(2*p - 1)
Suppose 2*h - h + 180 = 5*f, 2*f = 3*h + 85. Let c be (-1)/(-5) + 3/f. Determine o, given that -4/7 - c*o + 2/7*o**2 = 0.
-1, 2
Let b be -4 + 3 + (6 - 3). Let u(g) be the second derivative of 3*g + 0 + 1/5*g**b - 2/15*g**3 + 1/30*g**4. Factor u(i).
2*(i - 1)**2/5
Factor 1/2*z - 1/2*z**2 + 1.
-(z - 2)*(z + 1)/2
Suppose 2/3 + 2/3*u**2 - 4/3*u = 0. Calculate u.
1
Suppose 4*o - 65 + 0 = 5*t, 3*o + 5*t = 5. Suppose -6*s + o = -s. Factor 2/9*n + 2/9*n**s - 4/9.
2*(n - 1)*(n + 2)/9
Suppose 0 = 4*i - 5*m + 10*m - 18, 3*m = -2*i + 10. Factor 2/7*l + 2/7*l**4 + 0 + 6/7*l**3 + 6/7*l**i.
2*l*(l + 1)**3/7
Let k(w) be the third derivative of w**6/960 + w**5/160 + w**4/96 + 2*w**2 + 16. Factor k(q).
q*(q + 1)*(q + 2)/8
Let w(r) be the second derivative of -r**5/105 - r**4/42 + r**2 - 3*r. Let f(a) be the first derivative of w(a). Factor f(h).
-4*h*(h + 1)/7
Let 0*d + 0*d**3 - 2/11*d**4 + 4/11*d**2 - 2/11 = 0. What is d?
-1, 1
Factor 1/4*i**4 + 4*i**3 + 125/4 + 45/2*i**2 + 50*i.
(i + 1)*(i + 5)**3/4
Determine n so that -8/3*n - 2/9*n**2 - 8 = 0.
-6
Suppose 2*l = -0*l - v, 0 = l + 4*v. Solve l*h**3 - 2/3*h**5 + 2/3*h + 4/3*h**4 + 0 - 4/3*h**2 = 0 for h.
-1, 0, 1
Let q(n) = -n**2 - 4*n + 4. Let d be q(-6). Let r be ((-3)/(-6))/((-7)/d). Factor -2/7*a**3 + 4/7 - r*a**2 + 2/7*a.
-2*(a - 1)*(a + 1)*(a + 2)/7
Let v(i) be the first derivative of -1 + 0*i + 0*i**5 + 0*i**3 + 1/4*i**6 - 3/8*i**4 + 0*i**2. Factor v(u).
3*u**3*(u - 1)*(u + 1)/2
Let m = -19 - -21. Let l(v) = -5*v**3 - v. Let u be l(-1). Solve -k - k - 2 + u + 0*k - 2*k**m = 0.
-2, 1
Let f be ((-4)/(-6))/(16/24). Let s = 3 + f. Factor -18/11*i**2 + 10/11*i - 4/11*i**s - 2/11 + 14/11*i**3.
-2*(i - 1)**3*(2*i - 1)/11
Let d = -8 + 11. Let j = -22 - -32. Factor -1 - 6 + 14*c - 6*c**2 + 3 + j*c**4 - 14*c**d.
2*(c - 1)**2*(c + 1)*(5*c - 2)
Let d(a) be the second derivative of -a**4/21 - 2*a**3/21 + 4*a**2/7 + 5*a. Factor d(w).
-4*(w - 1)*(w + 2)/7
Let z(q) = 8*q + 9. Let m be z(4). Suppose m*g - 42*g + 3 = 0. Factor 0*k + 0*k**2 + 2/9*k**g + 0.
2*k**3/9
Let v(g) = -4*g**3 - 4*g**2 - 5. Let l(y) = y**3 + y**2 + 1. Let z(d) = 2*d + 1. Let s be z(2). Let i(b) = s*l(b) + v(b). Suppose i(h) = 0. Calculate h.
-1, 0
Let z(i) be the third derivative of -i**6/390 + i**5/130 - i**3/39 - 21*i**2. Suppose z(o) = 0. Calculate o.
-1/2, 1
Let h = -4 - -14. Factor h*m - 10*m + 0*m**2 + 1 - m**2.
-(m - 1)*(m + 1)
Find i, given that -5 - i**3 + 16*i + 0*i**3 - 4*i**3 + 5*i**2 - 11*i = 0.
-1, 1
Suppose 9 = -0*z + 3*z. Factor -6*j**2 + 13*j**4 - 16*j**4 - 5*j**3 - 4*j**z.
-3*j**2*(j + 1)*(j + 2)
Let z be (0 + 1)*(0 + 70). Let b be (-21)/z*5/(-6). Factor b*f**3 + 1/4*f + 0 - 1/2*f**2.
f*(f - 1)**2/4
Suppose 0 = n + 3*i - 3, 14 = -n + i + 13. Let 0 + n*z + 2/5*z**2 = 0. What is z?
