s**4. Let c(p) be the first derivative of r(p). Solve c(x) = 0 for x.
-1, 1
Let o(j) = -11*j**4 + 3*j**3 + 7*j**2 - 4*j. Let h(c) = c**4 - c**3 - c. Let q(i) = -20*h(i) + 4*o(i). What is z in q(z) = 0?
-1/4, 0, 1
Let q = -8/7 - -68/35. Solve -q*r**3 + 1/5*r**4 + 6/5*r**2 + 1/5 - 4/5*r = 0 for r.
1
Suppose 3*a - 12 = 3. Suppose l = -a, 2*l = -0*s - s - 8. Factor -m + 0*m + 4*m - s - m**2.
-(m - 2)*(m - 1)
Let z(d) be the first derivative of -4 + 3/14*d**2 + 3/28*d**4 + 9/35*d**5 + 0*d - 1/7*d**6 - 3/7*d**3. Let z(y) = 0. Calculate y.
-1, 0, 1/2, 1
Let k = 23 + -24. Let y(u) = -3*u**3 + 6*u**2 - 9*u. Let v(o) = -o. Let p(i) = k*y(i) + 6*v(i). Factor p(w).
3*w*(w - 1)**2
Let b be (14/(-21))/(2/(-9)). Suppose -3*v + b*v + 12*v - 18*v**2 - 2 = 0. What is v?
1/3
Let g(p) be the first derivative of 7*p**3/4 + 15*p**2/8 - 3*p/2 - 7. Factor g(i).
3*(i + 1)*(7*i - 2)/4
Let u(r) = -r**2 - 6*r + 7. Suppose -2*z = -6 + 2, -2*t = -z + 16. Let i be u(t). Determine f so that 1 + f**3 + i*f + 2*f - f**4 - 3*f**3 = 0.
-1, 1
Let t(p) be the third derivative of p**5/60 - p**4/12 + p**3/6 - 8*p**2. Find l such that t(l) = 0.
1
Let v(n) = -4*n**2 - n - 1. Let f(j) = 3*j + 15. Let t be f(-6). Let c(s) = -s**2 - s. Let a(b) = t*c(b) + v(b). Let a(x) = 0. Calculate x.
1
Let h(r) be the second derivative of r**4/54 - 4*r**3/27 + r. Factor h(n).
2*n*(n - 4)/9
Let s(f) be the third derivative of f**9/52920 + f**8/7840 + f**7/2940 + f**6/2520 - f**4/6 + f**2. Let c(g) be the second derivative of s(g). Solve c(q) = 0.
-1, 0
Let f be (-6)/4*4/(-3). Determine z, given that 33*z + 2 - 33*z - f*z**2 = 0.
-1, 1
Let b(k) = k**2 + 3*k - 5. Let j be b(2). Let y(z) be the second derivative of 5/8*z**j + 0 + 2*z**2 + 3*z - 3*z**3 + 5/4*z**4. Factor y(r).
(r + 2)*(5*r - 2)**2/2
Factor 3/2*x**2 + 9/2*x + 3.
3*(x + 1)*(x + 2)/2
Suppose -6*o + 8*o = 4. Let b(w) be the first derivative of 1 - 4/3*w - 1/9*w**3 + 2/3*w**o. Factor b(k).
-(k - 2)**2/3
Suppose -4*p - 2 = 14. Let v = p - -9. Factor 4*x**v - 2*x**3 + 6*x**4 - 6*x**2 + 4*x**3 - 2*x**5 - 4*x.
2*x*(x - 1)*(x + 1)**2*(x + 2)
Let z(l) = -12*l**5 - 21*l**4 + 3*l**3 + 12*l**2 + 9*l. Let w(g) = 3*g**5 + 5*g**4 - g**3 - 3*g**2 - 2*g. Let i(q) = -9*w(q) - 2*z(q). Factor i(s).
-3*s**2*(s - 1)*(s + 1)**2
Let n = 916/69 - 60/23. Let j(l) be the first derivative of -8*l**2 - n*l**3 - 1 - 2*l. Factor j(f).
-2*(4*f + 1)**2
Let g = -968/5 + 194. Factor 2/5*f**2 - 2/5*f**4 - g*f**5 + 2/5*f**3 + 0 + 0*f.
-2*f**2*(f - 1)*(f + 1)**2/5
Let l(u) be the first derivative of 49*u**6/33 - 56*u**5/55 + 2*u**4/11 - 8. Determine m, given that l(m) = 0.
0, 2/7
Let 2*k**3 + 1 + 0*k**3 - 2*k**2 + 1 - 2*k + 0 = 0. Calculate k.
-1, 1
Let x = -13 + 13. Factor 2*m**2 - 4 + x - 8*m - 5*m**2.
