h that v(w) = 0.
3
Let m(r) be the second derivative of -r**4/12 - 2*r**3 - 18*r**2 - 20*r. Let m(c) = 0. Calculate c.
-6
Let i(t) be the first derivative of 3*t**4/2 - 9*t**3 + 18*t**2 - 12*t + 16. Let i(r) = 0. Calculate r.
1/2, 2
Let n(f) be the second derivative of 3*f**5/160 - 7*f**3/16 - 9*f**2/8 + 10*f. Factor n(k).
3*(k - 3)*(k + 1)*(k + 2)/8
Factor 10 + 35*j + 53*j**4 + 67*j**2 - 22*j**2 - 48*j**4 + 25*j**3.
5*(j + 1)**3*(j + 2)
Let y(q) = -q**3 + 6*q**2 - 4*q - 3. Let c be y(5). Factor 6*l + c*l**3 - 12*l**2 + 4*l**2 + 2*l**2 - 2.
2*(l - 1)**3
Determine i, given that 0*i**4 + 0*i + 0*i**3 + 0*i**2 - 2/9*i**5 + 0 = 0.
0
Let c be -12 + (-5)/((-50)/(-6)). Let f = c + 13. Factor 2/5*b**4 + 0 + 6/5*b**3 + 6/5*b**2 + f*b.
2*b*(b + 1)**3/5
Let l(d) be the third derivative of -d**6/24 - d**5/3 - 25*d**4/24 - 5*d**3/3 + 11*d**2. Factor l(g).
-5*(g + 1)**2*(g + 2)
Let g(j) = 5*j**2 - 6*j + 7. Let p(z) = z**2 + 1. Let d(f) = -2*g(f) + 6*p(f). Solve d(q) = 0.
1, 2
Let n(x) be the first derivative of x**8/3920 - x**7/980 + x**6/840 + 5*x**3/3 - 2. Let g(c) be the third derivative of n(c). Solve g(o) = 0.
0, 1
Let b(r) be the third derivative of -r**5/90 - 5*r**4/24 + 4*r**3/9 + 12*r**2. What is z in b(z) = 0?
-8, 1/2
Let 0*s**4 - 3/4*s**5 + 3/2*s**3 + 0 + 0*s**2 - 3/4*s = 0. Calculate s.
-1, 0, 1
Let l = 31/35 - 2/7. Suppose 6/5*r - l*r**3 + 0 - 3/5*r**2 = 0. Calculate r.
-2, 0, 1
Solve -54*r**3 + 4*r**4 + 5 - 1 - 16*r + 24*r**2 + 38*r**3 = 0.
1
Suppose -4*j + 3 = -5*o + 31, -5*j = 3*o - 2. Determine p, given that -13*p**o + 15*p**4 - 1 - 4*p**2 + 3 = 0.
-1, 1
Factor 3/2*d**4 + 3/2*d**2 - 3 + 9/2*d - 9/2*d**3.
3*(d - 2)*(d - 1)**2*(d + 1)/2
Let p(n) be the first derivative of -2*n**6/3 - 5*n**5/3 - 13*n**4/12 + n**3/9 + n**2/6 - 16. Find b, given that p(b) = 0.
-1, -1/3, 0, 1/4
Let y(h) be the third derivative of 0 + 2*h**3 - 4/35*h**7 + 4*h**2 - 1/4*h**5 - 3/4*h**4 + 3/224*h**8 + 0*h + 27/80*h**6. Let y(g) = 0. Calculate g.
-2/3, 1, 2
Determine c, given that 0 + 3/2*c**3 + 0*c + 3/2*c**2 - 3/2*c**5 - 3/2*c**4 = 0.
-1, 0, 1
Find u, given that -4/3*u + 2/3*u**2 + 0 = 0.
0, 2
Let y(u) = -24*u**2 - 76*u - 16. Let h(d) = -d**2 - d. Let r(j) = -8*h(j) + y(j). Suppose r(p) = 0. What is p?
-4, -1/4
Suppose -w + 4*j = -5*w + 144, 5*j - 10 = 0. Let p be (36/45)/(4/w). Find d such that -22/5*d**2 - 4/5*d - 42/5*d**3 + 0 - p*d**4 - 2*d**5 = 0.
-1, -2/5, 0
Let u(r) = -27*r**2 - 10*r - 13*r + 18 - 7*r. Let q(n) = 28*n**2 + 29*n - 19. Let l(p) = -6*q(p) - 7*u(p). Find d such that l(d) = 0.
-2, 2/7
Let i(p) be the third derivative of 0*p - 3*p**2 + 0*p**3 - 1/48*p**4 - 3/80*p**5 + 0 - 7/480*p**6. Determine w so that i(w) = 0.
-1, -2/7, 0
Let u(t) = -t**2 - 24*t + 25. Let z be u(1). Suppose 0 + z*g - 3/4*g**3 + 3/4*g**2 = 0. Calculate g.
