3 = 0.
-1, 2
Let s(v) be the first derivative of -9 + 0*v + 1/15*v**5 + 7/24*v**4 + 1/2*v**3 - 7/2*v**2. Let g(q) be the second derivative of s(q). Factor g(n).
(n + 1)*(4*n + 3)
Let h(o) = 10*o**2 - 1148*o - 290. Let c(u) = -7*u**2 + 1148*u + 291. Let v(r) = 2*c(r) + 3*h(r). Factor v(d).
4*(d - 72)*(4*d + 1)
Suppose -4*n + 5 = -4*x - 23, 8 = -n - 4*x. Suppose -8 = n*i - 28. Factor -8/13*p**2 - 8/13*p**4 + 0 - 2/13*p - 2/13*p**i - 12/13*p**3.
-2*p*(p + 1)**4/13
Suppose 335*q - 684*q - 113*q - 147*q**2 - 363 = 0. Calculate q.
-11/7
Suppose -5*m + 2*l = -2*l - 20, 4*m - 42 = -2*l. Factor -20*h - 2*h**2 + m + 6*h**2 - 4*h**4 + 8*h**2 + 4*h**3.
-4*(h - 1)**3*(h + 2)
Let z(b) = -9*b**3 + 10*b**2 + 8*b + 9. Let m(c) = 7*c**3 - 9*c**2 - 8*c - 8. Let t(l) = 5*m(l) + 4*z(l). Determine h so that t(h) = 0.
-2, -1
Let x(o) be the first derivative of 2*o**3/51 - 94*o**2/17 + 186*o/17 - 165. Let x(w) = 0. Calculate w.
1, 93
Solve 92/11*v**2 - 2/11*v**3 + 0 + 0*v = 0.
0, 46
Let q(d) be the second derivative of d**6/90 - 61*d**5/60 + 80*d**4/3 - 50*d**3 + 355*d. Solve q(m) = 0.
0, 1, 30
Let h be 8*1 - (18 - 10). What is t in 0 + 2/3*t**4 + h*t**3 - 1/3*t + 1/3*t**5 - 2/3*t**2 = 0?
-1, 0, 1
Suppose 0 = 3*b - 5*z + 16, 0*b - 11 = 3*b - 4*z. Let h(u) be the first derivative of 1 + u + 1/6*u**b - 3/4*u**2. Factor h(d).
(d - 2)*(d - 1)/2
Suppose -a = -5*r + 45, 5*r + 3*a + 0*a - 45 = 0. Let b be (90/24)/(r/12). Suppose 0*n**2 + 0*n + 0 - 2/3*n**b + 0*n**3 + 2/9*n**4 = 0. Calculate n.
0, 1/3
Factor -3*u**2 + 107*u - 45 - 111*u + 52*u.
-3*(u - 15)*(u - 1)
Let p(x) = -2*x**2 + 48*x + 38. Let n(w) = -w**2 + 48*w + 39. Let z(k) = 6*n(k) - 5*p(k). Factor z(s).
4*(s + 1)*(s + 11)
Let m(t) = t**3 + 13*t**2 - 15*t - 10. Let d be m(-14). Let -2*l**2 + 651*l - 661*l + 4 - d = 0. What is l?
-5, 0
Let w(g) be the third derivative of -1/25*g**5 + 0*g - 3/20*g**4 - 4/15*g**3 - 1/300*g**6 - 3*g**2 + 0. Factor w(f).
-2*(f + 1)**2*(f + 4)/5
Let y = 15206 - 60823/4. Suppose -2*d**2 - 9/2 + y*d**3 + 21/4*d = 0. What is d?
2, 3
Let b(y) = 6*y**2 + 276*y + 3. Let a be b(-46). Let x(i) be the first derivative of 0*i**2 - 3 + i**4 + 0*i + 2/3*i**a + 2/5*i**5. Factor x(m).
2*m**2*(m + 1)**2
Let o(g) be the first derivative of -20*g**2 - 5/3*g**3 - 80*g + 15. Determine w so that o(w) = 0.
-4
Let -69/7*u**2 - 3/7*u**5 - 30/7*u + 48/7 + 33/7*u**3 + 3*u**4 = 0. What is u?
-2, -1, 1, 8
Let g(d) be the first derivative of 0*d**3 + 0*d**2 + 0*d - 27 - 1/30*d**5 + 0*d**4. Determine u so that g(u) = 0.
0
Let t be (3/9)/(-2*(-5)/72). Suppose -13 = -5*s + 2. Let -3/5*q**s - t*q - 12/5*q**2 + 0 = 0. Calculate q.
-2, 0
Let z = -410 + 8201/20. Let r(k) be the third derivative of -2*k**2 - 1/120*k**6 + 0 + 2/3*k**3 - z*k**5 + 0*k**4 + 0*k. Factor r(q).
