2*h*(h - 1)**2/3
Let k(p) be the first derivative of -7*p**4/4 + 55*p**3/9 - 14*p**2/3 + 4*p/3 - 3. Factor k(q).
-(q - 2)*(3*q - 1)*(7*q - 2)/3
Suppose 0 = 5*k - 3*k - 4. Factor 3/2*m**k - 3*m + 2 - 1/4*m**3.
-(m - 2)**3/4
Let z(j) = j**3 + 4*j**2 + 4*j + 3. Let p be (-1)/(3*(-1)/(-9)). Let l be z(p). Find v such that l + 2/3*v**3 - 10/9*v**4 + 4/9*v**2 + 0*v = 0.
-2/5, 0, 1
Let a(z) = -4*z + 1. Let h be a(-1). Suppose -3*m + 4*p + 26 = 0, -2 = -2*m - h*p - 0*p. Factor 24*k**4 - 3*k**5 + 21*k**5 - 4*k**5 + m*k**3 - 4*k**2.
2*k**2*(k + 1)**2*(7*k - 2)
Suppose 1/3*o + 1/12*o**3 + 0 - 1/3*o**2 = 0. What is o?
0, 2
Factor -48*h**3 - 20*h + 30*h**2 - 40 + 9*h**4 - 4*h**4 + 73*h**3.
5*(h - 1)*(h + 2)**3
Let c(j) = 8*j**3 - 4*j**2 + 8. Let v be (33/9 - 3)*-6. Let g(r) = -r**3 - r - 1. Let h(i) = v*g(i) - c(i). Factor h(q).
-4*(q - 1)**2*(q + 1)
Let o(t) = 6*t**3 - 3*t**2 - 2*t + 9. Let c(d) = -7*d**3 + 4*d**2 + d - 10. Let z(r) = 5*c(r) + 6*o(r). Factor z(x).
(x - 1)**2*(x + 4)
Let i = 10 - 10. What is t in 0*t**2 - 3*t**2 + i*t**2 - t + 4*t**3 + 6*t**2 = 0?
-1, 0, 1/4
Let z(u) = -u**3 + 7*u**2 - 7*u + 8. Let l be z(6). Factor 5 - 6*g + 64*g**l - 63*g**2 + 4.
(g - 3)**2
Let b(c) be the first derivative of c**6/2 + 9*c**5/5 + 9*c**4/4 + c**3 - 11. Suppose b(u) = 0. What is u?
-1, 0
Let x be -12*(6/(-3) + 3)/(-10). Factor -x*m**2 + 2/5*m**4 - 2/5*m**3 + 4/5 + 2/5*m.
2*(m - 2)*(m - 1)*(m + 1)**2/5
Suppose -d + 3*d + 5*i = 26, 0 = 4*d + 2*i - 20. Determine m, given that m**d + 31/5*m**4 + 3*m**5 - 4/5 - 27/5*m**2 - 4*m = 0.
-1, -2/3, -2/5, 1
Let w(r) be the third derivative of 0*r**3 + 0*r**4 + 0 + 0*r + 1/735*r**7 - r**2 + 0*r**5 - 1/420*r**6. Factor w(p).
2*p**3*(p - 1)/7
Let s(y) = y**3 + 4*y**2 + 2*y - 2. Let i be s(-2). Suppose m - 12 = -3*l, 0 = -5*m + 5*l - 0*l. Factor 2*c**m + i*c - 2*c.
2*c**3
Let h(q) = q**5 - q**2. Let b(n) = -4*n**5 - n + 6*n**4 + 2 + 2*n**3 + 5*n**5 + 0 - 6*n**2 - 4*n**4. Let g(j) = -b(j) + 2*h(j). Determine i so that g(i) = 0.
-1, 1, 2
Let k(r) be the first derivative of 0*r + 2/9*r**3 + 1/40*r**6 - 1 - 1/9*r**4 - 1/60*r**5 - r**2. Let w(x) be the second derivative of k(x). Factor w(f).
(f + 1)*(3*f - 2)**2/3
Find v, given that 15*v**2 + 13 + 27*v - 87*v - 8 + 25*v**3 + 15 = 0.
-2, 2/5, 1
Let b = 65/3 - 21. Solve o - 1/3*o**2 - b = 0.
1, 2
Suppose -4*b + 1 = -7. Let u(x) be the second derivative of -x**3 - 2*x**b + 0 + 1/5*x**5 + x + 1/2*x**4. Solve u(a) = 0 for a.
-2, -1/2, 1
Suppose y + 8 = 5*c, c - 4 = 2*y + 3. Let i(f) = 2*f + 1. Let p be i(c). Let -5*a**2 - 18*a - 27 - a**2 + p*a**2 = 0. Calculate a.
-3
Let 20/9*o + 2/9*o**2 + 50/9 = 0. Calculate o.
