0.
0
Let f be (9 + -5)*5/(18 - 3). Factor -4/3 - 8/3*z**3 + 8/3*z**2 - f*z**4 + 4/3*z**5 + 4/3*z.
4*(z - 1)**3*(z + 1)**2/3
Suppose 4*z - 2*z = 0. Find c such that 3*c**2 - 4*c**2 + z + 1 + 0*c**2 = 0.
-1, 1
Factor -6/5*i + 3/5 + 3/5*i**2.
3*(i - 1)**2/5
Let k(o) be the second derivative of 0 - o - 3/2*o**2 + 0*o**3 + 0*o**5 + 1/2*o**4 - 1/10*o**6. Factor k(v).
-3*(v - 1)**2*(v + 1)**2
Solve -3*g - 2*g + 0*g + 7*g - 2*g**2 = 0.
0, 1
Suppose -j + 2 = -4. Let a(y) be the third derivative of 2*y**2 + 0 + 1/96*y**4 + 0*y - 1/840*y**7 + 1/240*y**5 - 1/480*y**j + 0*y**3. Factor a(u).
-u*(u - 1)*(u + 1)**2/4
Find z, given that -7/3*z - 2 + 5/3*z**2 = 0.
-3/5, 2
Let k(s) = 7*s**2 + 2 + 3*s - 2*s - 2*s**3 - 10*s**2. Let v be k(-2). Solve -54*c**2 - 12*c + c - 4 - 3*c - 12*c - 14*c**v - 46*c**3 = 0 for c.
-1, -2/7
Let z(k) = k**3 - k**2 + 1. Let p(b) = -12*b**3 + 15*b**2 - 9*b - 9. Let s(g) = -p(g) - 15*z(g). What is i in s(i) = 0?
-2, 1
Suppose -4*i**4 + 4*i**4 + i**4 - 2*i**4 = 0. Calculate i.
0
Let q be (33/462)/(1 - (1 + -1)). Let y(p) be the first derivative of 1 + 0*p + 1/7*p**2 - 4/21*p**3 + q*p**4. Factor y(s).
2*s*(s - 1)**2/7
Suppose 0 = 2*m - 2*d - 10, -m - 2*d - 4 = -0*m. Let c be m + (-10)/7 + 0. Factor -2/7*o**2 - 2/7*o + c.
-2*(o - 1)*(o + 2)/7
Let c be 9/(-51) - 0/2. Let w = c - -55/119. Find m, given that -2/7*m**2 + w - 2/7*m + 2/7*m**3 = 0.
-1, 1
Let t(f) be the first derivative of -3*f**4/4 - 4*f**3 - 15*f**2/2 - 6*f - 5. Solve t(q) = 0.
-2, -1
Let c(z) be the third derivative of z**8/112 - z**6/10 - z**5/10 + 3*z**4/8 + z**3 + 19*z**2. Find j, given that c(j) = 0.
-1, 1, 2
Let c(n) be the first derivative of n**4/8 + 2*n**3/3 - n**2/4 - 2*n + 72. Factor c(d).
(d - 1)*(d + 1)*(d + 4)/2
Let x(f) be the third derivative of -2*f**2 + 0*f + 1/120*f**6 - 1/12*f**4 + 0*f**3 + 0 + 1/60*f**5. Factor x(z).
z*(z - 1)*(z + 2)
Let i(n) be the first derivative of -n**5/20 + n**4/8 - n**2/4 + n/4 + 17. Factor i(t).
-(t - 1)**3*(t + 1)/4
Let g(r) = r**3. Let c be g(0). Let i(j) be the third derivative of c - 2*j**2 + 0*j**3 - 1/60*j**6 + 1/15*j**5 - 1/12*j**4 + 0*j. Factor i(w).
-2*w*(w - 1)**2
Let u(w) = -9*w - 161. Let j be u(-18). Factor -5/4*r**2 - j - 1/4*r**3 - 2*r.
-(r + 1)*(r + 2)**2/4
Let q(g) be the third derivative of 1/504*g**8 + g**2 + 0*g**6 + 0*g**5 + 0*g**4 + 0*g**3 + 0 - 1/315*g**7 + 0*g. Factor q(s).
2*s**4*(s - 1)/3
Let v(d) be the first derivative of 1/3*d**3 - 1/2*d**2 + 0*d - 1. Solve v(r) = 0.
0, 1
Let k(v) be the first derivative of v**3/3 + v**2 + v + 20. Solve k(h) = 0 for h.
-1
Let k = 873 + -870. Suppose 4/3*a**2 + 0*a + 6*a**k + 10/3*a**5 + 0 + 8*a**4 = 0. What is a?
-1, -2/5, 0
Let a(u) be the second derivative of -u**6/15 + 5*u**4/6 - 4*u**2 - 3*u. Let q = -2 - -1. Let o(k) = -k**2 + 1. Let g(m) = q*a(m) - 6*o(m). Factor g(c).
