 1
Let z(j) = 4*j**2 + 16*j + 64. Let s(r) = r**2. Let p(v) = -6*s(v) + 2*z(v). Factor p(q).
2*(q + 8)**2
Let d = -2 + 4. Factor 3*b - b**d - b**2 - 3*b + 2.
-2*(b - 1)*(b + 1)
Solve 2/5*t**3 + 0 - 2/5*t**2 + 0*t = 0.
0, 1
Let x(h) be the first derivative of -h**4/6 + h**2 - 4*h/3 - 2. Determine n, given that x(n) = 0.
-2, 1
Let w(p) be the second derivative of -2*p**7/21 - 2*p**6/5 - 2*p**5/5 - 18*p. Factor w(h).
-4*h**3*(h + 1)*(h + 2)
Suppose d + 0 = 2. Let b(n) be the second derivative of -1/12*n**4 - d*n**2 - n + 0 + 2/3*n**3. Let b(a) = 0. What is a?
2
Let d(u) be the third derivative of -u**6/60 - 2*u**5/15 - u**4/3 - 49*u**2. Determine f so that d(f) = 0.
-2, 0
Suppose -6 = -2*d + 4. Factor -20/3*w**2 + 8/3*w**4 + 2/3*w**d + 2/3*w**3 + 16/3 - 8/3*w.
2*(w - 1)**2*(w + 2)**3/3
Let z be 5/(405/186)*-60. Let a = z - -138. Factor 0*b**2 + a*b**4 - 2/9*b**3 + 0 + 0*b.
2*b**3*(b - 1)/9
Let g = 18 - 15. Factor 0*b**2 - b**3 + 0*b**g + b**4 - 2*b**2.
b**2*(b - 2)*(b + 1)
Suppose 0 = -5*i - 0*i + 15. Solve 2*c - 4*c**3 - i*c**2 - 5*c - 1 + 3*c**3 = 0 for c.
-1
Suppose 3*h + 32 = 2*v, -h = 2*v - 0*h - 16. Suppose a = -a + v. Factor -3*r**3 + r**4 - 3*r**2 + 2*r**4 + 32*r**a - 29*r**5.
3*r**2*(r - 1)*(r + 1)**2
Suppose 4*o + a = 11, -3*o - 5 = -4*a + 1. Let z(g) be the second derivative of -1/30*g**4 + 1/5*g**2 + 0 + 1/50*g**5 - 1/15*g**3 + o*g. Factor z(x).
2*(x - 1)**2*(x + 1)/5
Let t = -5/3 + 13/6. Factor p**2 + 1/2*p**3 + 0 + t*p.
p*(p + 1)**2/2
Let o(g) be the second derivative of 3*g - 1/100*g**5 + 1/10*g**3 - 1/5*g**2 + 0*g**4 + 0. Factor o(d).
-(d - 1)**2*(d + 2)/5
Let j(b) = -7*b**4 + 7*b**3 - 9*b - 9. Let y(m) = 2*m**4 - 2*m**3 + 2*m + 2. Suppose -n - n = -4. Let v(p) = n*j(p) + 9*y(p). Solve v(o) = 0 for o.
0, 1
Let m(d) be the second derivative of d**5/5 - 2*d**4/3 - 14*d**3/3 - 8*d**2 + 14*d. Factor m(r).
4*(r - 4)*(r + 1)**2
What is x in -5/4*x**3 + 5/4*x + 0 + 5/4*x**4 - 5/4*x**2 = 0?
-1, 0, 1
Factor -36/7 + 20/7*y**2 + 4/7*y**3 + 12/7*y.
4*(y - 1)*(y + 3)**2/7
Let t(f) = 3*f**3 + 20*f**2 + 7*f + 6. Suppose 0 = -4*l + 5 - 25. Let p(c) = 2*c**3 + 13*c**2 + 5*c + 4. Let x(j) = l*t(j) + 8*p(j). Factor x(a).
(a + 1)**2*(a + 2)
Let f be 0 - (-3 + 3 - 2). Factor f - 6 + x**2 + 6 + x**2 - 4*x.
2*(x - 1)**2
Let x(g) be the third derivative of 2*g**5/5 + 3*g**4/8 - 2*g**2. Factor x(v).
3*v*(8*v + 3)
Let i(u) be the third derivative of u**7/630 + u**6/270 - u**5/90 - u**4/18 + u**3/2 + 2*u**2. Let f(n) be the first derivative of i(n). Factor f(j).
4*(j - 1)*(j + 1)**2/3
Let b(h) = h**2 + 2*h + 4. Let w(k) = -2*k**2 - k - 4. Let z(c) = 7*b(c) + 6*w(c). Find g such that z(g) = 0.
-2/5, 2
Determine o, given that 2*o**3 + 8*o - 6*o**2 - 4 - 1/4*o**4 = 0.
