 3*c = 3*q + 21. Suppose -5 = -g - f, c*f + 0*f = -3*g + 12. Let -1/3*i - 2/3*i**g - 1/3*i**3 + 0 = 0. Calculate i.
-1, 0
Let g = -4 + 8. Factor 3*f**g - 4*f - 2*f**3 - 2*f**3 - 6*f**2 - 4*f**4 - 1.
-(f + 1)**4
Let o(l) = 4*l**2 - l - 2. Let u(z) be the third derivative of z**5/20 - z**3/6 + 4*z**2. Let m(b) = -2*o(b) + 3*u(b). Factor m(x).
(x + 1)**2
Let g(y) be the second derivative of 0 - y + 0*y**3 + 0*y**2 + 1/18*y**4. Factor g(c).
2*c**2/3
Let x(k) be the second derivative of 81*k**5/40 - 3*k**4/2 + k**3/3 + 3*k. Factor x(f).
f*(9*f - 2)**2/2
Let l(p) = -11*p**2 - 39*p - 64. Let f(a) = 10*a**2 + 38*a + 64. Let y(c) = 7*f(c) + 6*l(c). Factor y(k).
4*(k + 4)**2
Let t(o) = o + 3*o**2 - 8*o**3 + o**2 + 0*o**2 + 4 - o**2. Let k(n) = 9*n**3 - 3*n**2 - n - 5. Let p(b) = 4*k(b) + 5*t(b). Find y, given that p(y) = 0.
-1/4, 0, 1
Let i(s) be the second derivative of -s**4/14 + 4*s**3/21 - s**2/7 - 4*s. Find r such that i(r) = 0.
1/3, 1
Let s be (1 + (-2)/1)*1. Let a be -3*(s + (-28)/(-30)). Factor -a*l**2 + 1/5*l**4 + 1/5*l + 0 - 1/5*l**3.
l*(l - 1)**2*(l + 1)/5
Let o(b) be the second derivative of 0 + 4*b + 2*b**2 - 1/2*b**5 + 1/15*b**6 - 7/3*b**3 + 3/2*b**4. Factor o(r).
2*(r - 2)*(r - 1)**3
Let l = -82/11 + 760/99. Factor 2/9*x + 0 - l*x**3 + 0*x**2.
-2*x*(x - 1)*(x + 1)/9
Let l(o) be the third derivative of o**8/2016 - o**7/210 + o**6/60 - o**5/45 + 9*o**2. Factor l(h).
h**2*(h - 2)**3/6
Let o(c) be the third derivative of c**8/20160 - c**6/720 + c**5/30 + 4*c**2. Let q(b) be the third derivative of o(b). Let q(n) = 0. Calculate n.
-1, 1
Let d(j) be the third derivative of 2*j**7/315 + j**6/120 - j**5/180 - 3*j**2. Factor d(m).
m**2*(m + 1)*(4*m - 1)/3
Let o(z) be the third derivative of z**9/30240 + 11*z**8/30240 + z**7/630 + z**6/270 + z**5/15 + 4*z**2. Let k(f) be the third derivative of o(f). Factor k(a).
2*(a + 1)*(a + 2)*(3*a + 2)/3
Let t(w) be the second derivative of w**5/4 - 5*w**4/4 - 5*w**3/6 + 15*w**2/2 - 18*w. Let t(o) = 0. What is o?
-1, 1, 3
Let o(n) be the third derivative of -n**5/120 + 5*n**4/12 - 25*n**3/3 + 9*n**2 - 1. Factor o(r).
-(r - 10)**2/2
Let t(h) be the third derivative of h**8/336 + 2*h**7/105 + h**6/30 - h**5/30 - 5*h**4/24 - h**3/3 - 7*h**2. Factor t(s).
(s - 1)*(s + 1)**3*(s + 2)
Let l = 0 - -4. Suppose -19 = -5*v + z, 3*v - l*z = v + 22. Factor 0*x - 2/9 - 2/9*x**4 + 4/9*x**2 + 0*x**v.
-2*(x - 1)**2*(x + 1)**2/9
Determine n, given that 93*n + 36 + 5*n**3 - 96 - 22*n**2 - 13*n - 13*n**2 = 0.
2, 3
Let x(a) = -a**3 + a**2 - a. Let w(z) = -z**4 + 14*z**3 - 14*z**2 + 12*z. Suppose 0 = -2*u - 20 - 24. Let p(k) = u*x(k) - 2*w(k). Factor p(o).
2*o*(o - 1)**3
Factor -9/5 - 12/5*n**3 + 3*n**2 + 6/5*n.
-3*(n - 1)**2*(4*n + 3)/5
Let l(j) be the second derivative of -j**5/4 - 17*j**4/6 - 62*j**3/15 - 12*j**2/5 - j - 17. Solve l(r) = 0.