-(m + 2)*(3*m + 2)
Let r = 43 + -30. Find u such that r*u**2 - 3 - 11*u**2 - 2*u - 3*u = 0.
-1/2, 3
Let v(f) be the first derivative of -1/16*f**4 + 0*f - 1/6*f**3 + 3 + 0*f**2. Factor v(c).
-c**2*(c + 2)/4
Let k(g) be the first derivative of -g**6/90 + 2*g**4/3 + 7*g**3/3 + 8. Let s(l) be the third derivative of k(l). Factor s(a).
-4*(a - 2)*(a + 2)
Let w(p) be the third derivative of p**5/360 + p**4/24 + p**3/4 - 4*p**2. Let w(n) = 0. What is n?
-3
Let u(g) be the first derivative of -5*g**6/2 - g**5 - 8. Factor u(f).
-5*f**4*(3*f + 1)
Let b(z) = 31*z**5 + 23*z**4 - 8*z**3 + 3*z**2 + 3*z - 3. Let w(x) = 32*x**5 + 24*x**4 - 8*x**3 + 4*x**2 + 4*x - 4. Let q(p) = -4*b(p) + 3*w(p). Factor q(n).
-4*n**3*(n + 1)*(7*n - 2)
Factor 1/4*z**3 + 1/2*z**4 + 1/2*z - 5/4*z**2 + 0.
z*(z - 1)*(z + 2)*(2*z - 1)/4
Suppose 0 = 5*m + 3*z - 24, 1 = z - 2. Suppose -f = -m*f. Suppose f*l - 1/2*l**4 + 1/2*l**2 + 7/4*l**5 - 7/4*l**3 + 0 = 0. What is l?
-1, 0, 2/7, 1
Let a be (-20)/(-6)*(-18)/(-15). Find r such that 2 + r**3 + 5*r**a + 3*r + 1 - 7*r**2 - 4*r**3 - 1 = 0.
-1, -2/5, 1
Factor 3 + 0*g - 6*g - 1 - 2*g**2 - 6.
-2*(g + 1)*(g + 2)
Let a(t) be the second derivative of t**9/6048 - t**8/1680 + t**7/1680 + t**3/2 + t. Let d(m) be the second derivative of a(m). Factor d(g).
g**3*(g - 1)**2/2
Let c = -12 + 15. Factor -3 - 2*y**2 + c - 2 - 4*y.
-2*(y + 1)**2
Let q be (11 + 7 + -19)*(0 + -3). What is l in 0 - 2/3*l**q - 2/3*l + 4/3*l**2 = 0?
0, 1
Let z(i) be the first derivative of i**4/12 - i**3/6 - i**2 + i + 1. Let d(m) be the first derivative of z(m). Determine c, given that d(c) = 0.
-1, 2
Let w = 200 - 599/3. Let m be 70/(-21)*6/(-5). Find f such that 0*f + w + 1/3*f**m + 0*f**3 - 2/3*f**2 = 0.
-1, 1
Let i(s) be the second derivative of 2*s**6/5 + 2*s**5 + 7*s**4/3 - 8*s**3/3 - 8*s**2 - 6*s. Factor i(z).
4*(z + 1)**2*(z + 2)*(3*z - 2)
Let y(v) be the third derivative of v**6/180 - v**4/36 + 3*v**2. Solve y(j) = 0 for j.
-1, 0, 1
Let n(h) be the third derivative of h**7/1575 + 2*h**6/225 + 8*h**5/225 + 16*h**2. Factor n(v).
2*v**2*(v + 4)**2/15
Suppose -3*q = -a + 1, -q - q = -3*a + 17. Factor -a*y - y**2 + y**4 + 7*y + y**3 - y.
y*(y - 1)*(y + 1)**2
Let w(f) = -f**3 - 7*f**2 - 5*f - 5. Let s(h) = 3*h**3 + 20*h**2 + 14*h + 14. Let q(c) = -6*s(c) - 17*w(c). Factor q(i).
-(i - 1)*(i + 1)**2
Let k(o) be the third derivative of -o**8/1176 + o**7/735 + o**6/420 - o**5/210 + 11*o**2. Factor k(v).
-2*v**2*(v - 1)**2*(v + 1)/7
Let i = 5 + -6. Let o be (-1)/i + (-12)/20. Determine k so that -2/5*k + 0 + 4/5*k**2 - o*k**3 = 0.
0, 1
Suppose 0 = 2*h - 3*r + 10, 8 = 3*r - 4. Let z(p) be the first derivative of p**3 + 1/2*p + 1/10*p**5 + p**2 + 1/2*p**4 + h. Find v such that z(v) = 0.
-1
Determine v, given that 2/11*v**2 + 2/11*v - 4/11 = 0.