0
Let r be 2 - (-6)/(-2) - -30. Let d = r + -27. Let -2/3*b - 4/9*b**4 + 2/9 + 2/9*b**d + 2/3*b**3 = 0. Calculate b.
-1, 1/2, 1
Let h = -249 - -5977/24. Let p(u) be the third derivative of -2*u**2 - 1/120*u**6 + 0*u + 0 + 1/60*u**5 + h*u**4 - 1/6*u**3. Solve p(q) = 0.
-1, 1
Let v(b) = 14*b**3 + 5*b**2 - 15*b + 11. Let n(f) = -5*f**3 - 2*f**2 + 5*f - 4. Let w(r) = -17*n(r) - 6*v(r). Factor w(y).
(y + 1)**2*(y + 2)
Let a(k) be the first derivative of 2*k**4 - 10*k**3/3 + k**2 - 7. Factor a(v).
2*v*(v - 1)*(4*v - 1)
Let y(q) = 7*q**2 + 5*q - 25. Let t(n) be the third derivative of -n**5/20 - n**4/8 + 2*n**3 + 7*n**2. Let f(r) = 13*t(r) + 6*y(r). Factor f(v).
3*(v - 2)*(v - 1)
Solve 24*i - 2 + 12*i**3 + 26*i**2 + 2 + 2*i**4 + 8 = 0.
-2, -1
Let k(p) = 23*p**2 - 8*p + 20. Let t(j) = -4*j + 8*j**2 - 2 + j + 9. Let q(a) = -6*k(a) + 17*t(a). Factor q(l).
-(l + 1)*(2*l + 1)
Let z(u) be the first derivative of u**4/8 + 3*u**3/2 + 27*u**2/4 - 2*u - 4. Let n(o) be the first derivative of z(o). Factor n(f).
3*(f + 3)**2/2
Suppose -3*h - 24 = -4*t + 3, h = -5. Determine q so that -3*q**2 - 2 + t*q**2 - 4*q**2 + 6*q + 0*q**2 = 0.
1/2, 1
Let b be (8/(-24))/((-1)/6). Solve 3/2*i + 3/4*i**4 + 0*i**b - 3/4 - 3/2*i**3 = 0 for i.
-1, 1
Suppose 2*n = -0*n - 4*d + 30, 0 = 4*n + 4*d - 76. Suppose -5*g + n = 2*z, g - 4*z = z + 10. Factor -1/4*b**g + 0*b - 3/4*b**4 - 3/4*b**3 + 0 - 1/4*b**2.
-b**2*(b + 1)**3/4
Suppose 0 = -2*w - v + 2*v - 15, 2*w - 3*v = -21. Let q be (5/(-30))/(w/27). Factor 3/2*p - q - 3/2*p**3 + 0*p**2 + 3/4*p**4.
3*(p - 1)**3*(p + 1)/4
Suppose 2*r - 2 = 2*p, r = -r - p + 8. Suppose -3*s - z = -2*s - 4, 2*s + 2 = r*z. Solve 2/5*i**s - 2/5*i + 2/5*i**3 - 2/5 = 0.
-1, 1
Let v(z) be the third derivative of -2/315*z**7 + 3*z**2 + 1/90*z**6 + 0 + 0*z**3 + 1/45*z**5 - 1/18*z**4 + 0*z. What is a in v(a) = 0?
-1, 0, 1
Suppose 23 = 5*t + 3. Let x(p) = 2*p**4 + 5*p**3 - p**t - p - 5*p**3. Let r(u) = -3*u**4 + 4*u**3 - 6*u**2 + 6*u - 1. Let c(m) = -2*r(m) - 4*x(m). Factor c(z).
2*(z - 1)**4
Let x be 0 + (0/2)/(-2). Let r be 0/(0 + (-1 - x)). Suppose -3*a**3 - 3*a + 3*a**2 + 1 + r*a + 2*a**3 = 0. What is a?
1
Let c(v) be the second derivative of 0*v**3 + 1/10*v**5 + 1/15*v**6 - 1/6*v**4 - 1/21*v**7 + 0 + 3*v + 0*v**2. Suppose c(b) = 0. What is b?
-1, 0, 1
Let x(i) = 5*i**2 - i + 8. Let r(h) = 14*h**2 - 2*h + 23. Let z(t) = -6*r(t) + 17*x(t). Let d be z(6). Find y such that -y**3 - y**d - 3*y + 3*y + y**2 + y = 0.
-1, 0, 1
Let j(x) be the first derivative of 5*x**6/6 + 7*x**5 + 45*x**4/2 + 110*x**3/3 + 65*x**2/2 + 15*x + 2. Factor j(p).
5*(p + 1)**4*(p + 3)
Let w = 148/231 + 2/77. Let b(l) be the first derivative of 0*l - 1 + w*l**3 - 2*l**2. Let b(z) = 0. Calculate z.