-6, -2/5
Let k(z) be the second derivative of -z**7/126 + z**6/30 - z**5/20 + z**4/36 - 6*z. Suppose k(j) = 0. What is j?
0, 1
Suppose v - r - 16 = r, 0 = -4*v + 2*r + 34. Suppose -4*x = -x - v. Factor -1/5 + 1/5*m**3 - 3/5*m**x + 3/5*m.
(m - 1)**3/5
Let q(d) = -d - d - 2*d + 5*d. Let o be q(2). Factor 2/9*s**o - 2/3*s + 4/9.
2*(s - 2)*(s - 1)/9
Suppose 4*r - 2 = 3*r. Let u(m) be the second derivative of 8/27*m**3 + 8/27*m**4 + 0 - r*m + 1/9*m**2. Let u(i) = 0. What is i?
-1/4
Let h be 40/12 - 4/12. Solve 9*t**2 + 0*t**4 - 6*t - 13*t**3 + 3*t**4 + h*t + 4*t**3 = 0 for t.
0, 1
Let n(c) be the second derivative of 1/60*c**5 + 0*c**3 + c - 1/24*c**4 - c**2 + 0. Let b(m) be the first derivative of n(m). Factor b(i).
i*(i - 1)
Let s(t) be the third derivative of -t**6/90 - 8*t**5/45 + t**4/18 + 16*t**3/9 + 2*t**2 - 13*t. Let s(j) = 0. What is j?
-8, -1, 1
Let v = -100 - -103. Factor 1/2*m**v - 3/2*m**2 + 3/2*m - 1/2.
(m - 1)**3/2
Let h(m) be the first derivative of 0*m + 0*m**2 - 1/5*m**4 - 7/15*m**6 - 18/25*m**5 - 2 + 0*m**3. Factor h(p).
-2*p**3*(p + 1)*(7*p + 2)/5
Let z = 464/539 + -2/539. Factor 2/7*w**2 + 2/7*w**5 + 0 + 0*w + z*w**4 + 6/7*w**3.
2*w**2*(w + 1)**3/7
Let m(f) = -f**2 + 4*f + 2. Let h be m(3). Factor 70*k**4 + 44*k**3 + 0*k - 2*k + 25*k**h + 2*k + 8*k**2.
k**2*(k + 2)*(5*k + 2)**2
Let t(i) be the first derivative of -2 + 2/27*i**3 - 4/9*i - 1/9*i**2. Factor t(p).
2*(p - 2)*(p + 1)/9
Suppose 7*p = 6 - 6. Suppose -4/5*y**4 + 0*y**2 + p*y + 6/5*y**5 + 0 - 2/5*y**3 = 0. Calculate y.
-1/3, 0, 1
Let s(z) be the first derivative of z**5/5 - z**3/3 + 14. Find b such that s(b) = 0.
-1, 0, 1
Let d(g) = -g - 35. Let y be d(-35). Determine l so that y*l + 0 + 0*l**2 + 3/2*l**4 + 3/2*l**3 = 0.
-1, 0
Let t(u) be the second derivative of -u**8/6720 - u**7/840 - u**6/360 - u**4/12 - 5*u. Let s(f) be the third derivative of t(f). Suppose s(d) = 0. What is d?
-2, -1, 0
Let s(z) be the second derivative of z**4/3 + 14*z**3/3 + 7*z. Factor s(m).
4*m*(m + 7)
Solve 4*z + 6*z**3 + 0 - 12*z - 8*z**2 + 0 = 0.
-2/3, 0, 2
Let a(s) be the third derivative of 1/45*s**6 - 1/18*s**5 + 0*s - 4*s**2 + 0*s**3 + 0 + 1/18*s**4 - 1/315*s**7. Factor a(f).
-2*f*(f - 2)*(f - 1)**2/3
Let m(s) be the first derivative of -53/3*s**3 - 12*s**2 - 4*s - 27/5*s**5 - 55/4*s**4 - 5/6*s**6 - 2. Solve m(k) = 0.
-2, -1, -2/5
Let a(m) = -8*m - 37 + 2*m**3 + 101*m + 27*m**2 + 168. Let s(g) = 2*g**3 + 28*g**2 + 92*g + 132. Let i(n) = -4*a(n) + 3*s(n). Factor i(l).
-2*(l + 4)**3
Let i(p) be the second derivative of -p**5/180 + p**4/36 - 2*p**2 + 4*p. Let y(j) be the first derivative of i(j). Factor y(n).
-n*(n - 2)/3
Suppose -5*n + 8 = -n. Factor 0 - 8*s**2 + 11*s**n - 3.
