
h**2*(h + 2)**2
Let z(j) = -7*j - 39. Let t be z(-6). Let q be (-2)/(-8) + 1/4. Suppose 1/2*h + 1/2*h**2 - q - 1/2*h**t = 0. Calculate h.
-1, 1
Let k(c) be the first derivative of c**5/20 - 3*c**4/16 + c**3/4 - c**2/8 + 13. Factor k(x).
x*(x - 1)**3/4
Suppose 3*r + 2*r - 40 = 0. Find z, given that -4*z + 3*z**3 + r*z**2 - 5*z**2 - 2*z = 0.
-2, 0, 1
Suppose 18*v + 84 = 22*v. Let f be -2 + ((-138)/v)/(-1). Determine h, given that 6*h**3 + 8/7 + 2/7*h**2 - f*h = 0.
-1, 2/7, 2/3
Factor -26*f**2 + 19*f**2 + 2*f**2 + 90 + 35*f.
-5*(f - 9)*(f + 2)
Let 28/5*u**2 + 4*u**4 + 36/5*u**3 + 4/5*u**5 + 8/5*u + 0 = 0. Calculate u.
-2, -1, 0
Let x(a) be the second derivative of -1/10*a**6 + 0*a**2 - a - 3/10*a**5 + 0*a**3 + 0 - 1/4*a**4. Solve x(m) = 0 for m.
-1, 0
Let r(y) = -y**2 + 4*y - 4. Let z(t) = -3*t**2 + 11*t - 11. Let w = -9 + 5. Let d(n) = w*z(n) + 11*r(n). Factor d(g).
g**2
Let w(z) = 4*z**5 + 7*z**4 + 5*z**3 - 13*z**2 - 3*z + 7. Let b(q) = -q**4 - q**2 + 1. Let s(f) = 10*b(f) - 2*w(f). Determine n, given that s(n) = 0.
-2, -1, 1/2
Let r(f) = 4*f**2 - 4. Let a(j) = 17*j**2 - 17. Suppose k + 4*p = 5*p - 1, 0 = -5*p - 5. Let u(z) = k*a(z) + 9*r(z). Factor u(n).
2*(n - 1)*(n + 1)
Let 4/11*y + 0 + 2/11*y**2 = 0. Calculate y.
-2, 0
Let r(b) be the third derivative of -b**7/105 + b**5/15 - b**3/3 + 8*b**2. What is v in r(v) = 0?
-1, 1
Let a(c) be the first derivative of 2*c**3/3 + 19*c**2 - 37. Find z, given that a(z) = 0.
-19, 0
Let z(k) be the third derivative of -7*k**5/60 + k**4/2 + 2*k**3/3 - 11*k**2. Determine v so that z(v) = 0.
-2/7, 2
Let p(m) be the third derivative of 0 + 5*m**2 - 1/30*m**5 + 0*m + 1/12*m**4 + 0*m**3 + 1/240*m**6. Suppose p(d) = 0. Calculate d.
0, 2
Factor -5/3*x**2 - 4*x - 4/3 + 3*x**4 + 4*x**3.
(x - 1)*(x + 1)*(3*x + 2)**2/3
Let d = 232 + -230. Factor 8/9 - 8/9*q + 2/9*q**d.
2*(q - 2)**2/9
What is b in 6*b - 8*b**3 - 3 + 3*b**4 + 7*b**3 - 5*b**3 = 0?
-1, 1
Let g(j) be the first derivative of j**4 - 6*j**2 + 8*j - 73. Factor g(t).
4*(t - 1)**2*(t + 2)
Let o be (1 - (-3 - -2))*14/70. Factor 0 + o*j**3 + 0*j - 4/5*j**2.
2*j**2*(j - 2)/5
Let m(z) be the third derivative of z**7/525 + z**6/50 + 13*z**5/150 + z**4/5 + 4*z**3/15 - 2*z**2. Factor m(y).
2*(y + 1)**2*(y + 2)**2/5
Let k(q) = -4*q**2 + 0*q - 4*q + 3 - 5*q**3 + 2*q**2 + q. Let r(l) = -14*l**3 - 6*l**2 - 8*l + 8. Let t(p) = 8*k(p) - 3*r(p). Determine x so that t(x) = 0.
-1, 0
Let f(m) be the first derivative of -2/3*m + 0*m**3 + 2/15*m**5 + 2/3*m**2 - 1/3*m**4 + 2. Factor f(y).
2*(y - 1)**3*(y + 1)/3
Let w(u) = 4*u - 15. Let k be w(6). Let t be 0*(30/k + -3). Suppose t + 2/5*y**2 + 0*y = 0. Calculate y.
0
Let o = -2 - -8. Factor -2*a**3 + 12*a**2 - 6*a**3 + 15*a + 11*a**3 + o.
