-4*b - 3*s + 40 = 0, -5*b = -2*b + 4*s - 37. Let m = 10 - b. Factor 2*k**2 + 2*k**4 + m*k**3 + 1/2*k + 1/2*k**5 + 0.
k*(k + 1)**4/2
Let y(p) = -p**3 - 2*p**2 - 2. Let i be y(-4). Let b be 6/(-8) - i/(-8). Let 2*f**b - 2*f + 3*f**3 - 7*f**3 + 4*f**2 = 0. Calculate f.
0, 1
Let v(d) be the third derivative of d**5/120 + d**4/16 - d**3/3 + 2*d**2. Factor v(j).
(j - 1)*(j + 4)/2
Let m(u) be the second derivative of -u**9/378 + u**8/140 - u**6/90 + 7*u**3/6 + u. Let d(p) be the second derivative of m(p). What is t in d(t) = 0?
-1/2, 0, 1
Let x(d) be the second derivative of d**7/14 - 19*d**6/30 + 3*d**5/2 + 5*d**4/6 - 11*d**3/2 + 9*d**2/2 + 3*d. Let x(c) = 0. What is c?
-1, 1/3, 1, 3
Suppose -34 = 3*u - 4*g, 2*g - 9 = -5*u - 31. Let n = -3 - u. Factor 2/7*c**n - 2/7*c + 0 - 2/7*c**2 + 2/7*c**4.
2*c*(c - 1)*(c + 1)**2/7
Let h be -1*(1 - 8 - 1). Suppose -h = -3*p - p. Let 2*d**2 - d + 2*d**2 - 3*d**p = 0. Calculate d.
0, 1
Let b(n) = -20*n**4 - 88*n**3 - 264*n**2 - 288*n - 100. Let x(y) = 7*y**4 + 29*y**3 + 88*y**2 + 96*y + 33. Let f(w) = 3*b(w) + 8*x(w). Factor f(j).
-4*(j + 1)**2*(j + 3)**2
Let i be 28/12*3 + -3. What is y in y**4 - 5*y**2 + 4*y**2 + 2*y**i - 2*y**4 = 0?
-1, 0, 1
Suppose 4*y - 3*h + 2*h - 7 = 0, 7 = y + 5*h. Suppose 2*c**y + 5*c**2 - 3*c**2 + 0*c**4 - 2*c**4 - 2 = 0. Calculate c.
-1, 1
Factor 1/6*r**4 + 5/3*r**3 + 13/6*r**2 + 6 - 10*r.
(r - 1)**2*(r + 6)**2/6
Suppose 0 = -0*z + 4*z - 16. Suppose 2*n + z = -i, 3*i + i + 5*n + 10 = 0. Factor 1/4*p**2 + 0*p - 1/4*p**3 + i.
-p**2*(p - 1)/4
Let i be (-2)/(-7) + 99/21. Suppose 5*b + 2*y + 25 = -3*y, 3*b - i*y = -23. Let d(g) = g**2 + 6*g + 5. Let q(t) = -t - 1. Let p(o) = b*q(o) - d(o). Factor p(a).
-(a - 1)*(a + 1)
Let k(t) be the second derivative of -t**4/4 + 5*t**3 - 75*t**2/2 + 14*t. Factor k(i).
-3*(i - 5)**2
Find v such that -6*v**4 + 4*v**4 - 2*v**3 - 9*v**3 + 5*v**3 - 4*v**2 = 0.
-2, -1, 0
Let c(h) be the third derivative of h**8/168 - 2*h**7/105 + h**5/15 - h**4/12 + h**2. What is j in c(j) = 0?
-1, 0, 1
Let c(j) be the third derivative of j**6/200 + j**5/50 + j**4/40 + 5*j**2. What is o in c(o) = 0?
-1, 0
Suppose -2/19*v**2 + 2/19 - 2/19*v**3 + 2/19*v = 0. Calculate v.
-1, 1
Let m(z) be the second derivative of -z**6/6 + 3*z**5/4 - 5*z**4/4 + 5*z**3/6 - 18*z. Let m(d) = 0. What is d?
0, 1
Let l(v) = -v**2 + 4*v - 1. Let i(o) = -o**3 + 7*o**2 - 7*o + 9. Let x be i(6). Let q be l(x). Factor -z**q + z - z.
-z**2
Let m(z) = 13*z**3 + 5*z**2 + z + 3. Let q be (-18)/2*(-2)/3. Let s(c) = -c**3 - c**2 + 1. Let n(i) = q*s(i) - 2*m(i). Solve n(g) = 0.
-1/4, 0
Suppose -2*q + 5*x = 25, 3*q - 13 = -2*x - 3. Let g be (-4)/(-66)*(4 - 1). Factor 2/11 - g*s**4 + q*s**2 + 4/11*s**3 - 4/11*s.