2*(c - 1)**2*(c + 1)**2
Let x(v) = v**2 + 2*v. Let k be x(0). What is m in -2/5*m + k + 4/5*m**3 + 2/5*m**2 = 0?
-1, 0, 1/2
Let b(h) be the first derivative of -h**6/120 - h**5/10 - 3*h**4/8 + 4*h**3/3 + 5. Let a(p) be the third derivative of b(p). Determine f so that a(f) = 0.
-3, -1
Let c = 61 - 57. Let s(u) be the first derivative of 3 - 1/2*u**c + 0*u - 2/5*u**5 + 2/3*u**3 + 1/3*u**6 + 0*u**2. Factor s(r).
2*r**2*(r - 1)**2*(r + 1)
Factor 10/7*c + 2/7*c**2 + 0.
2*c*(c + 5)/7
Factor 0 + 3/4*w + 3/2*w**2 + 3/4*w**3.
3*w*(w + 1)**2/4
Let h be 12/(-3)*5/(-70). Let a(g) be the first derivative of 2/21*g**3 + h*g**2 - 1 + 2/7*g. Let a(m) = 0. Calculate m.
-1
Let x(n) be the second derivative of n**8/6720 - n**7/1680 + n**6/1440 + n**3/3 - n. Let g(a) be the second derivative of x(a). Factor g(r).
r**2*(r - 1)**2/4
Let o(v) be the third derivative of -v**5/270 + v**4/108 - 6*v**2. Determine r, given that o(r) = 0.
0, 1
Suppose 3*m - 10 + 1 = 0. Suppose -3*p + 3*l = -0*l - m, -3*p + 4 = -4*l. Factor -50/7*q**5 - 8/7*q - 138/7*q**3 + 20*q**4 + p + 8*q**2.
-2*q*(q - 1)**2*(5*q - 2)**2/7
Let j(x) = -4*x + 0*x**2 + 8 + x**2 - 4*x**2. Let c(v) = -5*v**2 - 8*v + 15. Let n(a) = 4*c(a) - 7*j(a). Factor n(d).
(d - 2)**2
Let f = -6/13 - -56/65. Let c be 1*(2 - -2)/2. Find r such that 2/5*r**3 - f - 6/5*r**c + 6/5*r = 0.
1
Factor 2*q**5 + 4*q**4 - q**4 - 3*q**5 - 23*q**3 + 21*q**3.
-q**3*(q - 2)*(q - 1)
Let -5/2*z**5 + 5*z**3 + 0 + 0*z**2 + 0*z**4 - 5/2*z = 0. What is z?
-1, 0, 1
Let u(w) be the second derivative of -3*w**5/5 + 5*w**4/3 + 4*w**3/3 - 40*w. Factor u(n).
-4*n*(n - 2)*(3*n + 1)
Let b(f) be the second derivative of f**4/15 - 2*f**3/5 - 21*f. Factor b(k).
4*k*(k - 3)/5
Suppose 2*u = -3*u - 20. Let z = -2 - u. Factor 0*a**2 - 2*a**2 + 0*a**4 + z*a**4.
2*a**2*(a - 1)*(a + 1)
Factor 12/7*k**3 - 30/7*k - 9/7 + 27/7*k**2.
3*(k - 1)*(k + 3)*(4*k + 1)/7
Let n(h) = -h**3 - 9*h**2 - 9*h + 4. Let o(v) = 2*v**3 + 14*v**2 + 14*v - 6. Let j(f) = -8*n(f) - 5*o(f). Let j(m) = 0. What is m?
-1, 1
Let r(w) be the third derivative of -w**7/525 - w**6/300 + w**2 + 5. Solve r(n) = 0 for n.
-1, 0
Suppose 3*m = m. Solve 2/5*a**2 + 2/5*a + m = 0 for a.
-1, 0
Suppose -3/8*f**2 + 0 + 3/8*f**3 + 0*f = 0. Calculate f.
0, 1
Let h(z) be the first derivative of 5*z**7/189 + 4*z**6/45 + z**5/10 + z**4/27 - 4*z + 1. Let y(j) be the first derivative of h(j). Factor y(r).
2*r**2*(r + 1)**2*(5*r + 2)/9
Let s(a) be the third derivative of 1/27*a**3 - 1/135*a**5 - 1/1512*a**8 + 1/945*a**7 + 0 + 1/270*a**6 - 1/108*a**4 - a**2 + 0*a. Factor s(y).
-2*(y - 1)**3*(y + 1)**2/9
Let a(l) = l - 20. Let k be a(24). Let w = -4 + 7. Solve 6 - 2 + 6*g**k - 2 - 20*g**w - 12*g + 24*g**2 = 0.
1/3, 1
Let h**2 - 7*h**5 + h**3 + 6*h**5 + 0*h**2 - h**4 = 0. Calculate h.
