3. Let k = -319/3 - b. Solve 2/3*c**2 + k + 8/3*c = 0.
-2
Let l(d) be the second derivative of d**5/40 - d**4/4 + 11*d**3/12 - 3*d**2/2 - d. Factor l(k).
(k - 3)*(k - 2)*(k - 1)/2
Suppose 0 = -3*u - 0*u - 54. Let g = 34 + u. Suppose 1 - 2*m - m**3 + 3*m - 17*m**2 + g*m**2 = 0. What is m?
-1, 1
Factor 0 + 25/4*h**3 + 5/4*h**4 + 0*h + 15/2*h**2.
5*h**2*(h + 2)*(h + 3)/4
Suppose -3 = -0*r - r + 4*d, -4*d = 0. Find a such that -5*a**2 - 8*a + 30*a**r - 14*a**2 - 5*a**2 + 44*a**4 - 42*a**5 = 0.
-2/3, -2/7, 0, 1
Suppose -3*u + 1 = 3*b - 8, -4*u + 9 = b. Factor 2/3 + 4/3*l**2 - 4/3*l**3 - 2/3*l**5 - 2*l**4 + u*l.
-2*(l - 1)*(l + 1)**4/3
Let c(q) be the second derivative of q - 1/6*q**4 - 4*q**2 + 0 - 4/3*q**3. Suppose c(n) = 0. What is n?
-2
Let x be (-3 - 1204/(-396)) + 2/11. Factor 8/9*o - x - 8/9*o**2.
-2*(2*o - 1)**2/9
Let n(l) = -l**3 + l**2 + l. Let m(o) = -o - 4 + 0*o + 29*o**3 + 0*o + 28*o**2 + 5*o**2. Let j(a) = m(a) - n(a). Determine b, given that j(b) = 0.
-1, -2/5, 1/3
Let y(c) be the third derivative of 3*c**7/70 + c**6/2 + 12*c**5/5 + 6*c**4 + 8*c**3 + 39*c**2. Factor y(i).
3*(i + 2)**3*(3*i + 2)
Let m be (24 - 24)/(2/2). Let r(b) be the first derivative of -1/20*b**4 + 1/15*b**3 + m*b**2 + 0*b + 2. Factor r(a).
-a**2*(a - 1)/5
Let q(p) be the first derivative of -2*p**3/9 + 4*p**2/3 - 8*p/3 + 10. Factor q(l).
-2*(l - 2)**2/3
Let m(t) be the first derivative of -t**5/100 + t**4/60 + 4*t - 1. Let g(y) be the first derivative of m(y). Factor g(i).
-i**2*(i - 1)/5
Suppose -g = -4*g + 2*r + 11, -r + 2 = g. Let m = 0 + 2. Factor 0 - 1/3*b - 2/3*b**m + 1/3*b**g + 2/3*b**4.
b*(b - 1)*(b + 1)*(2*b + 1)/3
Suppose -2*o + 5*i - i + 20 = 0, 2 = 2*o + 2*i. Factor 4*g**3 + 5*g**4 + 2*g**2 - 2*g - 3*g**o - 4*g**2 - 2*g**3.
2*g*(g - 1)*(g + 1)**2
Suppose -b = 3*b - 20. Let q = 3 - -1. Factor 3*a**3 - b*a**4 + 3*a**4 - a**3 + 0*a**3 + q*a**2.
-2*a**2*(a - 2)*(a + 1)
Let t(u) be the second derivative of 2*u + 0*u**2 - 1/3*u**3 + 0 + 1/20*u**5 + 1/12*u**4. Factor t(f).
f*(f - 1)*(f + 2)
Let g(i) = 5*i**5 + 10*i**4 - 2*i. Let f(s) = 25*s**5 + 50*s**4 - 11*s. Let p(q) = -2*f(q) + 11*g(q). Determine j so that p(j) = 0.
-2, 0
Suppose 0*s + 2/9 - 2/9*s**2 = 0. Calculate s.
-1, 1
Let u be (6/(-12))/((-2)/4). Suppose p - u = -2*h + 3, 0 = 4*h - 4*p - 8. Suppose 8*x - 4*x**3 - 4*x - h*x**2 + 2*x**3 = 0. Calculate x.
-2, 0, 1
Suppose 3*y - 3*v = 15, -4*v + 6*v = 0. Suppose -2*j - 2*j = y*f - 40, 2*j - 18 = -2*f. Solve 16*m + 8*m**2 - f - 33*m**2 + 4*m = 0.
2/5
Let q(a) = a**3 - 5*a**2 + 4*a + 6. Let s be q(3). Suppose s*m - 3/5 + 3/5*m**2 = 0. What is m?
-1, 1
Let f = 1111/10 - 111. Let y(x) be the second derivative of 0*x**4 + 0*x**2 + 0 + 1/3*x**3 + x - f*x**5. Let y(n) = 0. Calculate n.