0, 1
Let r = 544/1385 + 2/277. Factor -2/5*t**2 + 0*t + r.
-2*(t - 1)*(t + 1)/5
Suppose -5*r = -5*x - 15, 2*x + x = -r + 3. Suppose -r*t + t = 0. Let 0*h**3 + 0*h**2 + t + 2/5*h**4 + 0*h = 0. Calculate h.
0
Let n be -3*(-4)/(-8)*-2. Let l(u) be the second derivative of -1/18*u**n + 0*u**2 + 0 - u - 1/12*u**4. Suppose l(i) = 0. What is i?
-1/3, 0
Suppose i = 3*i + 4*i. Factor 1/3*t**2 + 0*t + 4/3*t**4 + 5/3*t**3 + i.
t**2*(t + 1)*(4*t + 1)/3
Suppose 5 = -3*v + 20. Factor -12 + 9*p**4 + 12*p + 0*p**5 + 24*p - 3*p**v + 3*p**3 - 33*p**2.
-3*(p - 2)*(p - 1)**3*(p + 2)
Let w(p) be the second derivative of p**5/10 - 5*p**4/12 + 2*p**3/3 - p**2/2 - 20*p. Factor w(o).
(o - 1)**2*(2*o - 1)
Let q(x) = -x**2 - 14*x + 8. Let c be q(-13). Let f be 2 + -5 - (-70)/c. Factor -f*j**3 + 1/3*j + 1/3 - 1/3*j**2.
-(j - 1)*(j + 1)**2/3
Let j(u) = 2*u + 1. Let s be j(2). Factor 20*k + 3 + s*k**2 - 4 + 5 + 20*k**2.
(5*k + 2)**2
Let a(t) = 7*t**2 - 2*t - 1. Let j be a(2). Suppose -54*f**2 + 4*f + 9*f**4 - 2 - 8*f**5 + 70*f**2 - j*f**4 + 4*f**3 = 0. What is f?
-1, 1/4, 1
Let u(l) be the third derivative of -1/3*l**3 - 1/30*l**5 - 2*l**2 + 0 - 1/6*l**4 + 0*l. Factor u(a).
-2*(a + 1)**2
Factor -2*t - t - 5*t - 8*t - 4*t**2.
-4*t*(t + 4)
Let y(c) be the second derivative of 1/60*c**6 + 0 - 2*c - 1/60*c**5 + 0*c**3 - 1/24*c**4 - c**2. Let v(m) be the first derivative of y(m). Factor v(i).
i*(i - 1)*(2*i + 1)
Suppose -3*c = -3*b - 30, 7*b - 3*b - 14 = -2*c. Suppose 2*t + t = c. Find d such that 2/9*d**t - 2/9*d**2 + 2/9*d**4 + 0*d + 0 - 2/9*d**5 = 0.
-1, 0, 1
Suppose 1/4*l + 0 + 10*l**4 + 33/4*l**3 + 5/2*l**2 + 4*l**5 = 0. Calculate l.
-1, -1/4, 0
Suppose -5*t + 11 + 4 = f, 2*f = -4*t + 18. Let p be (-2)/f + (-6)/(-15). Factor 0 + 2 - 2*w**2 + p*w**2.
-2*(w - 1)*(w + 1)
Let b = 17/7 + -27/14. Find x, given that -1/2*x**3 - 1/2 + 1/2*x**2 + b*x = 0.
-1, 1
Let f(j) be the second derivative of j**6/255 + j**5/85 - j**4/34 + 23*j. Determine n, given that f(n) = 0.
-3, 0, 1
Let j(v) be the third derivative of v**8/224 - v**7/420 - v**6/40 + v**5/60 + v**4/16 - v**3/12 - v**2. Solve j(w) = 0 for w.
-1, 1/3, 1
Suppose 3*v = 5*v - 4. Factor b**4 + 0*b**3 + 4*b**3 - 2*b**3 - v*b**4 + 3*b**2.
-b**2*(b - 3)*(b + 1)
Factor 12/5*z + 3/5*z**3 + 0 + 12/5*z**2.
3*z*(z + 2)**2/5
Let r(c) be the second derivative of c**5/150 + c**4/15 + 4*c**3/15 + c**2 + c. Let k(j) be the first derivative of r(j). Factor k(f).
2*(f + 2)**2/5
Suppose 0 = -5*w - 2 + 12. Suppose -4*q - 3*t = 9, 0 = -4*q - 2*t - 28 + 22. Factor q*i**w + i - 2/3 - 1/3*i**3.
-(i - 1)**2*(i + 2)/3
Let f(r) be the first derivative of 0*r**2 - 1/3*r + 1/9*r**3 + 3. Find w, given that f(w) = 0.
-1, 1
Let o = 21196/3 + -6989. Let c = 77 - o. Solve 2/3 + c*q**2 - 4/3*q = 0.