-(q - 1)*(q + 2)**2
Let d(l) be the first derivative of l**5/120 - l**4/24 - 21*l**2/2 + 26. Let b(q) be the second derivative of d(q). Factor b(h).
h*(h - 2)/2
Let d be 486/(-10449) - (-53)/215. Let -d*j - 6/5 + 1/5*j**2 = 0. Calculate j.
-2, 3
Let p(h) be the third derivative of 0 - 20*h**2 + 0*h**5 + 1/144*h**4 + 0*h**3 + 0*h - 1/720*h**6. Factor p(c).
-c*(c - 1)*(c + 1)/6
Let p(v) = 2*v - 21. Let i(n) = -n + 11. Let b(y) = -11*i(y) - 6*p(y). Let w be b(3). Factor 15*d**2 - 3*d**3 - 12*d - 6*d**w + 3*d**2.
-3*d*(d - 2)**2
Let -20/3*o**2 - 8/3*o + 8/3*o**4 + 2/3*o**5 + 2/3*o**3 + 16/3 = 0. Calculate o.
-2, 1
Factor 22/3*x + 14/3*x**3 + 40/3*x**2 - 4/3.
2*(x + 1)*(x + 2)*(7*x - 1)/3
Let -1/6*n**2 + 7 - 41/6*n = 0. What is n?
-42, 1
Let s(l) be the third derivative of l**8/672 + 13*l**7/420 - l**6/8 + l**5/60 + 29*l**4/48 - 5*l**3/4 + 164*l**2. Factor s(j).
(j - 1)**3*(j + 1)*(j + 15)/2
Let u be 400/160*(-124)/(-6) + -9. Solve 80/3*z - 148/3*z**2 - 16/3 + 8/3*z**5 + u*z**3 - 52/3*z**4 = 0 for z.
1/2, 1, 2
Suppose -1591 = 4*b - 1603. Let t(i) be the first derivative of i**2 - 2/3*i**b + 4 + 0*i. Let t(d) = 0. What is d?
0, 1
Suppose 8*f = 7*f. Let x(l) = -l**3 + l + 14. Let p be x(f). Factor 4*b**3 + 3*b**2 - 5*b**3 - p + 13 + 3*b**3.
(b + 1)**2*(2*b - 1)
Let n(m) be the third derivative of 3/280*m**8 + 1/300*m**6 + 7*m**2 + 0*m + 0*m**3 + 2/175*m**7 + 0*m**5 + 0 + 0*m**4. Solve n(z) = 0.
-1/3, 0
Let u = 50/89 - -167/178. What is w in -3/8*w**2 - u - 3/2*w = 0?
-2
Let l(h) be the third derivative of 25*h**8/4032 + 5*h**7/252 + h**6/36 - h**5/20 + 15*h**2. Let a(y) be the third derivative of l(y). Factor a(x).
5*(5*x + 2)**2
Solve 52/7*i**3 - 128/7*i - 128/7 + 88/7*i**2 + 4/7*i**5 - 32/7*i**4 = 0 for i.
-1, 2, 4
Let u = -32 - -34. Factor 52 - 50 - u*b**2 + 0*b**2.
-2*(b - 1)*(b + 1)
Let g(w) be the third derivative of -w**6/60 - w**5/6 + w**3/3 - w**2 + 24. Let s be g(-5). Suppose -2/9*y**4 + 0*y**s + 2/9*y**3 + 0 + 0*y = 0. Calculate y.
0, 1
Factor -34/3 + 1/6*s**2 - 13/6*s.
(s - 17)*(s + 4)/6
Factor 26/9*o**2 - 10/9*o**3 - 8/9*o - 8/9.
-2*(o - 2)*(o - 1)*(5*o + 2)/9
Let f(z) be the first derivative of z**4/22 + 4*z**3/11 + 36*z + 10. Let u(a) be the first derivative of f(a). Factor u(h).
6*h*(h + 4)/11
Let y(s) be the second derivative of s**5/40 - s**4/4 - 25*s**3/12 - 9*s**2/2 + 51*s. Factor y(j).
(j - 9)*(j + 1)*(j + 2)/2
Suppose 0 = -3*v + 231 - 225. Let n = -53 + 277/5. Suppose 26/5*l - n + v*l**2 = 0. Calculate l.
-3, 2/5
Factor 5 + 1/2*u**2 + 7/2*u.
(u + 2)*(u + 5)/2
Let 49 + o - 10*o**2 - 57*o + 11 + 6*o**2 = 0. Calculate o.
-15, 1
Let k(v) = -v**3 + 9*v**2 - v + 12. Let p be k(9). Suppose -p*t + 6*t = 33. Factor 3*j**2 + 2*j - 14*j - 2 + t.