0, 2
Let s be (0 + -3)/(21/(-14)). Determine f so that -3*f + 2*f + s*f + 4*f**2 - 5*f**2 = 0.
0, 1
Suppose 0 = -2*v - 3*z - 0*z - 24, 0 = 3*v - 2*z + 10. Let w be (v - -5)/((-1)/2). Solve -50/3*k**3 + 32/3*k + 10/3*k**w + 8/3 = 0 for k.
-2/5, 1
Let g(j) = 2*j - 4. Let k be g(2). Let b(a) be the third derivative of 3*a**2 + k - 1/72*a**4 + 0*a + 0*a**3 - 1/180*a**5. Suppose b(o) = 0. What is o?
-1, 0
Solve 0 - 2/3*x**3 + 8/3*x**2 - 2*x = 0 for x.
0, 1, 3
Let c = 5907/224 + 235/32. Let a = 34 - c. Suppose 0 - 2/7*d - a*d**2 = 0. What is d?
-1, 0
Let j(d) be the second derivative of d**5/100 + d**4/60 - d**3/30 - d**2/10 + 6*d. Factor j(m).
(m - 1)*(m + 1)**2/5
Suppose j + r - 8 = 0, 1 - 15 = -3*j - r. Let i be (48/(-18))/((-2)/j). What is w in -2*w**5 + 0 + i*w**3 + 4*w - 6*w + 0 = 0?
-1, 0, 1
Let p(v) be the second derivative of -v**4/24 + v**3/6 - v**2/4 + 4*v. Factor p(a).
-(a - 1)**2/2
Let b(k) be the first derivative of k**5/15 - k**3/3 - k**2/3 - 8. Factor b(h).
h*(h - 2)*(h + 1)**2/3
Let i(c) be the third derivative of -1/30*c**5 + 0*c + 0 - 1/12*c**4 + 1/3*c**3 + 3*c**2 + 1/60*c**6. Find g, given that i(g) = 0.
-1, 1
Let v be (24/36)/(4/18). Factor l**2 - 7 + v + 3.
(l - 1)*(l + 1)
Let m(v) = 2*v**2 + 2*v - 1. Let f be m(-2). Factor 3*x**3 + 6*x**2 + 3*x**4 - 12*x**2 - f*x + 3*x**2.
3*x*(x - 1)*(x + 1)**2
Suppose 40*a = 43*a. Factor -1/5*n**3 + 0 + a*n**2 + 1/5*n.
-n*(n - 1)*(n + 1)/5
Let d(f) be the second derivative of f**6/45 + f**5/6 + f**4/2 + 7*f**3/9 + 2*f**2/3 + 7*f. Factor d(m).
2*(m + 1)**3*(m + 2)/3
Let z be (-7)/(-84)*-4 + 16/30. Factor -1/5*o**4 + 1/5*o**2 + 0 - z*o**3 + 1/5*o.
-o*(o - 1)*(o + 1)**2/5
Let 4/7*g**2 - 22/21*g**3 + 0*g - 8/7*g**4 + 0 + 10/21*g**5 = 0. What is g?
-1, 0, 2/5, 3
Let x(o) be the third derivative of -o**5/60 - o**4/2 - 6*o**3 - 7*o**2. Factor x(p).
-(p + 6)**2
Suppose -3*y - 17 = 4*k - 5, 0 = 2*y - 5*k - 15. Factor -4/7*n**3 + 0*n**2 + 0 + 2/7*n + y*n**4 + 2/7*n**5.
2*n*(n - 1)**2*(n + 1)**2/7
Determine s so that -4/9*s**5 + 0*s + 4/9*s**3 + 0 - 4/9*s**2 + 4/9*s**4 = 0.
-1, 0, 1
Let v(k) be the first derivative of k**6/60 - k**5/15 + k**4/12 + 5*k**2/2 + 3. Let r(j) be the second derivative of v(j). Let r(x) = 0. What is x?
0, 1
Let w(t) = t**3 - 5*t**2 + 3*t - 10. Let r be w(5). Let b(v) be the first derivative of 8/27*v**3 + 2*v**4 + 0*v + 18/5*v**r + 0*v**2 + 3. Factor b(f).
2*f**2*(9*f + 2)**2/9
Let m(a) = -a**4 - 2*a**3 + 0*a**3 - a**5 + 3*a**3. Let p(d) = -2*d**4 + 4*d**2. Let h(o) = -2*m(o) - p(o). Find x such that h(x) = 0.
-2, -1, 0, 1
Let t(k) = k**2 + 2*k - 5. Let a be t(-5). Solve -10*y**2 + a*y + 2*y**3 + 2*y**3 - 2*y - 2 = 0.
1/2, 1
Suppose -3*c = 17 - 5. Let g be c*(58/(-28) - -2). Solve -10/7*h + 2*h**2 + g - 6/7*h**3 = 0.
1/3, 1
Let j