2
Suppose -2*r + 9 = -1. Let m be (10/r)/((-21)/(-6)). Let 6/7*c**4 - 2/7*c**5 - 2/7 - m*c**2 + 6/7*c - 4/7*c**3 = 0. Calculate c.
-1, 1
Let b be 4/(-6)*(-45)/10. Solve -3*s**b + 6*s**2 - 2*s**2 - 5*s**3 + 4*s**4 = 0 for s.
0, 1
Let g(s) be the first derivative of -s**7/140 - 7*s**6/240 - s**5/40 + s**4/16 + s**3/6 + 3*s**2/2 - 3. Let t(f) be the second derivative of g(f). Factor t(k).
-(k + 1)**3*(3*k - 2)/2
Suppose -2*r + 3*o - 13 = -r, -2*o + 8 = 0. Let d(a) = 4*a**3 - 3*a + 1. Let q(g) = g**3 + 1. Let h(k) = r*d(k) + q(k). Factor h(f).
-3*f*(f - 1)*(f + 1)
What is p in 2/13*p**4 + 0 + 0*p + 2/13*p**2 + 4/13*p**3 = 0?
-1, 0
Let h(i) be the second derivative of 25/14*i**7 + 17/6*i**3 - 3/2*i**4 - 23/5*i**5 - i**2 + 8*i + 2/3*i**6 + 0. Find q such that h(q) = 0.
-1, -2/3, 1/5, 1
Solve 3*d**5 - 14 + d**2 + 3*d + 18*d**3 + 11*d**2 + 12*d**4 + 14 = 0.
-1, 0
Let t be ((-79)/(-5))/((-672)/(-80)). Let v = -3/14 + t. Suppose -2/3*o + 0 + v*o**2 = 0. What is o?
0, 2/5
Let g(u) be the third derivative of -u**5/20 + 7*u**4/8 - 3*u**3 + 23*u**2. Factor g(b).
-3*(b - 6)*(b - 1)
Solve -1/2*x**3 + 2*x**2 + 0 - 2*x = 0.
0, 2
Suppose 0 = -3*c - 2*q + 2 - 0, 0 = -4*c - 2*q + 4. Factor 2*s**5 + 4*s**4 - 3*s**2 - s**2 - c*s + 0*s + 0*s**5.
2*s*(s - 1)*(s + 1)**3
Let g(n) = n**2 - 5*n - 3. Suppose 25 = 5*m + 4*a + a, 5*m - 3*a = 33. Let q be g(m). Determine f so that -f + 0*f - 4*f - f**q + 6*f = 0.
-1, 0, 1
Let 3/7*a**3 - 36/7 - 24/7*a + 3/7*a**2 = 0. What is a?
-2, 3
Let x(k) = -6*k**3 - k**2 - k + 2. Let a be x(-2). Let m be (-4)/(-3) - 28/a. Determine j, given that 0 - 3/2*j + m*j**2 = 0.
0, 2
Let p be -1 - 5/(-1) - -3. Find d such that 5*d + 2*d**2 + p + d - 3 = 0.
-2, -1
Let t(n) be the first derivative of n**3/15 - n**2/10 - 2*n/5 - 5. Factor t(x).
(x - 2)*(x + 1)/5
Let m = 99/5 + -292/15. Let h be (4/10)/(6/5). Find g such that m*g**4 + h*g**3 + 0*g**2 + 0 + 0*g = 0.
-1, 0
Suppose -5*o + 10*t + 25 = 5*t, 5 = -o - 4*t. Factor 5*z**3 + 4*z + 14*z**2 + 7*z**3 + o*z**3 - 2 - 7*z**3.
2*(z + 1)**2*(4*z - 1)
Determine q, given that 4/13 + 2/13*q**2 + 6/13*q = 0.
-2, -1
Let j be -3 + 20/3 + -3. Factor 4/3*f + 0 - j*f**2.
-2*f*(f - 2)/3
Let r be 6/96 - (1 + -1). Let n(a) be the first derivative of 0*a + 1/6*a**3 + r*a**4 + 2 + 1/8*a**2. Let n(q) = 0. Calculate q.
-1, 0
Let i(v) be the third derivative of v**7/945 + v**6/108 + v**5/30 + 7*v**4/108 + 2*v**3/27 - 4*v**2. Determine x, given that i(x) = 0.
-2, -1
Let j(l) be the second derivative of -2*l**7/105 + 2*l**5/15 - 2*l**3/3 - l**2/2 + 6*l. Let z(v) be the first derivative of j(v). Factor z(g).
-4*(g - 1)**2*(g + 1)**2
Let d(z) be the second derivative of 5*z**4/3 + 32*z**3 - 40*z**2 + 14*z + 2. Let d(b) = 0. Calculate b.
-10, 2/5
Let u(k) be the third derivative of 1/20*k**5 + 8/3*k**3 + 0 - 1/2*k**4 + 0*k - 1/480*k**6 - k**2. Factor u(i).