-5
Let u(n) = n**2 + n - 13. Let d be u(-4). Let j be ((-12)/16 - d)*2. Solve 1/2*y - 1/6*y**5 + 1/6 - j*y**4 + 1/3*y**2 - 1/3*y**3 = 0.
-1, 1
Factor -1/2*y**3 + 0*y + 0 + 1/2*y**2.
-y**2*(y - 1)/2
Factor -3 - a + 4 - 3*a + 2*a**2 + a**2.
(a - 1)*(3*a - 1)
Let r be (-96)/42 - -2 - (-2)/7. Factor r*h**2 + 0*h + 3/5*h**3 + 0.
3*h**3/5
Suppose -2*n - 12 = 3*s - 5*n, 3*s + 10 = 2*n. Let k(v) = -v**3 - 3*v**2 - 2*v + 2. Let w be k(s). Factor -4*y**w + 9/2*y**4 - 2*y + 0 + 3/2*y**3.
y*(y - 1)*(3*y + 2)**2/2
Let t(m) = -5*m**2 + 2*m. Let x(r) = r**2 + r. Let u(q) = 3*t(q) + 12*x(q). Factor u(s).
-3*s*(s - 6)
Let d(v) = -2*v - 3. Suppose 5 = -2*r - 3. Let c be d(r). Suppose -2*a**2 - 6*a**3 - 4*a**c + 2*a**4 + 2*a**5 - 2*a**4 - 6*a**4 = 0. What is a?
-1, 0
Let x = -288 + 2022/7. Determine j so that -x*j**2 + 4/7*j + 2/7*j**4 + 0 + 0*j**3 = 0.
-2, 0, 1
Let w(v) be the third derivative of -v**8/840 - v**7/420 + v**6/90 + v**3/3 + v**2. Let t(r) be the first derivative of w(r). Suppose t(m) = 0. What is m?
-2, 0, 1
Let x(o) be the first derivative of -2*o**7/105 + o**6/30 + 2*o**2 - 2. Let y(l) be the second derivative of x(l). Factor y(z).
-4*z**3*(z - 1)
Factor -10/7 - 8/7*v + 2/7*v**2.
2*(v - 5)*(v + 1)/7
Suppose -13 + 27 = 2*h. Suppose h*l = 3*l. What is c in l - 2/9*c**2 + 4/9*c = 0?
0, 2
Let m(y) = -2*y**2 - 26*y + 7. Let x(z) = -z**2 - 13*z + 4. Let a(l) = -4*m(l) + 7*x(l). Factor a(s).
s*(s + 13)
Let x be 2 - (-3 - (-8)/4)*1. Let y(r) be the first derivative of 1 + 0*r**2 - 4/15*r**x + 0*r + 1/10*r**4. Factor y(q).
2*q**2*(q - 2)/5
Let j(x) = 3*x**3 - 9*x**2 + 7*x + 9. Let u(h) = 5*h**3 - 14*h**2 + 11*h + 14. Let q(o) = 8*j(o) - 5*u(o). Find r such that q(r) = 0.
-2, -1, 1
Let q(b) be the third derivative of -b**8/336 + 2*b**7/315 + b**6/360 - b**5/90 + 5*b**2. Factor q(z).
-z**2*(z - 1)**2*(3*z + 2)/3
Suppose 0 = -2*a + 5*g - 0*g + 1, 13 = 4*a + g. Factor 0*j**4 + 7*j + 3 + 12*j**a + 6*j**2 + 3*j**4 + 5*j + 12*j**2.
3*(j + 1)**4
Let w(x) = -x**3 - 1 + 2 + 1 + 9*x + 8*x**2. Let c be w(9). Find l such that 2*l**5 - 4*l + 4*l**c - l**5 - 4*l**4 + 2*l**3 + 0*l**4 + l**3 = 0.
-1, 0, 1, 2
Let a be ((-4)/20)/((-36)/15). Let c(s) be the second derivative of a*s**4 + 0 + 2*s + 0*s**2 + 1/6*s**3. Find o such that c(o) = 0.
-1, 0
Let g(q) be the first derivative of -q**6/45 + q**4/9 - q**2/3 + 4*q + 2. Let k(p) be the first derivative of g(p). Factor k(a).
-2*(a - 1)**2*(a + 1)**2/3
Let u = 0 + 5. What is l in -l**2 + l**3 - 6*l**4 + 4*l**4 - l**u + 0*l**3 + 3*l**4 = 0?
-1, 0, 1
Let c(f) be the second derivative of f**4/36 + f**3/18 + 5*f. Factor c(b).
b*(b + 1)/3
Let v = -31 + 37. Let z(a) be the third derivative of -3/32*a**4 - 11/480*a**v + 1/12*a**3 + 1/280*a**7 + 0*a - a**2 + 0 + 1/16*a**5. Factor z(i).