-1, 0, 1
Let h(j) be the second derivative of 0 - 1/2*j**2 + 5/24*j**4 + 1/4*j**3 + 2*j. Suppose h(u) = 0. Calculate u.
-1, 2/5
Let i(n) be the third derivative of -n**5/300 - n**4/12 - 5*n**3/6 - 16*n**2. Factor i(d).
-(d + 5)**2/5
Let d(a) be the second derivative of -a**4/4 - 2*a**3 - 5*a. What is o in d(o) = 0?
-4, 0
Suppose 0 = -11*b + 13*b. Let b*p - 2/11*p**2 + 2/11 = 0. What is p?
-1, 1
Suppose -3*l - 46 = 4*h, 3*h - h = 2*l - 16. Let a be (h/(-3))/5*3. Factor 2*p**2 + 4*p - 5*p**2 - p**3 + a*p - 2*p**3.
-3*p*(p - 1)*(p + 2)
Let l(x) be the third derivative of 9*x**8/448 + 3*x**7/35 + 7*x**6/160 - 3*x**5/20 - x**4/8 - x**2. Solve l(j) = 0.
-2, -1, -1/3, 0, 2/3
Let d(r) be the first derivative of 4/3*r**3 + 16/3*r - 1/6*r**4 + 3 - 4*r**2. Let d(g) = 0. What is g?
2
Solve -4/21*t**3 - 2/21*t**4 + 0 + 2/21*t**2 + 4/21*t = 0 for t.
-2, -1, 0, 1
Let o be 9 - 13/(143/99). Determine g, given that 8/5*g**4 + o + 2*g**2 - 4/5*g + 22/5*g**3 = 0.
-2, -1, 0, 1/4
Suppose 3*w - 4*k - 11 = 8, -5 = 3*w + 2*k. Let f(i) = 2*i**3 - 2*i - 6. Let g(j) = 1. Let t(r) = w*f(r) + 6*g(r). Factor t(m).
2*m*(m - 1)*(m + 1)
Solve 9/7 - 3/7*s**3 + 3/7*s - 9/7*s**2 = 0 for s.
-3, -1, 1
Let n = -7 - -4. Let i be ((-2)/(-10))/(n/(-10)). What is f in 0*f**2 + 0*f + i*f**3 - 2/3*f**4 + 0 = 0?
0, 1
Let g(m) = -15*m**5 - 6. Let i(b) be the second derivative of -b**6/30 + b**2/2 + 5*b. Let d(a) = g(a) + 6*i(a). What is l in d(l) = 0?
-2/5, 0
Factor 0 + 2/25*s - 2/25*s**2.
-2*s*(s - 1)/25
Suppose -3*h + 3*f + 12 = 0, -2*h - 5*f - 16 = -5*h. Factor 2/9*t**h + 8/9*t - 8/9 - 2/9*t**3.
-2*(t - 2)*(t - 1)*(t + 2)/9
Factor 8*z**3 + 4*z + 2*z**4 + 4*z**3 - 2*z**2 - 18*z**3 + 2*z**5.
2*z*(z - 1)**2*(z + 1)*(z + 2)
Let g(w) be the second derivative of -w**4/32 + w**3/2 - 3*w**2 - 11*w. Factor g(u).
-3*(u - 4)**2/8
Let a(t) be the first derivative of t**4/4 - t**3/3 - t**2/2 - t + 5. Let o(s) = -2*s**3 + 3*s + 1. Let z(u) = -2*a(u) - 2*o(u). Factor z(c).
2*c*(c - 1)*(c + 2)
Let f be ((-1)/2)/((-2)/(-56)). Let d be f/(-30) + 2/6. Determine b so that 0 - 6/5*b**2 + d*b = 0.
0, 2/3
Let s(g) be the third derivative of g**6/12 + g**5/15 - 2*g**2. Solve s(f) = 0.
-2/5, 0
Let a(j) be the second derivative of -j**4/30 + 4*j**3/15 - 12*j. Factor a(f).
-2*f*(f - 4)/5
Let q(d) = 2*d**2 - 3*d - 3. Let s be q(3). Let n(t) be the second derivative of 0 + 1/120*t**s - 1/20*t**5 + 1/8*t**4 - 1/6*t**3 + 1/8*t**2 - t. Factor n(w).
(w - 1)**4/4
Suppose -3*p + 5*p = 6. Let r(d) be the third derivative of 0 - 1/6*d**p + 3*d**2 + 1/16*d**4 + 1/80*d**6 + 1/15*d**5 + 0*d. Factor r(s).
(s + 1)*(s + 2)*(3*s - 1)/2
Let t(x) be the second derivative of x**7/315 + x**6/54 + 2*x**5/45 + x**4/18 + x**3/27 + 3*x**2/2 + 3*x. Let b(p) be the first derivative of t(p). Factor b(c).