-2, 1
Suppose -l + 0*l = -2. Factor -n**4 - n**4 - 2*n**3 - 4*n**3 - 2*n + 0*n**2 - 6*n**l.
-2*n*(n + 1)**3
Let d(u) be the first derivative of u**4/26 - 2*u**3/39 - u**2/13 + 2*u/13 - 4. Let d(l) = 0. Calculate l.
-1, 1
Factor i - i + 3*i**2 - 6*i - 6*i.
3*i*(i - 4)
Let z(n) be the second derivative of -1/60*n**5 + 0*n**3 - n + 0 + 1/18*n**4 + 0*n**2. Let z(a) = 0. Calculate a.
0, 2
Factor 0 + 1/2*q**2 - 1/4*q**3 + 3/4*q.
-q*(q - 3)*(q + 1)/4
Factor 6/5*s + s**2 + 1/5.
(s + 1)*(5*s + 1)/5
Let i be ((-4)/(-6))/(2/9). Suppose 25 = i*x + 2*x. Factor 2*h**3 - h**4 + 0*h**5 + 2*h**2 - 1 + 2*h**5 - h - 3*h**x.
-(h - 1)**2*(h + 1)**3
Let b(c) be the third derivative of -1/150*c**5 + 0*c - 1/120*c**4 + 0 + 0*c**3 + 4*c**2 + 1/525*c**7 + 1/1680*c**8 + 0*c**6. Factor b(z).
z*(z - 1)*(z + 1)**3/5
Let t be (-11)/3*1645/15. Let h = t + 403. Factor -8/9*q**3 - 8/3*q - 10/3*q**2 + h.
-2*(q + 2)**2*(4*q - 1)/9
Let b be -2 - 5/((-20)/12). Let a be 6/6 - (-3 + b). Suppose -2/5 - 6/5*d**2 + 2/5*d**a + 6/5*d = 0. Calculate d.
1
Solve 1/3*u**2 - 1/3*u + 0 = 0 for u.
0, 1
Let w(x) be the third derivative of x**10/189000 - x**5/60 - 6*x**2. Let z(i) be the third derivative of w(i). Factor z(u).
4*u**4/5
Let h(j) be the second derivative of 0*j**4 + 0*j**2 + 0*j**6 - j - 1/5*j**5 + 0 + 1/3*j**3 + 1/21*j**7. Let h(l) = 0. Calculate l.
-1, 0, 1
Let z(q) be the first derivative of -16*q**5/15 + 2*q**4 - q**3 + q**2/6 + 9. Determine m, given that z(m) = 0.
0, 1/4, 1
Factor 1/3*v - 1/3*v**3 - 1/3*v**2 + 1/3.
-(v - 1)*(v + 1)**2/3
Suppose -2*q + 8 = -q. Let j be 64/10*(q + -3). Factor 10*n**2 + 3*n**2 + 2*n + j*n**3 + 3*n**2.
2*n*(4*n + 1)**2
Let d(r) = 8*r + 1. Let v be d(1). Suppose -2*t - 17 = -4*a - 3, 0 = -4*a + 20. Find j such that j**2 - 19*j**2 + t*j**2 - v*j + 25*j**3 - 1 = 0.
-1/5, 1
Let u(c) = 4*c**4 - 2*c**3 - 16*c**2 - 4*c. Let p(o) = o**4 + o**3 - o**2. Suppose -v + 10 = 2*l - 0*v, -5*l + v = -32. Let j(n) = l*p(n) - u(n). Factor j(x).
2*x*(x + 1)**2*(x + 2)
Let 2/7*v**2 - 4/7*v + 4/7*v**3 - 2/7 = 0. What is v?
-1, -1/2, 1
Let b(v) be the third derivative of -v**6/300 + v**5/50 - v**4/20 + v**3/15 - 4*v**2. Determine s so that b(s) = 0.
1
What is n in -28 + 7*n**2 - 2*n - 3*n**2 + 23*n + 3*n = 0?
-7, 1
Suppose -2 = -4*b + 2. Let g be -2*b*(-1)/6. What is d in 2/3*d**2 + 0 + g*d**3 + 1/3*d = 0?
-1, 0
Let g(i) = i**3 - 7*i**2 + 7*i - 7. Let x(o) = 4*o**2 - 4*o + 4. Let t(s) = 4*g(s) + 7*x(s). Find d such that t(d) = 0.
0
Let q(t) be the second derivative of 1/110*t**5 - 1/33*t**3 + 0 - 1/11*t**2 + 3*t + 1/66*t**4. Factor q(r).
2*(r - 1)*(r + 1)**2/11
Factor -1/3*q**3 + 0*q - q**2 + 0.
-q**2*(q + 3)/3
Let h(w) = -w**2 + w - 1. Let s(t) = 4*t**4 - 16*t**3 - 28*t**2 + 68*t + 16. Let z(n) 