(i - 1)**3*(3*i - 2)/4
Let j(f) be the third derivative of f**6/480 - f**5/80 + f**3/6 - 8*f**2. Factor j(y).
(y - 2)**2*(y + 1)/4
Let z be (-201)/(-39) + 4/(-26). Let u(l) be the third derivative of 25/12*l**6 + 0 + 0*l - 8/3*l**3 + z*l**4 - 5*l**5 - 2*l**2. Factor u(x).
2*(5*x - 2)**3
Let m(l) = 5*l**3 + 205*l**2 + 2935*l + 13725. Let j(d) = d**2 + d - 1. Let c(a) = 5*j(a) + m(a). Factor c(n).
5*(n + 14)**3
Let h(r) = -25*r**3 - 5*r**2 + 20*r - 20. Let g(c) = -c**3 + c - 1. Let u(y) = 20*g(y) - h(y). Factor u(v).
5*v**2*(v + 1)
Factor 0 - 1/4*k**2 + 1/2*k.
-k*(k - 2)/4
Let r(b) be the second derivative of -b**7/168 - b**6/60 + 7*b**5/80 - b**4/12 + 37*b. Factor r(q).
-q**2*(q - 1)**2*(q + 4)/4
Let f(k) be the first derivative of -k**6/36 + k**5/30 + k**4/24 - k**3/18 - 23. Factor f(w).
-w**2*(w - 1)**2*(w + 1)/6
Find u such that -16/17*u + 50/17*u**5 + 38/17*u**3 + 8/17 + 110/17*u**4 - 46/17*u**2 = 0.
-1, 2/5
Let p be 2/7 - (-260)/(-28). Let m(x) = x + 9. Let g be m(p). Factor 4*l**2 + g*l**2 - 2*l**2 - 4*l.
2*l*(l - 2)
Let y(a) = 3*a**2 + 3*a - 2. Let j(p) = 16*p**2 + 14*p - 11. Let c(k) = 2*j(k) - 11*y(k). Factor c(o).
-o*(o + 5)
Let r(x) be the third derivative of -x**5/150 + x**2. Factor r(u).
-2*u**2/5
Let o(t) be the second derivative of -1/2*t**3 + 1/6*t**4 + 1/360*t**6 - 3*t + 0 + 0*t**2 + 1/30*t**5. Let s(a) be the second derivative of o(a). Factor s(d).
(d + 2)**2
Factor -34*c**2 - c**3 - 7 - 8 - 4*c**3 - 35*c + 9*c**2.
-5*(c + 1)**2*(c + 3)
Suppose 2*k + 3 = 5*f - 2*f, k + 5*f = 5. Factor 4/11*u**3 + k*u + 0*u**2 + 6/11*u**4 + 0.
2*u**3*(3*u + 2)/11
What is m in -4/3*m**3 + 14/3*m**2 - 14/3*m + 4/3 = 0?
1/2, 1, 2
Let a(h) be the second derivative of -5*h - 3/100*h**5 + 3/10*h**2 + 1/10*h**3 + 0 - 1/20*h**4. What is m in a(m) = 0?
-1, 1
Let b(v) = 28*v**2 + 27*v + 12. Let y(l) = -57*l**2 - 53*l - 25. Let a(p) = 14*b(p) + 6*y(p). Determine f, given that a(f) = 0.
-3/5
Suppose 5/4*n - 1/2 + 1/4*n**3 - n**2 = 0. What is n?
1, 2
Let w = 17 + -15. Determine g so that -18 + 4*g + 38 - 20 + 2*g**w = 0.
-2, 0
Factor -5*k - 3*k**2 - 6*k**3 + 9*k + 11*k - 6.
-3*(k - 1)*(k + 2)*(2*k - 1)
Let m(v) be the third derivative of 0*v**4 - 1/3*v**3 + 0 + 0*v + 1/720*v**6 - 1/240*v**5 + v**2. Let w(r) be the first derivative of m(r). Factor w(h).
h*(h - 1)/2
Suppose 0 = 3*f - 2*t + t - 13, f = 5*t + 23. Find s, given that s**4 + 5*s**2 - 7*s**2 + 2*s**f + 3*s**2 = 0.
-1, 0
Determine x so that 12*x**4 + 0 - 21/2*x**3 - 3/2*x**5 + 0*x**2 + 0*x = 0.
0, 1, 7
Let y(a) = 5 - 6 + 2*a - 2. Let g be y(3). Factor -1/2*l + 0 + 1/2*l**g + 0*l**2.
l*(l - 1)*(l + 1)/2
Suppose 5 = -3*p + c, 7*c = -5*p + 2*c + 5. Let n be (0 + 8/(-28))*p. Determine z so that 0*z**2 + 2/7*z**4 + 0*z**3 + n*z**5 + 0 + 0*z = 0.
-1, 0
Let j(s) be the third derivative of s**6/30 - 2*s**5/15 + 15*s**2. Determine f, given th