2*(c + 1)**3*(3*c + 1)/9
What is i in -3/8*i**5 + 3/4*i**2 + 3/2*i**4 + 0*i - 15/8*i**3 + 0 = 0?
0, 1, 2
Determine j so that 11*j + 2*j**3 - 10*j**3 + 65*j**2 - 90 - 27*j**3 + 4*j + 5*j**4 = 0.
-1, 2, 3
Let k(n) be the second derivative of -n**9/21168 - n**8/23520 - n**4/6 - 6*n. Let f(j) be the third derivative of k(j). Factor f(a).
-a**3*(5*a + 2)/7
Suppose -3*u = -0*u. Let 40*g + 0*g**4 + u*g**4 - 37*g + 3*g**5 - 6*g**3 = 0. What is g?
-1, 0, 1
Suppose -6*x = -3 - 15. Factor -7*v**2 + x*v**2 + 3*v**3 - 5*v**3 - v - v.
-2*v*(v + 1)**2
Suppose 0*r - 1 = 3*v + 4*r, -v = 5*r + 15. Suppose -6*u + u = 3*p + 15, v = -p. Determine h so that 0 + 2/5*h**2 + u*h = 0.
0
Determine z so that 1/2*z**2 + 3/2*z**3 + 0*z - 2*z**4 + 0 = 0.
-1/4, 0, 1
Let g(m) be the third derivative of 1/15*m**5 + 0*m - m**2 + 1/336*m**8 + 0 + 0*m**3 + 1/24*m**4 + 1/20*m**6 + 2/105*m**7. Suppose g(l) = 0. Calculate l.
-1, 0
Let y(k) be the third derivative of k**8/1512 + 4*k**7/945 + k**6/108 + k**5/135 + 8*k**2. Suppose y(l) = 0. Calculate l.
-2, -1, 0
Suppose 0 = -2*o + 8 - 4. Let k be (-2 - -2)*-1*(2 + -1). Factor k*w + 0 + 2/9*w**o.
2*w**2/9
Solve -1/4*v**4 + 0*v**2 - 1/2*v**3 + 0 + 0*v = 0 for v.
-2, 0
Let p(u) be the first derivative of u**6/12 + u**5/5 - u**3/3 - u**2/4 + 7. Factor p(x).
x*(x - 1)*(x + 1)**3/2
Let t be -3 - (74/(-481) - (-272)/(-91)). Factor t*s**2 + 0 + 12/7*s**4 - 8/7*s**5 - 6/7*s**3 + 0*s.
-s**2*(2*s - 1)**3/7
Let i(d) be the third derivative of -d**6/1440 + d**5/480 + d**4/48 - d**3/2 - 3*d**2. Let z(b) be the first derivative of i(b). Factor z(n).
-(n - 2)*(n + 1)/4
Let h = -71 - -75. Let u(i) be the third derivative of 0 + 0*i - 3/160*i**6 + 11/240*i**5 - 4*i**2 - 1/48*i**h + 0*i**3. Factor u(m).
-m*(m - 1)*(9*m - 2)/4
Factor -211*c**2 - 40*c + 101 + 216*c**2 - 21.
5*(c - 4)**2
Factor 121 - 6*r**4 + 8*r**3 - 8*r + 2*r**4 - 117.
-4*(r - 1)**3*(r + 1)
Let x(l) be the first derivative of l**4 + 0*l**5 + 0*l + 3 - 1/3*l**6 - l**2 + 0*l**3. Factor x(z).
-2*z*(z - 1)**2*(z + 1)**2
Let n(v) be the first derivative of 3 + 0*v**3 + 0*v - 1/30*v**5 + 3/2*v**2 - 1/12*v**4. Let y(j) be the second derivative of n(j). Find x, given that y(x) = 0.
-1, 0
Suppose v - 79 = -28. Suppose 0 = 4*y - v - 21. Factor 6*m**3 - 1 + 1 + 16*m**2 - 8*m - y*m**4.
-2*m*(m + 1)*(3*m - 2)**2
Factor -50*d + 20*d**4 + 48*d**3 - 20*d**2 - 31*d**5 + 14*d**5 + 19*d**5.
2*d*(d - 1)*(d + 1)*(d + 5)**2
Let a(x) = -2*x + 1. Let u be a(-3). Suppose -5*r + 13 + u = 0. What is z in -z**4 - z**3 - r*z**4 + 4*z**4 = 0?
-1, 0
Let a(f) be the first derivative of -2/9*f + 2/27*f**3 - 3 + 0*f**2. Determine u so that a(u) = 0.
-1, 1
Let l(x) be the third derivative of x**7/105 + x**6/10 + 3*x**5/10 + x**4/3 + x**2 - 12. Factor