3*(j - 3)*(j - 1)
Let p(h) be the second derivative of -1/60*h**6 - 9/4*h**2 - h**3 + 0 - 4*h + 1/10*h**5 + 1/12*h**4. Find d such that p(d) = 0.
-1, 3
Let a(n) be the third derivative of -n**7/490 - 3*n**6/280 + 3*n**5/70 + n**4/2 + 12*n**3/7 - 149*n**2. What is q in a(q) = 0?
-2, 3
Suppose 3*d + 3*q = 21 - 27, 0 = -4*d - 3*q - 6. Suppose 2/13*n**2 + d - 8/13*n = 0. Calculate n.
0, 4
Let v(j) be the first derivative of -11 + 1/3*j**3 + 0*j**2 - j. Factor v(w).
(w - 1)*(w + 1)
Let t = 74/77 - 18/77. Factor -40/11*h**2 + 0 + 50/11*h**3 + t*h.
2*h*(5*h - 2)**2/11
Let h be 4/(-3)*(-9 + 8). What is a in h*a**4 - 4/3*a**2 + 2/3*a - 2/3*a**5 + 0*a**3 + 0 = 0?
-1, 0, 1
Let i = 6 + -2. Let v be -1 - -3*i/(-6). Let o(a) = -8*a**2 + 4*a + 7. Let y(l) = -8*l**2 + 4*l + 6. Let b(d) = v*y(d) + 2*o(d). Factor b(k).
4*(k - 1)*(2*k + 1)
Let h = -12608 - -25221/2. Solve 35*x - h*x**2 - 245/2 = 0 for x.
7
Let l(c) be the first derivative of c**7/42 + c**6/8 + c**5/4 + 5*c**4/24 - 12*c**2 - 1. Let f(q) be the second derivative of l(q). Factor f(a).
5*a*(a + 1)**3
Let c = 80 - 78. Factor 11*y - 4*y**2 + y - 9*y + y**c.
-3*y*(y - 1)
Suppose -4*a = -3*j - 4, 3*a + 4*j - 31 = -3. Let -6*o**4 + 58*o**2 + 6*o**3 - 4*o - 56*o**2 - 2*o**5 + 4*o**a = 0. Calculate o.
-2, -1, 0, 1
Let g = 4559 - 18235/4. Factor g*m + 0 - 1/4*m**2.
-m*(m - 1)/4
Suppose 2*n + 3*q - 13 = 0, 365 = -2*n + 3*q + 360. Find r such that 0 - 1/9*r**3 + 0*r - 1/9*r**n = 0.
-1, 0
Let t be (-82)/(-56) - ((-273)/(-28) + -10). Solve -16/7 + 24/7*i - t*i**2 + 2/7*i**3 = 0 for i.
2
Let m(i) be the first derivative of -5*i**8/336 + i**7/14 - i**6/8 + i**5/12 + 31*i**2/2 + 23. Let u(p) be the second derivative of m(p). Factor u(o).
-5*o**2*(o - 1)**3
Let h(u) = -8*u**2 + 24*u. Let d be h(3). Let f(w) be the third derivative of 2/3*w**3 + d*w + 2/3*w**4 + 1/5*w**5 + 0 + 5*w**2. Factor f(k).
4*(k + 1)*(3*k + 1)
Let m(s) = -s**5 - s**4 - s**3 - 3*s**2 + 1. Let b(i) = -12*i**5 - 6*i**4 - 4*i**3 - 46*i**2 + 8*i + 10. Let l(w) = -b(w) + 10*m(w). Factor l(k).
2*k*(k - 2)*(k - 1)**2*(k + 2)
Let z = -688 - -688. Let x(a) be the first derivative of 4 + 2/15*a**5 - 2*a**4 - 22/9*a**3 + z*a + 4/9*a**6 - 2/3*a**2. Solve x(t) = 0.
-1, -1/4, 0, 2
Let p = -8 - -11. Suppose -1 - 14 = -5*a, 0 = 2*h - p*a + 1. Factor 10/9*x + 4/9 + 2/3*x**2 - 2/9*x**3 - 2/9*x**h.
-2*(x - 2)*(x + 1)**3/9
Let p = -647 + 1943/3. What is s in p*s**4 - 1/3*s**3 + s**5 + 0*s**2 + 0*s + 0 = 0?
-1, 0, 1/3
Factor 6*n**2 - 3*n**2 + 0*n**2 + 17*n - 61 + 55.
(n + 6)*(3*n - 1)
Let r(f) be the first derivative of -4/7*f**3 + 2 - 6/7*f**2 + 2/7*f**4 + 8/7*f. Solve r(v) = 0 for v.
-1, 1/2, 2
Let b(y) be the first derivative of 0*y**2 + 0*y + 12 + 1/60*y**6 + 0*y**3 + 1/40*y**4 + 1/25*y**5. Suppose b(z) = 0. Calculate z.
