q**2 - 20/9*q**3 - 2/9*q**4 = 0. What is q?
-7, -1
Let w(i) = -i**2 - 8*i - 12. Let a be w(-6). Let n(r) be the first derivative of 4 + 1/3*r**3 + a*r**2 + 0*r. Factor n(x).
x**2
Let h(k) be the first derivative of -1 + 0*k**2 + 1/120*k**6 + 1/12*k**3 - 1/40*k**5 - 2*k - 1/48*k**4. Let q(n) be the first derivative of h(n). Factor q(o).
o*(o - 2)*(o - 1)*(o + 1)/4
Let z(x) be the second derivative of -x**4/48 - x**3/4 - 5*x**2/8 + 19*x. Factor z(d).
-(d + 1)*(d + 5)/4
Let a be 14/6 - ((-4)/6 - -1). Factor 0*i + 2/5*i**4 + 1/5*i**3 + 1/5*i**5 + 0*i**a + 0.
i**3*(i + 1)**2/5
Let f be (1 - 5) + (-1 - -8). Let h = 119/69 + -9/23. Factor 0*i + h*i**2 + 10/3*i**f + 0.
2*i**2*(5*i + 2)/3
Let h(u) be the third derivative of -u**7/70 + u**6/10 - 2*u**4 + 8*u**3 + 15*u**2. Factor h(r).
-3*(r - 2)**3*(r + 2)
Suppose 4*i = 8*i - 8. What is m in 0*m - 21/5*m**3 + 0 + 24/5*m**4 + 3/5*m**i + 48/5*m**5 = 0?
-1, 0, 1/4
Let y(f) be the third derivative of f**8/100800 + f**7/12600 + f**6/3600 - 2*f**5/15 + f**2. Let n(j) be the third derivative of y(j). Factor n(g).
(g + 1)**2/5
Let h be 4*(18/8)/(-9). Let n be -2*((-16)/14 - h). Factor -2/7*d**2 + 0 + n*d.
-2*d*(d - 1)/7
Factor -2/15*g**4 - 16/15*g - 4/5*g**3 + 0 - 8/5*g**2.
-2*g*(g + 2)**3/15
Factor 0 + 3/4*d**4 + 0*d**2 - 1/2*d**3 + 0*d - 1/4*d**5.
-d**3*(d - 2)*(d - 1)/4
Let s(w) = -329*w**3 - 180*w**2 + 133*w - 11. Let a(x) = -164*x**3 - 90*x**2 + 66*x - 6. Let q(c) = 10*a(c) - 4*s(c). Solve q(v) = 0 for v.
-1, 2/9
Let f(h) be the first derivative of 3/4*h**2 - 2/3*h**3 + 5 + 1/2*h. Factor f(s).
-(s - 1)*(4*s + 1)/2
Let m(n) be the first derivative of -n**8/840 - n**7/210 + n**5/30 + n**4/12 - 2*n**3/3 + 1. Let z(d) be the third derivative of m(d). Factor z(y).
-2*(y - 1)*(y + 1)**3
Let -4/11*s + 0 + 2/11*s**2 = 0. What is s?
0, 2
Suppose -28*r = -32*r. Factor r*p - 2/15*p**3 + 0 + 0*p**2.
-2*p**3/15
Let y(z) be the second derivative of -z**6/225 + z**5/50 - z**4/30 + z**3/2 - 4*z. Let p(d) be the second derivative of y(d). Factor p(f).
-4*(f - 1)*(2*f - 1)/5
Let q be 15/(-20) + 30/8. Factor -1 + 3*f**4 + 1 - 2*f**3 - 3*f**2 + 3*f - f**q.
3*f*(f - 1)**2*(f + 1)
Find k such that 7/3*k + 1/3*k**4 + 2 - k**3 - k**2 = 0.
-1, 2, 3
Let d be (0/(-2) + 2)/2. Factor -6*w + 1 + 0*w - d + 3*w**2.
3*w*(w - 2)
Let n = -16/3 - -35/6. Let r be 4/14 + 19/7. Factor 9/2*l**r + 3*l**2 + n*l + 0.
l*(3*l + 1)**2/2
Let y be 5/(-3) + 2/(-6). Let g be y/(-2 - -4) - -3. Factor -4/3*m + g*m**2 + 0.
2*m*(3*m - 2)/3
Suppose -2*t + 4*j - 14 = 0, -4*t + 6*j - 3*j - 3 = 0. Factor t*i**3 + 2 - 4*i + 4*i**3 + 3*i**4 - 5*i**4 - 3*i**3.
-2*(i - 1)**3*(i + 1)
Let n(p) be the first derivative of -p**5/5 - 5*p**4/4 - 3*p**3 - 7*p**2/2 - 2*p + 2. Factor n(y).
-(y + 1)**3*(y + 2)
Let g(l) = 7*l**2 - 5*l + 3. Let a(c) = 10 - 6*c + 1 - 7 + 8*c**2. Let z(j) = 5*a(j) - 6*g(j). Factor z(d).
-2*(d - 1)*(d + 1)
Let v = 29 + -25. Let p(m) be the third derivative of -3*m**2 + 1/150*m**5 + 1/600*m**6 + 0*m**3 + 0 + 0*m + 1/120*m**v. Suppose p(a) = 0. What is a?
-1, 0
Factor 1/5*m**3 + 0 - 1/5*m**5 + 0*m**2 + 0*m**4 + 0*m.