3*(a + 1)**2*(a + 2)
Let o(g) be the first derivative of -g**5 + 5*g**3/3 + 8. Factor o(f).
-5*f**2*(f - 1)*(f + 1)
Let z(q) be the third derivative of -q**7/1260 - q**6/60 - 3*q**5/20 + q**4/24 - 5*q**2. Let g(j) be the second derivative of z(j). Factor g(y).
-2*(y + 3)**2
Let s be -1 - 4/8*-2. Let g(y) be the first derivative of 14/5*y**5 + 4/3*y**3 + 2 + s*y**2 + 0*y - 9/2*y**4. Factor g(d).
2*d**2*(d - 1)*(7*d - 2)
Let z(v) be the third derivative of 2*v**7/15 + 37*v**6/30 + 22*v**5/5 + 22*v**4/3 + 16*v**3/3 + 4*v**2. Factor z(g).
4*(g + 1)*(g + 2)**2*(7*g + 2)
Let i(j) = 2*j**3 - 2*j**2 - 4*j. Let b(p) = -p**4 - p**3 + 3*p**2 + 4*p + 1. Let q(l) = 4*b(l) + 6*i(l). Factor q(u).
-4*(u - 1)**3*(u + 1)
Let s(m) be the first derivative of -2*m**3/9 - m**2/9 - 10. Solve s(q) = 0.
-1/3, 0
Let q be ((-1379)/(-2730))/(2/5). Let v = -1/78 + q. Factor 0 - v*j**2 + 1/2*j.
-j*(5*j - 2)/4
Let f(a) be the first derivative of a**3/2 + 3*a**2 - 15*a/2 - 7. Factor f(x).
3*(x - 1)*(x + 5)/2
Let u be 81/21 - 2/(-6). Let y = u + -32/21. Let -4/3 - 2/3*s**3 - 10/3*s - y*s**2 = 0. What is s?
-2, -1
Suppose 2 = -o + 1. Let c(f) = f**3 - f**2 + f + 1. Let d(n) = 4*n**3 + 8*n**2 + 10*n + 4. Let b(r) = o*d(r) + c(r). Factor b(l).
-3*(l + 1)**3
Let d(y) = 6*y + 1. Let b be d(1). Suppose 3 = -2*h + b. Factor -h*c**3 - 2*c**2 + c - c.
-2*c**2*(c + 1)
Find h such that 3*h**4 + 4/3*h**5 - 8/3*h**2 - 2*h - 1/3 + 2/3*h**3 = 0.
-1, -1/4, 1
Solve -2/13*o**2 - 4/13*o + 0 = 0.
-2, 0
Let a(t) be the third derivative of t**7/14 + t**6/6 - 4*t**5/3 - 10*t**4/3 + 40*t**3/3 + 13*t**2. Factor a(y).
5*(y - 2)*(y + 2)**2*(3*y - 2)
Let k(q) = -q + 8. Let u be (-2)/3*(3 - 9). Let x be k(u). Let i(w) = w**2 - 2*w + 3. Let z(r) = -2*r**2 + 4*r - 7. Let p(y) = x*z(y) + 10*i(y). Factor p(d).
2*(d - 1)**2
Let p(u) = 3*u - 4 + 6 - 4*u + 2. Let c be p(2). Solve -2*o**c + 4/3*o - 10/3*o**3 + 0 = 0 for o.
-1, 0, 2/5
Suppose 0 = -m + 1 - 0, -5*h + 5*m = -20. Determine d so that d**2 - d**4 + 1/2*d - 1/2*d**h + 0*d**3 + 0 = 0.
-1, 0, 1
Let o(z) be the third derivative of 0 - 3/40*z**5 + 0*z - 1/16*z**4 + 1/2*z**3 + 2*z**2. Solve o(p) = 0.
-1, 2/3
Let f(c) be the first derivative of 3*c**5/5 - 3*c**4 + 6*c**3 - 6*c**2 + 3*c - 2. Suppose f(t) = 0. Calculate t.
1
Let n(g) be the second derivative of g**7/147 + 2*g**6/105 - g**5/35 - 4*g**4/21 - g**3/3 - 2*g**2/7 + 9*g. Factor n(z).
2*(z - 2)*(z + 1)**4/7
Let 48/5*w - 22/5*w**2 + 2/5*w**3 + 72/5 = 0. What is w?
-1, 6
Let i be (-2163)/(-360) + -3 + -3. Let j(s) be the third derivative of 0*s**3 - 2*s**2 + 1/24*s**4 + i*s**6 + 0 + 1/30*s**5 + 0*s. Factor j(k).
k*(k + 1)**2
Let o(w) = -w**2 + 3. Suppose 0 = -5*t - m + 9, 3*m - m = 5*t - 12. Let a(s) = s**2. Let i(f) = t*a(f) - o(f). Find c such that i(c) = 0.
