 - 48*q**5 - 4/3*q = 0?
-2/3, 0, 1/4
Suppose 2*x + 8 = x. Let u(n) = n**4 + n**2 - n. Let y(i) = -10*i**4 - 2*i**3 - 6*i**2 + 10*i. Let j(s) = x*u(s) - y(s). Factor j(k).
2*k*(k - 1)*(k + 1)**2
Let w(n) be the first derivative of 3*n**2/2 - 18*n - 10. Let v be w(7). Factor -1/5 + 1/5*x**4 + 0*x**2 + 2/5*x - 2/5*x**v.
(x - 1)**3*(x + 1)/5
Determine a so that 2/7*a**4 + 4/7*a**3 + 0 + 0*a + 2/7*a**2 = 0.
-1, 0
Let h(i) be the second derivative of 1/36*i**4 - 1/20*i**5 + 0 + 1/30*i**6 + 3*i + 0*i**3 + 0*i**2 - 1/126*i**7. Solve h(j) = 0.
0, 1
Let h(q) be the first derivative of 0*q**2 - 1/24*q**4 + 0*q - 1/36*q**6 + 0*q**3 + 1/15*q**5 - 3. Solve h(n) = 0.
0, 1
Let q(k) be the second derivative of 1/75*k**6 - 1/10*k**4 + 1/25*k**5 + 0*k**3 + 0*k**2 + 0 - 6*k. Solve q(b) = 0 for b.
-3, 0, 1
Let x(w) be the second derivative of 3*w**5/40 + w**4/4 - 7*w**3/4 + 3*w**2 - 3*w. What is y in x(y) = 0?
-4, 1
Let b(i) be the third derivative of 1/150*i**6 + 0*i**3 + 0 + 0*i - 1/30*i**4 + 1/150*i**5 + 3*i**2 - 1/525*i**7. Suppose b(u) = 0. Calculate u.
-1, 0, 1, 2
Solve -2*t**3 + 2*t**2 - 2 + 0*t**3 + 54*t - 52*t = 0 for t.
-1, 1
Solve 1/2*h**4 - h + 0 - 2*h**3 + 5/2*h**2 = 0.
0, 1, 2
Let n(z) = 3*z**2 - z. Let i be n(-1). Let p(c) be the first derivative of -1/4*c**2 + 0*c + 1/12*c**6 + 3 + 1/5*c**5 - 1/3*c**3 + 0*c**i. Factor p(w).
w*(w - 1)*(w + 1)**3/2
Let j(a) be the third derivative of a**5/60 - a**4/8 + a**3/3 - 8*a**2. Factor j(g).
(g - 2)*(g - 1)
Let b(a) be the third derivative of -a**7/1260 + a**6/180 - a**5/60 - 5*a**4/24 - 4*a**2. Let d(r) be the second derivative of b(r). Factor d(c).
-2*(c - 1)**2
Find u such that -4/3*u + 14/3*u**4 - 14/3*u**2 + 4/3*u**3 + 0 = 0.
-1, -2/7, 0, 1
Let x = 1300/3 + -432. Solve -50/3*p**3 - 10/3*p**2 + 42*p**5 + x*p + 0 + 30*p**4 = 0 for p.
-1, -1/3, 0, 2/7, 1/3
Let x(h) be the second derivative of h**5/20 + h**4/3 + h**3/6 - h**2 + h. Let b be x(-3). Factor -t**4 + 4*t**2 - 2 + 1 - 1 - t**b.
-2*(t - 1)**2*(t + 1)**2
Let r(w) be the third derivative of -w**7/1400 + w**6/450 - w**5/600 - 5*w**3/6 - w**2. Let k(o) be the first derivative of r(o). Find q, given that k(q) = 0.
0, 1/3, 1
Let l(r) be the second derivative of r**7/21 - 2*r**6/15 + r**4/3 - r**3/3 - 4*r. Factor l(z).
2*z*(z - 1)**3*(z + 1)
Suppose 0 = -9*y + 10*y - 2. Let g = 4 - y. Factor 0 - 2/9*t + 2/9*t**g.
2*t*(t - 1)/9
Let t(v) be the third derivative of -v**6/60 + v**4/4 - 2*v**3/3 + 22*v**2. Suppose t(j) = 0. Calculate j.
-2, 1
Let c(i) be the second derivative of i**6/600 + i**5/150 - i**4/120 - i**3/15 + i**2/2 + 4*i. Let h(b) be the first derivative of c(b). Factor h(g).
(g - 1)*(g + 1)*(g + 2)/5
Let o(p) be the first derivative of 0*p + 0*p**4 + 1/18*p**6 - 1/6*p**2 + 1 + 2/15*p**5 - 2/9*p**3. Factor o(b).
b*(b - 1)*(b + 1)**3/3
Let f(a) be the third derivative of a**8/1680 - a**6/360 + a**3/2 + a**2. Let k(o) be the first derivative of f(o). Factor k(n).
n**2*(n - 1)*(n + 1)
Suppose 8 = 2*u + 4. Factor -g + 2*g**2 - u*g - 7*g + 6*g.