-(i - 4)**3/4
Factor 4/3 - 2*d**3 + 4/3*d**2 + 14/3*d.
-2*(d - 2)*(d + 1)*(3*d + 1)/3
Let i be (-2 - -5)*16*4/168. Factor 0 + i*a**4 - 2/7*a**2 + 0*a - 6/7*a**3.
2*a**2*(a - 1)*(4*a + 1)/7
Let h(m) be the second derivative of 3*m**5/80 - m**4/8 - m**3/8 + 3*m**2/4 + 3*m. Factor h(p).
3*(p - 2)*(p - 1)*(p + 1)/4
Factor 2/13*j**2 + 2/13*j**3 - 2/13*j**4 - 2/13*j**5 + 0 + 0*j.
-2*j**2*(j - 1)*(j + 1)**2/13
Let q(m) = -2*m**2 + 3*m - 3. Let i(f) = -3*f**2 + 6*f - 5. Let j(v) = 3*i(v) - 5*q(v). Factor j(w).
w*(w + 3)
Let m be (-190)/(-120) + (-2)/8. Let j(l) be the first derivative of -m*l**3 + 7/3*l**2 - 1 - 2/3*l. Factor j(q).
-2*(q - 1)*(6*q - 1)/3
Let v(a) be the second derivative of a**6/40 - a**5/10 + a**4/8 + 3*a**2/2 + 4*a. Let z(u) be the first derivative of v(u). Factor z(h).
3*h*(h - 1)**2
Let y(v) = v**3 - 6*v**2 + v + 2. Let g be y(6). Suppose -5*l = -3*r - g, -r = -l + 2*r - 8. Solve 0*n - 2/3*n**2 - 3*n**l + 0 - 3*n**3 = 0.
-2/3, -1/3, 0
Factor 33 - 5*j**2 + j**2 + 16*j - 45.
-4*(j - 3)*(j - 1)
Let x(u) be the first derivative of -1/6*u - 1 - 2/9*u**3 + 1/3*u**2. Factor x(f).
-(2*f - 1)**2/6
Let h be (-14)/21*(-1506)/8 - 4. Factor -189*l**3 - 39/2*l**2 - 6 + 42*l - h*l**4.
-3*(l + 1)**2*(9*l - 2)**2/2
Let a be (-7)/(-15) + (12/10)/(-3). Let r(q) be the second derivative of 3*q + q**2 + 1/5*q**5 + 0 - 2/3*q**3 - a*q**6 + 0*q**4. Suppose r(w) = 0. Calculate w.
-1, 1
Let y(f) be the first derivative of 2/9*f**2 + 2 + 0*f - 2/9*f**5 - 1/9*f**4 + 10/27*f**3. Solve y(x) = 0.
-1, -2/5, 0, 1
Solve -4*z**2 + 2 + z + 6 - 4*z + 7*z = 0.
-1, 2
Let d be 4/(7 + (-3 - -10)). Factor -24/7*v**2 - 26/7*v**3 - 8/7*v - 12/7*v**4 + 0 - d*v**5.
-2*v*(v + 1)**2*(v + 2)**2/7
Suppose -3*m + 8*m = 20. Suppose -y - 2 = -m. Suppose -7*v**5 + 6*v**3 + 3*v**3 + 2 - 5*v**2 + 5*v**4 - 2 - y*v = 0. What is v?
-1, -2/7, 0, 1
Let t = 7 - 4. Suppose -d**4 + 2*d**4 - d**3 - d**t + 2*d - 1 = 0. Calculate d.
-1, 1
Let k be (-8)/(-24) + (-5)/(-3). Factor -2/3*q - 4/3 + 2/3*q**k.
2*(q - 2)*(q + 1)/3
Let d = -271 - -273. Factor 0*z**d + 2/5*z**4 - 2/5 - 4/5*z**3 + 4/5*z.
2*(z - 1)**3*(z + 1)/5
Let i(m) = 2*m**2 + 20*m - 36. Let z(o) = o**2 + o - 1. Let b(n) = i(n) - 4*z(n). Factor b(u).
-2*(u - 4)**2
Let c(r) = -4*r**2 + 29*r - 5. Let g be c(7). Let z(q) be the third derivative of 2*q**g - 1/24*q**4 + 0*q + 1/240*q**6 + 0 + 0*q**3 + 1/120*q**5. Factor z(v).
v*(v - 1)*(v + 2)/2
Suppose -6 = -2*z + 2*s, 5*z - 10 = 2*s + 5. Suppose 0 = q - z*q + 4. Factor 0 + 1/4*k**3 + 1/4*k**4 - 1/4*k - 1/4*k**q.
k*(k - 1)*(k + 1)**2/4
Let g be 6/(-33) + (-888)/(-44). Factor 2*p**3 + 19*p**5 - g*p**5 - p - 2*p + 2*p.
-p*(p - 1)**2*(p + 1)**2
Let i(y) be the first deriva