1
Let b(s) be the third derivative of -1/390*s**5 + 0*s**3 + 0*s - 1/260*s**6 + 0 - s**2 + 1/78*s**4. Factor b(c).
-2*c*(c + 1)*(3*c - 2)/13
Suppose -4*g + 20 = -5*u, u + 4 = 3*g - 0. Factor f**5 + g + 0 + f**2 - f**3 - f**4.
f**2*(f - 1)**2*(f + 1)
Let t(q) be the second derivative of -q**4/78 + 2*q**3/39 - q**2/13 + 4*q. Factor t(w).
-2*(w - 1)**2/13
Factor -6/5*p**3 - 24/5*p + 22/5*p**2 + 8/5.
-2*(p - 2)*(p - 1)*(3*p - 2)/5
Let u(b) = -4*b**2 - 2*b - 4. Let c be u(4). Let g be (c/285)/((-1)/5). What is r in g*r**3 + 0 + r**2 - 1/3*r = 0?
-1, 0, 1/4
Let d(m) be the second derivative of -m**5/50 - m**4/30 + m**3/15 + m**2/5 + 8*m. Factor d(j).
-2*(j - 1)*(j + 1)**2/5
Let v(m) be the third derivative of m**7/315 + m**6/45 - m**5/15 - m**4/9 + 5*m**3/9 + 3*m**2 + 2*m. Factor v(d).
2*(d - 1)**2*(d + 1)*(d + 5)/3
Let p(f) = 2*f**2 + 3*f - 4. Let n be p(-3). Factor -16/7*s - 2/7*s**n - 36/7*s**3 + 40/7*s**2 + 0 + 2*s**4.
-2*s*(s - 2)**3*(s - 1)/7
Let k(b) be the first derivative of -8*b**5/55 + 9*b**4/22 - 4*b**3/11 + b**2/11 + 1. Factor k(z).
-2*z*(z - 1)**2*(4*z - 1)/11
Factor -4*d**4 - 7*d + 7*d**3 - 13*d + 4*d**2 + 12*d + d**3.
-4*d*(d - 2)*(d - 1)*(d + 1)
Let l(q) be the first derivative of 3 + 1/18*q**6 + 0*q**2 + 1/9*q**3 - 1/12*q**4 + 0*q - 1/15*q**5. What is f in l(f) = 0?
-1, 0, 1
Let s(r) be the first derivative of -2*r**5 - 5*r**4/4 + 5*r**3/3 + 12. Factor s(q).
-5*q**2*(q + 1)*(2*q - 1)
Let s be 9/3 + 2 + -1. Factor 4*x + 9*x**4 - 4*x**3 - 9*x**2 - 2*x**2 - 3*x**2 + 5*x**s.
2*x*(x - 1)*(x + 1)*(7*x - 2)
Let t be (-6)/(-33) + 31/11. Find k, given that 83 + 3*k**2 + t*k**4 - 6*k**3 - 83 = 0.
0, 1
Factor 22/3*i**2 + 0*i + 0 - 2/3*i**3.
-2*i**2*(i - 11)/3
Let i = -117 + 117. Factor 2/3*s + i + 2/3*s**2.
2*s*(s + 1)/3
Let t be 5/((-15)/(-6)) + 23. Let l = -25 + t. Factor 0 - 1/4*r**2 + l*r + 0*r**3 + 1/4*r**4.
r**2*(r - 1)*(r + 1)/4
Determine z so that -13*z**2 - 7/2*z**5 + 15/2*z**3 + 13*z**4 + 0 - 4*z = 0.
-1, -2/7, 0, 1, 4
Let c(i) be the third derivative of i**6/60 - 2*i**5/45 + i**4/36 + 18*i**2. Solve c(b) = 0 for b.
0, 1/3, 1
Let o(x) = 15*x**3 + 18*x**2 + 21*x - 9. Let t(n) = -8*n**3 - 9*n**2 - 11*n + 5. Let g(r) = -5*o(r) - 9*t(r). Solve g(y) = 0 for y.
-2, -1, 0
Let f(h) = h**3 + 13*h**2 - h - 2. Let n be f(-13). Factor -n*s - 12*s**2 - 9*s - 8 + 2*s**4 + 4*s**3 + 2*s**4.
4*(s - 2)*(s + 1)**3
Let t(d) be the third derivative of -d**5/60 + d**4/3 + d**3/3 + 4*d**2. Let j be t(8). Factor 2/5*r**3 - 1/5 - 1/5*r**4 - 1/5*r**5 + 2/5*r**j - 1/5*r.
-(r - 1)**2*(r + 1)**3/5
Let p(q) be the first derivative of -q**4/16 + q**3/6 + q**2/8 - q/2 - 55. Determine k so that p(k) = 0.
-1, 1, 2
Factor 98/9 + 28/9*y + 2/9*y**2.
2*(y + 7)**2/9
Let y b