
Let i(t) be the first derivative of 3 + 1/14*t**4 + 2/21*t**3 + 0*t - 2/7*t**2. Factor i(y).
2*y*(y - 1)*(y + 2)/7
Let p(n) be the third derivative of -2*n**7/105 + 2*n**6/15 - n**5/5 - 4*n**2. Factor p(u).
-4*u**2*(u - 3)*(u - 1)
Let t = -25 - -37. Suppose -3*m = -7*m + t. Solve 3/2*p + m - 3/2*p**2 = 0 for p.
-1, 2
Let u(w) = -24*w**2 + 36*w + 12. Let v(z) = -71*z**2 + 107*z + 37. Let q(j) = 11*u(j) - 4*v(j). Factor q(g).
4*(g - 2)*(5*g + 2)
Let f be ((-5 - -2)*4)/(-2). Let x = f + -4. Solve -3/5*h**5 + 6/5*h**4 - 6/5*h**x + 3/5*h + 0 + 0*h**3 = 0.
-1, 0, 1
Let q be (10/2)/(0 + 1). Suppose -10 = -q*l - 0*l. Factor 1 - 6 - w**l + 2*w + 4.
-(w - 1)**2
Let h(m) = 3*m**4 - 23*m**3 + 7*m**2 + 11*m - 16. Let j(q) = 9*q**4 - 68*q**3 + 21*q**2 + 34*q - 47. Let i(p) = -17*h(p) + 6*j(p). Solve i(x) = 0 for x.
-1, 2/3, 1, 5
Let j(s) be the third derivative of 0*s - 1/390*s**5 - 1/26*s**4 - 3/13*s**3 + 0 + 8*s**2. Factor j(m).
-2*(m + 3)**2/13
Let j(d) = -d**4 - d**3 + d**2 - d - 1. Let b(i) = 18 + 10*i**4 + 4*i + 2 + 16*i**3 - 6*i**2 - 8*i. Let v(k) = -b(k) - 12*j(k). Solve v(q) = 0 for q.
-2, 1, 2
Let v(g) be the first derivative of 2*g**3 + 9*g**2 + 24*g + 6. Let b(h) = 5*h**2 + 18*h + 25. Let a(c) = -3*b(c) + 2*v(c). Factor a(j).
-3*(j + 3)**2
Let s = -15 + 15. Let b(q) be the second derivative of -1/6*q**4 + s + 7/90*q**5 + 0*q**2 + 2/27*q**3 + 2*q. Factor b(g).
2*g*(g - 1)*(7*g - 2)/9
Let h(a) be the second derivative of -5*a**7/252 + 5*a**6/36 - 7*a**5/24 - 5*a**4/72 + 10*a**3/9 - 5*a**2/3 + 25*a. Find g, given that h(g) = 0.
-1, 1, 2
Let z(x) be the first derivative of 0*x**2 - 3 + 2/9*x**3 + 0*x. Let z(r) = 0. Calculate r.
0
Let y(c) = -9*c**2 + 69*c + 54. Let a(x) = 2*x**2 - 14*x - 11. Let j(k) = -24*a(k) - 5*y(k). What is r in j(r) = 0?
-2, -1
Factor 1/4*z**2 - 1/2*z - 1/4 + 1/2*z**3.
(z - 1)*(z + 1)*(2*z + 1)/4
Let d be (3/6)/(3/36). Let x = d + -3. Factor -3*c**3 + 0*c**3 + 6 + 0*c**3 + x*c - 4*c**2 - 2*c**2.
-3*(c - 1)*(c + 1)*(c + 2)
Let a(n) be the third derivative of -n**6/360 - n**5/30 - n**4/6 - 4*n**3/9 - 9*n**2. Factor a(l).
-(l + 2)**3/3
Let h(q) be the second derivative of 7*q**4/60 + q**3/10 - 2*q**2/5 - 24*q. What is d in h(d) = 0?
-1, 4/7
Let z(i) be the second derivative of 3*i**8/11200 + i**7/6300 - i**6/400 - i**5/300 + 5*i**4/12 - 4*i. Let h(n) be the third derivative of z(n). Factor h(r).
(r - 1)*(r + 1)*(9*r + 2)/5
Let w(n) be the second derivative of -1/6*n**4 + 0*n**3 + 0 + n + n**2. Let g(p) = -p**2 + p + 2. Let o(x) = -4*g(x) + 3*w(x). Factor o(l).
-2*(l + 1)**2
Let n(g) be the third derivative of 0*g**3 - 3*g**2 + 1/120*g**4 - 1/1050*g**7 - 1/600*g**6 + 0 + 0*g + 1/300*g**5. Factor n(z).
-z*(z - 1)*(z + 1)**2/5
Factor -3/5*s**4 + 12/5*s**2 + 0 + 0*s + 0*s**3.
