 2)/2
Let u(l) be the third derivative of -l**8/80640 - l**7/20160 + l**5/30 - 3*l**2. Let s(p) be the third derivative of u(p). Solve s(n) = 0 for n.
-1, 0
Suppose -16 = -2*z + 4*r, 4*z = -r + 2 + 12. Suppose 14 = z*p - 2. Suppose -1/3*l**5 + 0 + 0*l - 1/3*l**3 - 2/3*l**p + 0*l**2 = 0. Calculate l.
-1, 0
Let 5*h**4 - 3*h**3 + 5*h - 9*h**2 + 18*h**3 + 24*h**2 = 0. What is h?
-1, 0
Let c(w) = -81*w**4 - 15*w**3 + 15*w**2 + 48*w + 33. Let h(r) = 5*r**4 + r**3 - r**2 - 3*r - 2. Let s(x) = -2*c(x) - 33*h(x). Suppose s(d) = 0. Calculate d.
-1, 0, 1
Let w be 8/16 - 7/(-2). Let -w*d + 8*d**4 + 4*d**3 - 11*d**4 + 17*d**4 - 14*d**2 = 0. What is d?
-1, -2/7, 0, 1
Let x = -28/3 + 32/3. Find c, given that x + 0*c**2 - 2/3*c**3 + 2*c = 0.
-1, 2
Let a(b) be the first derivative of 2/9*b**3 - 1/6*b**2 - 2/15*b**5 + 0*b + 1/18*b**6 + 0*b**4 - 1. Determine y so that a(y) = 0.
-1, 0, 1
Let r(p) be the third derivative of 0 + 0*p + p**2 - 1/300*p**5 - 1/120*p**4 + 1/600*p**6 + 1/30*p**3. Solve r(i) = 0.
-1, 1
Let q be 531/(-174)*1 - -3. Let s = 43/290 - q. Let -2/5 + s*p**2 - 1/5*p = 0. Calculate p.
-1, 2
Suppose u - 6 = -5*a + 22, 0 = 5*u + 10. Let w be (9/a)/(6/20). Find s, given that 0*s**3 - 5*s**3 + 4*s**3 - 3*s**w + 4*s**4 = 0.
0, 1/3, 1
Let h(u) = -u**3 - u**2 - u. Let v(x) = 3*x**3 - x**2. Let y(m) = -20*h(m) - 5*v(m). What is o in y(o) = 0?
-4, -1, 0
Let m be (-3 + 9)/((-18)/(-8)). Let 8/3*v - m*v**3 + 8/9 + 10/9*v**2 - 2*v**4 = 0. Calculate v.
-1, -2/3, 1
Factor -15/8*p - 3/8*p**2 + 0.
-3*p*(p + 5)/8
Let i(p) be the first derivative of p**4/24 + p**3/6 + p**2/6 + 15. Find c, given that i(c) = 0.
-2, -1, 0
Let p(f) be the first derivative of -f**6/12 + 3*f**4/8 + f**3/3 - 16. Factor p(y).
-y**2*(y - 2)*(y + 1)**2/2
Let l(g) be the first derivative of g**3/3 + g**2 + g - 42. Factor l(s).
(s + 1)**2
Factor -4/7*p**2 + 12/7 - 10/7*p + 2/7*p**3.
2*(p - 3)*(p - 1)*(p + 2)/7
Suppose -s = -4*s + 18. Find t such that -2*t**2 + 3*t**3 + 9*t + 8*t**2 + s*t**2 = 0.
-3, -1, 0
Let s(k) = k**2 + k + 1. Let m(z) = 5*z**2 + 11*z + 7. Let y(h) = m(h) - 4*s(h). Let a be y(-7). Let 1/2*j**4 - 1/2*j**2 + 1/2*j**a - 1/2*j + 0 = 0. What is j?
-1, 0, 1
Let k(d) be the first derivative of -1/16*d**4 + 1/8*d**2 - 9 + 0*d**3 + 0*d. Factor k(p).
-p*(p - 1)*(p + 1)/4
Suppose 0 = -8*d + 11*d - 9. Factor 3*l - 29*l**3 + 31*l**d - 9*l + 4.
2*(l - 1)**2*(l + 2)
Let v(j) be the third derivative of j**8/112 + 2*j**7/105 - j**6/30 - j**5/10 + j**4/24 + j**3/3 - 40*j**2. Factor v(f).
(f - 1)*(f + 1)**3*(3*f - 2)
Let r be ((-4)/42)/(11/(-77)). Suppose -r*q + 0 - 2/3*q**2 + 2/3*q**4 + 2/3*q**3 = 0. What is q?
-1, 0, 1
Let i(h) be the second derivative of h**7/28 - 3*h**6/20 + 9*h**5/40 - h**4/8 - 70*h. Factor i(k).