3*(s - 1)*(s + 1)
Let h(p) be the first derivative of 3/4*p**2 + 3 + 0*p + 1/6*p**3. Factor h(s).
s*(s + 3)/2
Let p(s) be the second derivative of -s**5/40 + s**4/24 + 5*s**3/12 + 3*s**2/4 - 2*s. What is d in p(d) = 0?
-1, 3
Let i be (1/2)/(23/138). Suppose -2*r**i - 10/3*r**2 + 2/3*r**4 + 2/3*r**5 + 0 - 4/3*r = 0. What is r?
-1, 0, 2
Suppose 16*k + 0*k**3 + 3*k**2 + k**3 + 1 - 13*k = 0. Calculate k.
-1
Factor -6/13*d**2 + 4/13*d + 0 - 10/13*d**3.
-2*d*(d + 1)*(5*d - 2)/13
Let p be ((-6)/9)/(21/(-9)). Suppose 12 = -6*l + 24. Factor p*c - 2/7*c**l + 4/7.
-2*(c - 2)*(c + 1)/7
Let q = -16 + 18. Factor q*m**2 - 3*m**2 - 3*m**3 + 7*m**2.
-3*m**2*(m - 2)
Factor 0 + 0*t**2 + 1/4*t**3 - 1/4*t**5 + 0*t**4 + 0*t.
-t**3*(t - 1)*(t + 1)/4
Let q(l) be the second derivative of -l**7/21 + 2*l**5/5 - l**4/3 - l**3 + 2*l**2 + 2*l. Factor q(u).
-2*(u - 1)**3*(u + 1)*(u + 2)
Factor 12*x - 108*x**2 - 1/3.
-(18*x - 1)**2/3
Factor 1/8*o**3 + 0 - 1/4*o + 1/8*o**2.
o*(o - 1)*(o + 2)/8
Let n(u) = -u**3 + 4*u**2 + u - 2. Let t be n(4). Factor 9*z**3 + 0*z**5 - z**4 + 6*z**4 + z**5 + 7*z**2 + t*z.
z*(z + 1)**3*(z + 2)
Let u(x) = x**5 + 6*x**4 - 2*x**2 + 3*x - 4. Let o(j) = -6*j**4 - j**3 + j**2 - 4*j + 5. Let v(t) = 4*o(t) + 5*u(t). Find n, given that v(n) = 0.
-1, -1/5, 0, 1
Let i be 1/7*-3 + 476/196. Factor 0 - 1/5*k - 1/5*k**i + 1/5*k**4 + 1/5*k**3.
k*(k - 1)*(k + 1)**2/5
Suppose 3*s = -6, 2*n + 3*s - 4 = 2*s. Let t be 1 - ((-20)/7 + n). Factor -2/7*i**3 - 2/7 - t*i**2 - 6/7*i.
-2*(i + 1)**3/7
Let i be ((-2)/(-16))/(22 + -21). Let w(s) be the second derivative of -i*s**2 - 1/24*s**3 - 3*s + 0 + 1/4*s**4. Let w(q) = 0. What is q?
-1/4, 1/3
Suppose 5*a - 11 = -3*b, -2*b - 14 = -2*a - 0*b. Let k(x) be the first derivative of -a*x**3 + 2 - 2/5*x**5 - 2*x**4 - 2*x - 4*x**2. Factor k(c).
-2*(c + 1)**4
Suppose 31*n**5 - 23*n**4 - 54*n + 9*n**2 + 2*n**4 + 39*n**3 - 28*n**5 = 0. What is n?
-1, 0, 2, 3
Let t = 5/111 - 1/296. Let a(f) be the third derivative of t*f**4 - 1/20*f**5 + 4*f**2 + 0 + 0*f + 1/3*f**3. Let a(h) = 0. Calculate h.
-2/3, 1
Suppose 0 = -4*d + d + 9. Let v = -3/13 + 47/91. Factor -v - 6/7*g**2 + 2/7*g**d + 6/7*g.
2*(g - 1)**3/7
Let d(m) be the second derivative of m**6/10 + 9*m**5/20 - 5*m**4/4 - 3*m**3/2 + 6*m**2 + 19*m. Find u such that d(u) = 0.
-4, -1, 1
Let n(h) be the first derivative of -h**6/10 + 9*h**4/20 - 2*h**3/5 + 14. Factor n(x).
-3*x**2*(x - 1)**2*(x + 2)/5
Let x(r) be the third derivative of -r**5/100 + r**4/20 - 17*r**2. Suppose x(m) = 0. What is m?
0, 2
Suppose m = j - 0*j + 3, 0 = 4*j + m - 13. Let u(y) = y**2. Let i be u(0). Factor -2/5*q**j - 4/5*q + i.
-2*q*(q + 2)/5
Let v = 14 - 14. Let i(p) be the third derivative of -1/150*p**5 + 4*p**2 + 1/30*p**4 + 0*