 4/((-33408)/31624) + (-8)/(-2). Let m = g + 1/116. Factor m*c - 2/9*c**2 + 0.
-2*c*(c - 1)/9
Suppose -6*u**2 - 20*u**3 + u**3 + 16*u**3 = 0. What is u?
-2, 0
Let d = -31/24 + 173/120. Let a(b) be the second derivative of -3/50*b**6 + 2/5*b**3 + 0 + 7/30*b**4 - 4/5*b**2 + 2*b - d*b**5. Let a(y) = 0. What is y?
-2, -1, 2/3
Let o be (-44)/(-12) + (-6125)/(-294). What is p in 1/2*p**2 - 7*p + o = 0?
7
Let a(q) = 1698*q + 3398. Let d be a(-2). Let 3/4*r**5 - 9/4*r**4 + 15/4 - 15/2*r**3 - 3/2*r**d + 27/4*r = 0. Calculate r.
-1, 1, 5
Let i = -1080 -