3*k**2*(k - 1)**3/2
Let n(p) be the first derivative of 2/15*p**3 + 0*p + 1 + 1/10*p**4 - 2/25*p**5 + 0*p**2 - 1/15*p**6. Factor n(w).
-2*w**2*(w - 1)*(w + 1)**2/5
Let b = -16 - -18. Find x such that -b*x**3 + 2/3*x**4 + 0 - 2/3*x + 2*x**2 = 0.
0, 1
Let m = -125/42 - -22/7. Find p, given that 1/6*p**5 - m*p**3 + 0*p + 0 + 1/6*p**4 - 1/6*p**2 = 0.
-1, 0, 1
Let a(l) be the second derivative of l**6/432 - l**5/120 + l**4/144 - 3*l**3/2 - 4*l. Let f(n) be the second derivative of a(n). Factor f(o).
(o - 1)*(5*o - 1)/6
Suppose 0 = 7*m - 4*m - 6. Let -8*p**2 - 4 - 10*p - 2*p**3 + 2*p**3 - m*p**3 + 0 = 0. What is p?
-2, -1
Let b(l) be the first derivative of -4*l**3/3 + 28*l**2 - 52*l - 36. Factor b(m).
-4*(m - 13)*(m - 1)
Let a(k) = -k**4 - k**2 - 1. Let n be 1 + 12/3 + -4. Let i(c) = -7*c**4 + 8*c**3 - 3*c**2 - 8*c + 1. Let f(p) = n*i(p) - 3*a(p). Find w, given that f(w) = 0.
-1, 1
Let k be (1 - 455/507)/(4/6). Let 2/13*d**2 + 2/13*d**3 - 2/13*d**4 - k*d + 0 = 0. Calculate d.
-1, 0, 1
Determine x so that -1/5*x**4 - 12/5 + 4/5*x + 9/5*x**2 + 0*x**3 = 0.
-2, 1, 3
Let d(h) = -1. Let v(a) be the first derivative of 1 - 6*a + 1/2*a**2 - 1/3*a**3. Let c(z) = -6*d(z) + v(z). Find j such that c(j) = 0.
0, 1
Let c be 7/3 + (-2)/6. Let k be (-2)/(-1 - -3)*-3. Factor 1 + h**3 - h**k + c*h**3 - 2*h - h**4.
-(h - 1)**3*(h + 1)
Let m(n) be the second derivative of 1/6*n**4 + 1/12*n**6 + 0*n**2 - 4*n + 0*n**3 + 1/84*n**7 + 0 + 1/5*n**5. Factor m(h).
h**2*(h + 1)*(h + 2)**2/2
Let x = 39 - 36. Factor 0 + 2/3*o + 6*o**x + 8/3*o**4 + 4*o**2.
2*o*(o + 1)**2*(4*o + 1)/3
Let i(t) be the second derivative of t**7/21 + 2*t**6/15 - t**5/5 - 4*t**4/3 - 7*t**3/3 - 2*t**2 - 2*t. Suppose i(f) = 0. What is f?
-1, 2
Let p be (-210)/(-12)*(-4)/(-5). Suppose 13 = 3*c - p. Factor c*i + i**3 - i**2 - 9*i.
i**2*(i - 1)
Suppose -2*c - 3*c - 3*r + 87 = 0, -4*c - 2*r + 68 = 0. Determine s, given that 9*s**2 - 19*s**2 - 11*s**2 + c*s**3 + 6*s = 0.
0, 2/5, 1
Let b(y) be the second derivative of 0*y**2 - 1/20*y**5 - 1/4*y**4 - 6*y - 1/42*y**7 + 1/10*y**6 + 0 + 1/3*y**3. Solve b(j) = 0 for j.
-1, 0, 1, 2
Suppose -3 = 3*s - 12. Factor 2/9*x**2 - 2/9*x + 2/9*x**s - 2/9.
2*(x - 1)*(x + 1)**2/9
Suppose -2*c - 17 = 2*l + 3, -8 = -2*l + 5*c. Let r be 1*-2*l/30. Factor 0*s + r*s**4 + 0*s**3 + 2/5*s**5 + 0*s**2 + 0.
2*s**4*(s + 1)/5
Let l be (12/(-18))/((-2)/18). Suppose -2*r + 0*r = -l. Factor 3*i - 3 + 2*i**2 + 1 - i - i**3 - i**r.
-2*(i - 1)**2*(i + 1)
Determine h so that -6/5*h + 3/5*h**2 + 3/5 = 0.
1
Let y(r) be the first derivative of -r**4/16 - r**3/12 + r**2/8 + r/4 + 7. Find s, given that y(s) = 0.
-1, 1
Factor 1/2*q**4 + 0*q - q**2 + 0 + 1/2*q**3.
q**2*(q - 1)*(q + 2)/2
Let z(w) be the third derivative of -w**6/120 - w**5/30 - w**4/24 + 7*w**2. Factor z(v).