-1, 1
Let g(n) be the second derivative of n**4/6 + 2*n**3/21 - 7*n. Factor g(r).
2*r*(7*r + 2)/7
Let c(g) be the third derivative of g**8/224 - g**7/140 - g**6/80 + g**5/40 + 6*g**2. Find n such that c(n) = 0.
-1, 0, 1
Let c(i) be the second derivative of -2*i + 0*i**2 + 1/30*i**5 - 1/9*i**3 + 0*i**4 + 0. Factor c(t).
2*t*(t - 1)*(t + 1)/3
Let r(f) = -f**2 + 7*f - 5. Let h be r(5). Find g, given that 9*g**4 + 2*g**3 - 8*g**4 - 5*g**h + 4*g**5 - g**2 - g**3 = 0.
-1, 0, 1
Let k(x) be the second derivative of x**5/10 - 4*x**3/3 - 6*x + 5. Factor k(l).
2*l*(l - 2)*(l + 2)
Let l = 14 - 206/15. Factor 2/15*h**2 + l*h + 0.
2*h*(h + 2)/15
Let i(f) = -f**4 + f**2 - f - 1. Let h(n) = -6*n**4 - 2*n**3 + 6*n**2 - 2. Let s(g) = h(g) - 2*i(g). Factor s(m).
-2*m*(m - 1)*(m + 1)*(2*m + 1)
Let x = 5 + -2. Suppose -4*f + x*f = 0. Let 10*w**5 - 3/2*w**3 + f*w - 6*w**4 + w**2 + 0 = 0. What is w?
-2/5, 0, 1/2
Solve 9*g**3 + 6*g**4 - 410*g + 410*g - 3*g**5 = 0.
-1, 0, 3
Suppose -4*i - 4*r = 17 + 19, -i - 5*r - 25 = 0. Let k = 7 + i. Factor -2/9*m**3 + 0 + 2/9*m**k + 0*m.
-2*m**2*(m - 1)/9
Determine f, given that 2/5*f**3 - 2/5*f + 2/5*f**2 - 2/5 = 0.
-1, 1
Let q(p) = p**2 - p. Let z(g) = -4*g**3 - 68*g**2 - 328*g + 400. Let u(w) = 8*q(w) - z(w). Factor u(b).
4*(b - 1)*(b + 10)**2
Let z(d) be the first derivative of -1 + d + 7/12*d**3 - 2*d**2. Factor z(k).
(k - 2)*(7*k - 2)/4
Determine k, given that 4/7 + 10/7*k**2 + 2*k = 0.
-1, -2/5
Let s(p) be the third derivative of p**6/180 + p**5/10 + 3*p**4/4 - p**3/6 + 2*p**2. Let c(m) be the first derivative of s(m). Factor c(o).
2*(o + 3)**2
Let f = -37 - -75/2. Find c such that 0 + 0*c - f*c**2 + 1/2*c**3 = 0.
0, 1
Let s(r) be the second derivative of 49*r**4/36 - 28*r**3/9 + 8*r**2/3 - 4*r. Factor s(m).
(7*m - 4)**2/3
Find c such that 18/17*c**2 + 8/17 + 26/17*c = 0.
-1, -4/9
Let z be (-10 + 2)/(4/(-2)). Let a = z - 1. Suppose -2/3*s**a - 2*s**2 + 2/3*s + 0 + 2*s**4 = 0. Calculate s.
-1, 0, 1/3, 1
Let x(k) be the first derivative of -2*k**3/27 + 4*k**2/3 - 8*k - 35. Factor x(p).
-2*(p - 6)**2/9
Suppose -5*d - 15 = -0*d. Let s be -4 + (-117)/(-15) + d. Suppose 2/5*o**3 - 6/5*o**2 + s*o + 0 = 0. What is o?
0, 1, 2
Let p(g) = -5*g**5 - g**4 + 9*g**3 - 2*g**2 - g. Let n(o) = -o**5 - o**4 + o**3 + o. Let f(x) = -6*n(x) + 2*p(x). Find r, given that f(r) = 0.
-1, 0, 1, 2
Let k(s) be the second derivative of -1/240*s**6 + 0*s**3 - s + 3/2*s**2 + 0 - 1/60*s**5 - 1/48*s**4. Let j(d) be the first derivative of k(d). Factor j(y).
-y*(y + 1)**2/2
Let f be (8*(-2)/(-12))/((-5)/(-3)). Factor -19/5*a**3 + 27/5*a**2 + f*a**4 - 8/5*a - 4/5.
(a - 2)**2*(a - 1)*(4*a + 1)/5
Factor 125/3 + 55*c**2 + 2/3*c**4 - 325/3*c - 31/3*c**3.
(c - 5)**3*(2*c - 1)/3
Let j be (24/84)/(6/14). Determine i, give