-2*(s - 1)**3*(s + 1)/11
Let u(o) be the first derivative of 1/2*o**4 - 1 + 2/5*o**5 - 2/3*o**3 - 1/3*o**6 + 0*o**2 + 0*o. Factor u(n).
-2*n**2*(n - 1)**2*(n + 1)
Let b(l) = l**3 + 6*l**2 + 4*l - 3. Let w be b(-5). Let u be w - (9/(-7) + 3). What is q in u*q - 2/7*q**4 - 2/7*q**3 + 0 + 2/7*q**2 = 0?
-1, 0, 1
Let r(a) be the third derivative of a**6/40 + a**5/5 + a**4/2 + 36*a**2. Factor r(p).
3*p*(p + 2)**2
Determine p, given that 8/11*p**3 - 4/11*p**2 - 8/11*p + 6/11 - 2/11*p**4 = 0.
-1, 1, 3
Suppose -4*q = -c - 4*c - 75, 0 = 4*q + 3*c - 83. Suppose -2*f + q = 3*f. Suppose 3*n + 3*n**3 - 2*n**2 + 2*n**f + 0*n**2 - 5*n - n**3 = 0. What is n?
-1, 0, 1
Factor 1331/6 - 121/2*i + 11/2*i**2 - 1/6*i**3.
-(i - 11)**3/6
Let x be 64/(-210) - (-8)/20. Let l(y) be the first derivative of 2/7*y + 2/7*y**2 + x*y**3 - 1. Factor l(a).
2*(a + 1)**2/7
Factor -1/2*v - 1/6*v**2 + 2/3.
-(v - 1)*(v + 4)/6
Factor -3/2*k**2 - 1 + 1/2*k**4 + 1/2*k**3 - 5/2*k.
(k - 2)*(k + 1)**3/2
Find d, given that -6*d**3 - 1221*d - d**5 + 8*d**2 + 0*d**5 - 8*d**4 + 1228*d = 0.
-7, -1, 0, 1
Let l = 41 + -39. Let v(h) be the second derivative of -h + 0 + 1/80*h**5 + 1/120*h**6 - 1/48*h**4 - 1/24*h**3 + 0*h**l. Suppose v(g) = 0. What is g?
-1, 0, 1
Determine p, given that 5*p**4 - 10*p - 9*p**2 + 16*p + 5*p**4 - 7*p**4 = 0.
-2, 0, 1
Let p = -54 + 272/5. Factor 0 - 2/5*n**2 - p*n.
-2*n*(n + 1)/5
Solve -12*j - 21*j + 35*j**2 + 3 - 5*j**2 = 0.
1/10, 1
Let x(a) be the third derivative of -a**8/84 + 2*a**7/35 + 5*a**2. Factor x(d).
-4*d**4*(d - 3)
Let u = -12 + 20. Let c = 19 - 14. Find n, given that -3*n**2 - 4*n**5 + 2*n**2 - u*n**4 - c*n**3 + 0*n**2 = 0.
-1, -1/2, 0
Let m(z) be the first derivative of 2*z**3/3 - 2*z**2 + 2*z - 3. Let m(h) = 0. Calculate h.
1
Factor 0*l**3 + 0 + 8/7*l**4 - 8/7*l**2 + 4/7*l**5 - 4/7*l.
4*l*(l - 1)*(l + 1)**3/7
Let w = -4 - -9. Factor -k**4 - 11*k**4 - w*k + 2*k - 8*k**3 - 15*k**2 - 16*k**3.
-3*k*(k + 1)*(2*k + 1)**2
Let j(w) = w**3 + 10*w**2 + 2*w + 22. Let l be j(-10). Factor 0 - 1/2*p**l + p.
-p*(p - 2)/2
Let w be (-10)/(-15)*3*(-3)/(-12). Find i, given that -2*i**4 + 0 + 0*i + w*i**2 + 3/2*i**3 = 0.
-1/4, 0, 1
Suppose 16 = 4*i + 8. Let -9*j**3 + 0 + i + 9*j + 2*j**2 - 3 - 1 = 0. What is j?
-1, 2/9, 1
Factor 63/8*v + 27/4 + 3*v**2 + 3/8*v**3.
3*(v + 2)*(v + 3)**2/8
Suppose r - 6*r + 3 = -2*g, 4*g - 7 = -3*r. Let c(o) be the first derivative of -g + 3/4*o**2 + 1/6*o**3 + o. Factor c(v).
(v + 1)*(v + 2)/2
Suppose -3*v + 18 = -2*v. Let g be (-5)/v - (-3)/6. Let 2/9*w**3 - g*w + 0 + 2/3*w**2 - 2/3*w**4 = 0. What is w?
-1, 0, 1/3, 1
Let b(x) be the third derivative of x**6/120 + 3*x**5/20 + 7*x**4/24 - x**3/2 + 2*x**2. Let m be b(-8). Factor -1/2*n**4 + 0*n + 0*n**2 + 0*n**3 - 3/2*n**m + 0.