-v*(v + 1)**2
Let y(f) be the first derivative of -3 + 2/5*f**5 + 1/4*f**4 + 1/6*f**6 + 0*f**2 + 0*f + 0*f**3. Factor y(o).
o**3*(o + 1)**2
Let w(h) = 4*h**3 - 6*h**2 - 3. Let z(b) = 9*b**3 - 13*b**2 + b - 7. Let q(o) = -7*w(o) + 3*z(o). Let d be q(3). Factor -9 + 2*j - 4*j**3 + d + 2*j**5.
2*j*(j - 1)**2*(j + 1)**2
Let c = -9 + 12. Factor -2*p**4 - p**4 + 2*p**4 - 9*p**2 - 3*p**c - 6 + 4*p**4 + 15*p.
3*(p - 1)**3*(p + 2)
Let g(u) = u**3 + u**2 + 1. Let y(b) be the second derivative of -b**5/5 - b**4/4 - 5*b**2/2 - 5*b. Let s(l) = -5*g(l) - y(l). Factor s(c).
-c**2*(c + 2)
Let j(f) = -2*f**3 - f**2 - 2*f. Let p(d) = d - 3. Let b be p(6). Let v(m) = 2*m + 2*m - 3*m + m**3 + m**2. Let i(g) = b*j(g) + 5*v(g). Factor i(w).
-w*(w - 1)**2
Let n(u) = -6*u**3 + u**2 - 3*u + 2. Let k be n(1). Let b = -1 - k. Factor 2/5*t**3 - 1/5 - 1/5*t**4 + 2/5*t**2 - 1/5*t - 1/5*t**b.
-(t - 1)**2*(t + 1)**3/5
Let n = 4 + -1. Suppose -k = n - 7. Factor 2*p**5 + 4 - 4*p**k - 4 + 6*p**4.
2*p**4*(p + 1)
Let s be (-6)/(-10) + (-129)/215. Let g be (1/(-3))/(2/(-4)). Factor -g*b**2 - 2/3*b + s.
-2*b*(b + 1)/3
Let z(f) = -6*f**3 + 15*f**2 + 3*f + 6. Let h(w) = -w + 7*w**3 - 5 + 0 - 2*w - 14*w**2. Let q(m) = 6*h(m) + 5*z(m). Factor q(u).
3*u*(u - 1)*(4*u + 1)
Let n(x) be the second derivative of -x**7/8820 - x**6/2520 - x**4/2 - 4*x. Let f(h) be the third derivative of n(h). Factor f(d).
-2*d*(d + 1)/7
Let v(a) = -a**3 - 4*a**2 + 4*a - 2. Let y be v(-5). Let z be (1 - 4)*(-6)/9. Factor y*s - 2*s**z + s + 4*s**2.
2*s*(s + 2)
Suppose -2*u = 15 - 49. Let -v + 16*v**4 + 7*v**2 + 6*v**3 - 6*v**5 - 2*v**5 - 3*v - u*v**2 = 0. What is v?
-1/2, 0, 1, 2
Let o(n) = 17*n**2 + 10*n + 9. Let p(d) = 11*d**2 + 7*d + 6. Let k = -14 - -9. Let h(u) = k*o(u) + 8*p(u). Factor h(w).
3*(w + 1)**2
Let v(g) be the third derivative of -g**7/4200 - g**6/900 + g**3/2 + g**2. Let n(m) be the first derivative of v(m). Find o, given that n(o) = 0.
-2, 0
Let i = -66 + 100. Let y be 1/6*i + -3. Factor y - 8/3*j + 2/3*j**2.
2*(j - 2)**2/3
Let x be 15/6*24/15. Let i(b) be the second derivative of 2*b - 1/30*b**5 - 1/9*b**2 + 2/135*b**6 + 1/9*b**3 - 1/54*b**x + 0. Determine q so that i(q) = 0.
-1, 1/2, 1
Let d(w) be the first derivative of 2*w**5/55 - w**4/11 - 8*w**3/11 - 14*w**2/11 - 10*w/11 + 14. Factor d(n).
2*(n - 5)*(n + 1)**3/11
Let h be (-1)/12 - 5/15. Let u = h + 7/6. Solve -u*v**2 + 9/4*v**3 - 5/4*v - 1/4 = 0.
-1/3, 1
Factor -8*m**3 - 2*m**4 - 4*m - 8*m**2 + 5*m**2 - 7*m**2.
-2*m*(m + 1)**2*(m + 2)
Solve -1/4 + 0*u**2 + 1/2*u**3 + 1/4*u**4 - 1/2*u = 0.
-1, 1
Suppose 2*z + 3*y - 21 = 0, y = -4*z - 2*y + 27. Let d be 26/56 - (-24)/84. Let -1/4*b**z - 3/4*b - 1/4 - d*b**2 = 0. What is b?
-1
Let v be (3 + -2)*3/72. Let t(o) be