-3*s**2*(s - 2)*(s + 2)/5
Factor 14*h + 2*h**3 + 16*h - 3 - 36*h + 7.
2*(h - 1)**2*(h + 2)
Let r(x) be the second derivative of x**5/50 + x**4/10 + 2*x**3/15 + 19*x. Let r(t) = 0. What is t?
-2, -1, 0
Let y(c) be the first derivative of 3*c**4/4 - c**3 - 15*c**2/2 - 9*c + 7. Solve y(j) = 0 for j.
-1, 3
Factor 0 + 5/2*u**2 - 5/4*u - 5/4*u**3.
-5*u*(u - 1)**2/4
Let d(i) be the third derivative of -1/48*i**4 + 1/120*i**6 - 1/672*i**8 + 0*i - i**2 - 1/60*i**5 + 1/12*i**3 + 1/420*i**7 + 0. Factor d(b).
-(b - 1)**3*(b + 1)**2/2
Let p(n) = -3*n**2 - 9*n + 6. Let w be 8 - (0/(-2) + 2). Let k(h) = 2*h**2 + 8*h - 5. Let z(i) = w*k(i) + 5*p(i). Determine s so that z(s) = 0.
0, 1
Let v(i) be the third derivative of i**8/168 - i**6/20 + i**5/15 + 9*i**2. Factor v(s).
2*s**2*(s - 1)**2*(s + 2)
Suppose 0 = 4*i - 3*i - 18. Suppose 3*s - x = 15, 2*s - 4*x = 3*s - i. Factor -22*b + 92/3*b**2 + s - 2/3*b**5 + 6*b**4 - 20*b**3.
-2*(b - 3)**2*(b - 1)**3/3
Let d be ((-16)/10)/(8/(-20)). Let n(z) be the second derivative of 1/4*z**4 - 3*z**2 + 0 - 1/2*z**3 + d*z. What is y in n(y) = 0?
-1, 2
Let j be (-2)/7 - 150/(-35). Suppose x - 4*c = 19, -3*x - x - 4*c = j. Suppose 51/4*n**2 + 1/2 + 9*n**5 - 53/4*n**4 - 19/4*n - 17/4*n**x = 0. Calculate n.
-1, 2/9, 1/4, 1
Suppose 236*d + k + 20 = 240*d, 0 = 3*k. Factor 128/7*y**d - 2/7*y**2 + 0 + 24/7*y**3 - 96/7*y**4 + 0*y.
2*y**2*(4*y - 1)**3/7
Find m such that -3/2*m**2 + 3/2*m**4 - 3/2*m**3 + 3/2*m + 0 = 0.
-1, 0, 1
What is i in -12*i + 10*i**2 + 4*i**2 - 2*i**2 + 4 - 4*i**3 + 0*i**2 = 0?
1
Let v(a) be the first derivative of -a**6/40 + 3*a**5/20 - 3*a**4/8 + a**3/2 + 3*a**2/2 + 5. Let o(k) be the second derivative of v(k). What is p in o(p) = 0?
1
Let b(l) be the first derivative of -l**4/66 - l**3/33 - l - 3. Let z(q) be the first derivative of b(q). Factor z(u).
-2*u*(u + 1)/11
Let m(t) be the second derivative of -t**4/102 + t**3/17 + 4*t**2/17 - 15*t. Find b such that m(b) = 0.
-1, 4
Let s be (1 - 4)/(-32 + 27). Factor 3/5*h**3 + 0*h + 0 - s*h**2.
3*h**2*(h - 1)/5
Let i(u) = -1 + u + 10 + 0 - 2*u. Let b be i(6). Let -6/7*j**4 + 0*j + 0 - 2/7*j**b + 4/7*j**2 = 0. Calculate j.
-1, 0, 2/3
Let d(b) be the first derivative of 2*b**5/15 - 2*b**3/9 - 9. Factor d(h).
2*h**2*(h - 1)*(h + 1)/3
Let z(l) be the second derivative of l**7/420 - l**6/80 - l**5/20 - l**4/4 + 4*l. Let m(o) be the third derivative of z(o). Factor m(a).
3*(a - 2)*(2*a + 1)
Let l(u) be the second derivative of -u**4/3 - 2*u**3/3 + 2*u. Factor l(b).
-4*b*(b + 1)
Let p(f) be the second derivative of -1/25*f**5 + 0*f**2 + 1/105*f**7 + 0 + 0*f**4 + 0*f**6 + 1/15*f**3 - f. Factor p(d).
2*d*(d - 1)**2*(d + 1)**2/5
Let u(j) = 3*j**2 + j + 6. Let t be u(3). Let -3*z**2 - z - 3*z**4 - 39*z**3 + t*z**3 + 2*z**4 = 0. Calculate z.