2*g*(g - 2)
Let w be (-14)/(-35) - ((-86)/(-5))/(-2). Factor -21/5*q**5 + 24*q**2 - w*q + 6/5 + 18*q**4 - 30*q**3.
-3*(q - 1)**4*(7*q - 2)/5
Let r(v) = 4*v**5 + 2*v**4 + 12*v**3 + 7*v**2 + 5*v - 3. Let n(z) = -z**5 + z**4 - z**3 - z + 1. Let b(j) = -3*n(j) - r(j). Factor b(w).
-w*(w + 1)**3*(w + 2)
Let r be ((-2)/(-4))/((-9)/((-162)/12)). Solve 0 - 3/4*g**4 - 3/4*g**3 + r*g**2 + 3/4*g = 0 for g.
-1, 0, 1
Factor -2*k**4 - 3*k**2 + 8*k**4 + 7*k**2 - 2*k**4 + 8*k**3.
4*k**2*(k + 1)**2
Suppose 8*x + j - 15 = 4*x, 4*x - 11 = -5*j. Solve -2*i**3 + 3*i**3 + i**3 - x*i + 2*i - 5*i**2 + 5*i**4 = 0 for i.
-1, -2/5, 0, 1
Let u(n) = -15*n**4 - 8*n**3 + 7*n**2 + 11*n - 11. Let v(a) = 4*a**4 + 2*a**3 - 2*a**2 - 3*a + 3. Let m(z) = 6*u(z) + 22*v(z). Let m(c) = 0. Calculate c.
-1, 0
Let r(m) be the first derivative of 2 - 1/2*m**4 + 0*m + 2/15*m**5 + 0*m**2 + 4/9*m**3. Find s, given that r(s) = 0.
0, 1, 2
Suppose 0 = 3*i - 15, -p - 3*p + 4*i - 8 = 0. Factor -p*m**2 + 2*m**2 + m**4 + 13*m**3 - 4*m - 14*m**3 + 5*m.
m*(m - 1)**2*(m + 1)
Factor 1/2*q**2 + 1/2*q**3 - 4*q - 6.
(q - 3)*(q + 2)**2/2
Suppose 125 + 0*c**3 - 67*c + 5*c**3 + 55*c**2 + 159*c + 83*c = 0. What is c?
-5, -1
Suppose 7 + 13 = -5*w. Let v be 4 + (w/2 - -1). Factor 0*c + 0 + 1/3*c**4 + 2/3*c**2 + c**v.
c**2*(c + 1)*(c + 2)/3
Suppose 4*h = -c - 37, -35 = 5*h + c + 4*c. Let u be (-36)/(-15) - (-4)/h. Factor -2*g**2 - 1 - u*g + 2 + 2*g**3 + 1.
2*(g - 1)**2*(g + 1)
Let f(l) be the third derivative of -l**10/6048 - l**9/1680 - l**8/2240 + l**7/2520 + l**4/8 - l**2. Let j(i) be the second derivative of f(i). Factor j(g).
-g**2*(g + 1)**2*(5*g - 1)
Let y(s) be the first derivative of 14*s**3/3 - 9*s**2 + 4*s - 8. Solve y(o) = 0.
2/7, 1
Let z(r) = -r**3 + r**2 + 5. Let o be z(0). Suppose 47 + 7 = g - 3*j, -o = -j. Let -2*b**3 - b**4 + 69 - b**2 - g = 0. What is b?
-1, 0
What is t in 0 + 2/7*t**2 - 8/7*t = 0?
0, 4
Find u, given that 2*u**4 + u**3 + 2*u**2 + u**3 + 2*u**3 = 0.
-1, 0
Suppose 3*q - 1 = -4. Let l = 3 + q. Suppose 2*p**l - 3*p**2 - p**3 + 0*p**2 = 0. What is p?
-1, 0
Let d(q) = -q**2 + 2*q + 4. Let j be d(0). Suppose -2*n - 2*h + j = 0, 3*h - h + 10 = 5*n. Factor -6/7*i - 24/7*i**2 + 4/7 - n*i**3.
-2*(i + 1)**2*(7*i - 2)/7
Let z(t) = -t**2 + 5*t - 1. Let d be z(2). Let u(s) be the first derivative of 0*s**2 + 0*s + 0*s**4 + 2/35*s**d - 2/21*s**3 - 2. What is r in u(r) = 0?
-1, 0, 1
Let h(d) be the third derivative of d**8/168 + d**7/105 - d**6/12 - d**5/30 + 2*d**4/3 - 4*d**3/3 + 5*d**2. Suppose h(k) = 0. What is k?