-n**4*(3*n + 1)/2
Let l(u) = u**2 - u - 1. Let i(p) = -12*p**2 + 20*p - 8. Let v(r) = i(r) + 16*l(r). Factor v(g).
4*(g - 2)*(g + 3)
Let a(j) be the first derivative of -j**5 + 5*j**4/2 + 5*j**3 + 2. Solve a(t) = 0.
-1, 0, 3
Let w = -9/17 + 79/85. Factor -w*i**2 - 2/5*i**3 + 2/5*i + 2/5.
-2*(i - 1)*(i + 1)**2/5
Let s(r) be the second derivative of r**4/4 + r**3 - 9*r**2/2 - 10*r. Find o, given that s(o) = 0.
-3, 1
Let s be ((-3)/(-15) - -4) + -4. Determine a, given that 0 + 2/5*a**4 + 0*a - s*a**5 - 2/5*a**2 + 1/5*a**3 = 0.
-1, 0, 1, 2
Factor -15*j + 5*j**5 + 7*j + 15*j**2 - 15*j**4 - 2*j + 5*j**3.
5*j*(j - 2)*(j - 1)**2*(j + 1)
Let t(n) be the first derivative of -2*n**3/9 + 8*n/3 - 7. Suppose t(g) = 0. Calculate g.
-2, 2
Suppose 3*o = 2*o + 3. Factor -p + 1/2*p**o + 0 + 1/2*p**2.
p*(p - 1)*(p + 2)/2
Suppose 3*h = 2*q - 2*h + 11, 0 = 5*q + 5*h - 25. Suppose -q*c**3 + 5*c**3 - 2*c**2 - 2*c**2 + 2*c - c**2 = 0. Calculate c.
0, 2/3, 1
Let h(g) be the second derivative of -8*g**7/21 - 2*g**6/15 + 12*g**5/5 + 11*g**4/3 + 4*g**3/3 - 53*g. Let h(k) = 0. What is k?
-1, -1/4, 0, 2
Let o(j) = -j**3 + 2*j**2 + 3*j. Let d be o(-2). Let g be d/(-15)*2/(-4). Factor -g*i**2 + 2/3*i + 0.
-i*(i - 2)/3
Let n(r) be the first derivative of r**6/2 + 3*r**5/5 - 25. Suppose n(q) = 0. What is q?
-1, 0
Let k(q) = 3*q**3 + 5*q**2 - 11*q + 3. Suppose 0 = 5*y - y + 32. Let i(a) = a**3 + 2*a**2 - 4*a + 1. Let m(z) = y*i(z) + 3*k(z). Find b such that m(b) = 0.
-1, 1
Let q be (4 + -5)/(1/(-4)). Let w be (q/6)/((-5)/(-15)). Factor 4*m - m**2 + w + 0*m**2 + 3*m**2.
2*(m + 1)**2
Let f(m) be the first derivative of -m**6/21 - 2*m**5/5 - m**4 - 4*m**3/21 + 15*m**2/7 + 18*m/7 + 36. Determine k, given that f(k) = 0.
-3, -1, 1
Suppose 4*p - p - 15 = 0. Let v(d) be the third derivative of 1/300*d**6 - 1/150*d**p + 0 + 0*d + 0*d**3 + 2*d**2 - 1/30*d**4. Factor v(x).
2*x*(x - 2)*(x + 1)/5
Let o(a) be the first derivative of -3/4*a**3 + 1 - 3/4*a**2 - 1/4*a. Solve o(f) = 0 for f.
-1/3
Suppose 1 = -11*n + 1. Determine s, given that n*s**3 - 1/3*s**5 + 1/3*s**4 + 0*s**2 + 0 + 0*s = 0.
0, 1
Let v(b) be the third derivative of 0*b + 2*b**2 + 2/3*b**4 + 19/120*b**6 + 1/336*b**8 + 0 + 1/30*b**7 + 2/3*b**3 + 5/12*b**5. Solve v(f) = 0.
-2, -1
Let s(h) = h**5 + 3*h**4 - 2*h**3 + 4*h. Let i(x) = -x**4 - x. Let n(d) = -3*i(d) - s(d). Find g such that n(g) = 0.
-1, 0, 1
Let b(y) = y**2 + 3*y + 2. Let k be b(-3). Suppose -n + k*n + 2*w - 8 = 0, 2*n + 8 = 2*w. Suppose 0*a**2 + 2/7*a**3 + n*a + 0 = 0. Calculate a.
0
Let -5*p**5 + 5*p**3 + 767 - 767 = 0. What is p?
-1, 0, 1
Let m(f) be the first derivative of f**6/30 - f**5/40 - 3*f - 6. Let w(j) be the first derivative of m(j). Find p, given that w(p) = 0.
0, 1/2
Let f(n) = n + 7. Let c be f(-7). Let d(x) be the second derivative of 0*x*