-1, 0
Let s = 293/21 - 41/3. Let w = -3 + 5. What is b in -4/7*b + s*b**w + 2/7 = 0?
1
Let u(d) be the third derivative of 0 + d**2 + 0*d - 7/90*d**6 + 0*d**3 + 1/18*d**4 - 1/30*d**5. Factor u(q).
-2*q*(2*q + 1)*(7*q - 2)/3
Let r be 2/14 - 39/(-21). Suppose 0*g**2 - 2 - 1 + 4 + g**r + 2*g = 0. What is g?
-1
Let u(j) = -j**5 - j**4. Let s(r) = -13*r**5 - 11*r**4 + 11*r**3 + 7*r**2 - 2*r. Let c(w) = -s(w) + 4*u(w). Factor c(n).
n*(n - 1)*(n + 1)**2*(9*n - 2)
Let o = 112 + -2015/18. Let x(s) be the first derivative of -4/9*s + 1/9*s**2 + 4/27*s**3 + 3 - o*s**4. Find d, given that x(d) = 0.
-1, 1, 2
Let j be ((-1)/8)/((-27)/108). Find v such that 1 + 3/2*v - 2*v**3 - v**2 + 0*v**4 + j*v**5 = 0.
-1, 1, 2
Suppose -60 = -3*z - 210. Let l be (-4)/(-18) - z/18. Factor -2*v - 2*v**l - 2*v**2 + 2*v.
-2*v**2*(v + 1)
Suppose -y - 2*o - 10 = -3*y, -3*y + o + 17 = 0. Suppose -3*u + y + 3 = 0. Factor 2*p**2 + 3*p**3 - 2 + p**5 + u - 3*p - 3*p**4 - p**3.
(p - 1)**4*(p + 1)
Let k be (-180)/(-975) + 1/(-5). Let r = 458/195 + k. Find q such that -2/3*q + 3*q**3 + 0 - 5/3*q**4 + 5/3*q**2 - r*q**5 = 0.
-1, 0, 2/7, 1
Let w be 3/2 - (-5)/(-10). Suppose 5*p - 9 = w. Let -2/3*n**4 + 2/3*n**p + 2/3*n - 2/3*n**3 + 0 = 0. What is n?
-1, 0, 1
Let z(k) be the first derivative of k**7/1680 - k**6/360 + k**5/240 + k**3/3 - 2. Let j(h) be the third derivative of z(h). Suppose j(a) = 0. What is a?
0, 1
Let q = 27/22 - 8/11. Suppose -3/4*k - 1/4*k**2 - q = 0. What is k?
-2, -1
Let m(k) be the third derivative of k**7/525 + k**6/600 - k**5/150 - k**4/120 + 23*k**2. Factor m(d).
d*(d - 1)*(d + 1)*(2*d + 1)/5
Let a be 0*2*(-5)/10. Find c such that -2/5*c**2 + a*c + 0*c**3 + 2/5*c**4 + 0 = 0.
-1, 0, 1
Determine g, given that 0*g + g**3 + 1/2*g**4 + 0 + 0*g**2 = 0.
-2, 0
Let f(t) = 4*t + 12 - 2*t - 15 + t**2. Let l be f(-3). Factor 0*c**2 + 0*c**3 + l*c + 0 - 2/5*c**4 + 2/5*c**5.
2*c**4*(c - 1)/5
Let w(p) be the second derivative of -p - 2/21*p**4 + 0 - 1/21*p**3 + 0*p**2. Suppose w(g) = 0. What is g?
-1/4, 0
Let n be 964/36 - (-4)/18. Factor -n*o**4 - 2*o**2 + 14*o**4 + 15*o**4 + 2*o**3 - 2*o.
2*o*(o - 1)*(o + 1)**2
Let s(t) be the second derivative of -t**4/6 + 5*t**3/3 - 4*t**2 - 15*t. Suppose s(a) = 0. What is a?
1, 4
Factor 1/5*z**2 + 0 - 1/5*z**3 + 0*z.
-z**2*(z - 1)/5
Factor -4*q + 3*q**3 - 40*q**2 + 31*q**2 + 10*q.
3*q*(q - 2)*(q - 1)
Let w be -3 - (-75)/14 - (-1)/7. Factor -5/2*m + w*m**3 + 3/2*m**4 - 1/2*m**2 - 1.
(m - 1)*(m + 1)**2*(3*m + 2)/2
Let p be 210/12*(2 + 57/(-30)). Factor 1/2*d + 0 + p*d**2.
d*(7*d + 2)/4
Let x(r) = 2*r**2 - 8. Let u(c) = 6*c**2 - 24. Let i(w) = 5*u(w) - 16*x(w). Factor i(a).
-2*(a - 2)*(a + 2)
Let v(b) = -b**3 + 19*b**2 - 20*b + 39. Let t be v(18). Let i(x