-2, 1
Let i = 23 - 21. Factor -10*c + 11*c**i + c**2 - 5*c - 3*c**3 + 6.
-3*(c - 2)*(c - 1)**2
Let s be ((-2)/(-6))/(119/42 - 2). Let -4/5*h + 2*h**2 - 8/5*h**3 + s*h**4 + 0 = 0. Calculate h.
0, 1, 2
Let k(l) be the first derivative of -2*l**5/45 + l**4/18 + 2*l**3/27 - l**2/9 + 1. Factor k(x).
-2*x*(x - 1)**2*(x + 1)/9
Let 18/5*c**4 + 2/5 - 4/5*c**2 - 24/5*c**3 + 8/5*c = 0. What is c?
-1/3, 1
Let r(p) be the third derivative of -p**6/24 + 19*p**5/4 - 1805*p**4/8 + 34295*p**3/6 + 27*p**2. Suppose r(h) = 0. What is h?
19
Let s(a) = a**3 - 8*a**2 + 7*a + 7. Let z be s(7). Suppose 3*y + 8 = z*y. Factor 2*f**3 + y*f - 4*f**2 - 3*f**2 + 3*f**2.
2*f*(f - 1)**2
Let j(l) be the third derivative of -l**8/5040 + l**7/2520 + l**3/6 + 6*l**2. Let u(x) be the first derivative of j(x). Find d such that u(d) = 0.
0, 1
Let d(g) = -g**3 + 3*g**2 + g + 2. Let u be d(2). Let f = u + -6. Factor -3*q**2 - 3*q - q**3 - q**2 + 1 + 7*q**f.
-(q - 1)**3
Suppose 2*g - 3 = g. Solve -s**g + 4*s**5 + 4*s**3 - s - s**2 - 5*s**4 - 2*s**5 + 2*s**2 = 0 for s.
-1/2, 0, 1
Let d = -50 + 50. Let g(j) be the second derivative of 1/12*j**4 + j + 1/2*j**2 + d + 1/3*j**3. Suppose g(q) = 0. What is q?
-1
Let x(k) be the first derivative of -k**7/14 - k**6/4 - 9*k**5/40 + k**4/8 + k**3/4 - k + 5. Let d(p) be the first derivative of x(p). Factor d(a).
-3*a*(a + 1)**3*(2*a - 1)/2
Let p(z) be the second derivative of 7*z**6/15 + 8*z**5/5 + 11*z**4/6 + 2*z**3/3 + 7*z. Factor p(x).
2*x*(x + 1)**2*(7*x + 2)
Let v be -1*((-6)/(-3) - 2). Suppose -a**3 + 0*a**4 + 3*a**3 - 2*a + v*a**3 - a**4 + 1 = 0. What is a?
-1, 1
Let c be 687/156 + (-2)/13. Let b(h) be the first derivative of h**2 - c*h**4 + 0*h - 4*h**5 + 1 + 5/3*h**3. Factor b(z).
-z*(z + 1)*(4*z + 1)*(5*z - 2)
Let j(w) be the second derivative of -2*w - 2/15*w**6 + 11/12*w**4 + 4/3*w**3 + 2/3*w**2 + 0 + 1/60*w**5. Find v, given that j(v) = 0.
-1, -2/3, -1/4, 2
Let z(k) = -4*k + 8*k**2 - 7 + 7. Let l(s) = 9*s**2 - 4*s. Let h = -3 - -9. Let p(t) = h*l(t) - 7*z(t). Let p(j) = 0. What is j?
0, 2
Let s(n) be the third derivative of -1/60*n**5 - 1/48*n**6 + 0*n**3 + 0*n + 0*n**4 + 0 + 3/70*n**7 + 2*n**2. Solve s(z) = 0.
-2/9, 0, 1/2
Suppose -2*a = -3*a. Let j(b) be the third derivative of 1/30*b**5 + a*b**4 + 0*b + 1/105*b**7 + 0*b**3 + 0 + b**2 + 1/30*b**6. Factor j(h).
2*h**2*(h + 1)**2
Suppose -u = -5*u - 3*q - 6, u + 2*q + 4 = 0. Suppose -v - j + 2 = u, 10 = v + 3*v + 3*j. Factor 0*z**v + 3*z + 5*z**2 + 7*z**3 + 3*z**4 - 2*z.
z*(z + 1)**2*(3*z + 1)
Let l(c) be the second derivative of 1/12*c**5 + 1/9*c**3 + 7/36*c**4 - 2*c + 0*c**2 + 0. Factor l(m).
m*(m + 1)*(5*m + 2)/3
Suppose 0 = -5*k + 15*k - 20. Find f, given that -f + 0 - 1/3*f**k = 0.
-