-1, 0, 1
Let u(v) be the first derivative of 0*v + 5 + 3/14*v**4 + 4/7*v**3 + 1/35*v**5 + 4/7*v**2. Solve u(w) = 0.
-2, 0
Let n = -1 + 1. Suppose 2*r**2 + 1 + n + 0 + 4*r + 1 = 0. What is r?
-1
Let s(h) be the second derivative of -h**4 + 7*h**3/2 + 3*h**2 - 29*h. Suppose s(y) = 0. Calculate y.
-1/4, 2
Let v = 27/80 - -1/16. Let x(h) be the first derivative of 1 + v*h**3 + 2/5*h**2 - 2/5*h. Factor x(d).
2*(d + 1)*(3*d - 1)/5
Factor 12*t - 3*t**3 - 5*t**3 - t**3 - 3*t**4.
-3*t*(t - 1)*(t + 2)**2
Let n be 6/(-9) + (-96)/18. Let a be (-1 + 1)*3/n. Factor 0*k + 0*k**2 + a - 2/5*k**4 - 4/5*k**3.
-2*k**3*(k + 2)/5
Let h(v) = -v**3 + v. Let l(p) = 3*p**3 - 3*p. Let x = 2 - 3. Let g(s) = x*l(s) - 6*h(s). Factor g(o).
3*o*(o - 1)*(o + 1)
Let m be (-1)/7*(-14)/4. Let a(i) be the first derivative of 1/2*i**2 + 0*i**3 + 2 + 1/6*i**6 + 0*i + 0*i**5 - m*i**4. Find n such that a(n) = 0.
-1, 0, 1
Determine l so that 8/17*l**2 - 8/17*l**4 - 8/17*l + 0 + 14/17*l**3 - 6/17*l**5 = 0.
-2, -1, 0, 2/3, 1
Let o be (-26)/(-4) + (-1)/2. Let k be (o*1)/(0 - -2). Solve 8*t + 6 + 5*t**2 + t**3 - k + 1 = 0 for t.
-2, -1
Let i(d) = d**4 + d**3 + d**2 - d. Let v(u) = 3*u**4 + 6*u**3 + 5*u**2 - 6*u. Let b(g) = -4*i(g) + v(g). Factor b(p).
-p*(p - 2)*(p - 1)*(p + 1)
Suppose u + 39 = 4*g, 0 = 3*g - u + 5 - 35. Find k such that k - 2*k + g*k**3 - k**4 + 0*k**2 - 3*k**2 - 12*k**3 = 0.
-1, 0
Suppose 1 - 3 = -2*a. Suppose -5*z + 32 = -4*f, 3*z - 4*z - f = -a. Factor -4*y**4 - 2*y**3 - 2*y**4 + z*y**4.
-2*y**3*(y + 1)
Factor 2/11*w**3 - 4/11*w**2 - 6/11*w + 0.
2*w*(w - 3)*(w + 1)/11
Let d(n) be the third derivative of -1/150*n**5 + 2*n**2 + 0*n + 0*n**3 - 1/120*n**4 - 1/600*n**6 + 0. Factor d(g).
-g*(g + 1)**2/5
Let j = 1279/21 - 175/3. Factor -12/7*v + 2/7*v**2 + j.
2*(v - 3)**2/7
Factor -4 - o + o**2 + 3 + 0*o**3 - o**3 + 2*o.
-(o - 1)**2*(o + 1)
Suppose 5*g - 3 = -c, 4*c - 8 = -3*g + 4. Let z be ((-2)/(-5))/(c/15). Factor -2*v**2 - 2*v - 6*v**2 - 2*v**3 + 4*v**z.
-2*v*(v + 1)**2
Suppose 0 = -5*c + 4*z, 5*c + 3*z = -0*z + 35. Let p(i) be the first derivative of 2/21*i**3 + 0*i**2 - 1/14*i**c + 0*i + 1. Find d, given that p(d) = 0.
0, 1
Suppose 0 = 9*l - 8*l - 4. Determine o, given that -13/4*o**2 - 1/4*o**l - 1 - 3/2*o**3 - 3*o = 0.
-2, -1
Let b(u) = -12*u**4 - 12*u**3 + 16*u**2 + 16*u + 8. Let z(w) = w**4 + w**3 - 1. Let r(h) = b(h) + 8*z(h). Let r(q) = 0. Calculate q.
-2, -1, 0, 2
Let v = -5 - -9. Factor -10*y**v + 2*y**4 + 9*y**4 - y**3.
y**3*(y - 1)
Let v(r) be the second derivative of -2/9*r**3 + 0*r**2 - 13/18*r**4 - 1/9*r**7 + 5*r + 0 - 9/10*r**5 - 23/45*r**6. Factor v(q).
-2*q*(q + 1)**3*(7*q + 2)/3
Let f = -108/5