-m**3*(m - 1)*(m + 1)/5
Let l(q) be the first derivative of -1 + 0*q**3 + 1/7*q**4 + 2/35*q**5 - 2/7*q**2 - 2/7*q. What is w in l(w) = 0?
-1, 1
Suppose -w + 4*w = 0. Let m be -2 + 13/((-195)/(-36)). Factor 2/5*n**3 - m*n + 0 + w*n**2.
2*n*(n - 1)*(n + 1)/5
Let f(i) be the second derivative of -i**4/30 - 11*i**3/15 + 12*i**2/5 + 14*i. Let f(t) = 0. Calculate t.
-12, 1
Let o(g) be the third derivative of -g**7/315 - g**6/90 + g**4/18 + g**3/9 - 3*g**2. Factor o(r).
-2*(r - 1)*(r + 1)**3/3
Let z be (-3 - (-66)/21)/(4/14). Factor -d + 1/2*d**2 + z.
(d - 1)**2/2
Let o(c) = 7*c**3 - 3*c**2 - 6*c + 6. Let z(l) = -6*l**3 + 3*l**2 + 5*l - 5. Let h(w) = 5*o(w) + 6*z(w). Factor h(r).
-r**2*(r - 3)
Suppose 5*o**3 - 13*o**3 + 3*o**3 - 20*o**2 - 15*o = 0. Calculate o.
-3, -1, 0
Determine b, given that 2/3*b**5 - 8/3 + 14/3*b**3 - 2/3*b**2 + 10/3*b**4 - 16/3*b = 0.
-2, -1, 1
Let f(y) be the first derivative of -3 + 3/8*y**2 - 1/4*y**3 - 1/4*y + 1/16*y**4. Factor f(j).
(j - 1)**3/4
Suppose -r = 4*f - 5*r - 20, 4*f - 20 = -4*r. Suppose f*n + 15 = 5*h, 2*n = -2*h - 0*n + 2. Determine d, given that -4*d**h + d + 3*d**2 + d**3 - d**2 = 0.
0, 1
Suppose 0 = -4*n + 4*i + 40, 0 = -n + 2*n - 5*i - 30. Let h = n - 1. Suppose 1/3*r - 2/3*r**3 + 0*r**2 + 1/3*r**5 + 0 + 0*r**h = 0. What is r?
-1, 0, 1
Let k(c) be the first derivative of 2 + 0*c + 2/9*c**3 - 2/45*c**5 - 2/9*c**2 + 0*c**4. Factor k(l).
-2*l*(l - 1)**2*(l + 2)/9
Let b be 12 + 3/(-3 + 2). Let k be (-365)/(-225) - 2/b. Suppose k*c**2 + 2/5 - 9/5*c = 0. Calculate c.
2/7, 1
Suppose -4*w - d + 10 = w, w + 2*d - 2 = 0. Factor -1 - 1 - 2*a + 3 + a**w.
(a - 1)**2
Determine p, given that -4*p**3 - 19*p + 7*p**3 - 6 + 10*p = 0.
-1, 2
Solve -19/10*b**3 - 1/10*b**5 - 8/5*b - 7/10*b**4 - 5/2*b**2 - 2/5 = 0.
-2, -1
Let i(s) be the second derivative of -s**5/5 - s**2/2 - s. Let d be i(-1). Factor -4*p + d*p - 4*p**2 + 5*p**2 + 3*p.
p*(p + 2)
Let q(i) be the third derivative of i**5/12 - 5*i**3/6 - 9*i**2. Find r such that q(r) = 0.
-1, 1
Suppose -y + 5 = -2*t, t = -4*t - 5. Let g(n) be the first derivative of -n**y - 1 + 0*n**2 + 0*n - 3/4*n**4. Factor g(d).
-3*d**2*(d + 1)
Suppose -12/5 - 18/5*g + 0*g**4 + 12/5*g**2 + 24/5*g**3 - 6/5*g**5 = 0. Calculate g.
-1, 1, 2
Let s(l) be the third derivative of -l**8/672 + l**7/210 + l**6/120 - l**5/15 + 7*l**4/48 - l**3/6 - 16*l**2 + 2*l. Factor s(v).
-(v - 1)**4*(v + 2)/2
Let x = 8 - 5. Factor 3/2*t**x - 1/2 - 1/4*t + 7/4*t**2.
(t + 1)*(2*t - 1)*(3*t + 2)/4
Let f(u) = 7*u**5 + 161*u**4 + 378*u**3 + 162*u**2 - 313*u. Let n(g) = -3*g**5 - 81*g**4 - 189*g**3 - 81*g**2 + 156*g. Let l(m) = 6*f(m) + 11*n(m). Factor l(c).
3*c*(c + 3)**3*(3*c - 2)
Let b(f) = -55*f**2 + 85*f - 70. Let q(g) = 8*g**2 - 12*g + 10. Let i(s) = -3*b(s) - 20*q(s). Factor i(k).
5*(k - 2)*(k - 1)
Let a = 1244/4403 + 2/629. Factor 0 + 2/7*t**5 - a*t**3 - 2/7*t**2 + 0*t + 2/7*t**4.
2*t**2*(t - 1)*(t + 1)**2/7
Let b(k) be the first derivative of 2*k**3/63 + 21. Determine h, given that b(h) = 0.
0
Let g(t) be the first derivative of -t**6/9 - 4*t**5/15 - t**4/6 - 3. What is n in g(n) = 0?
-1, 0
Let h be (-3)/(-18)*(2 - (2 + -2)). Let -x**5 + h*x**2 + 0 + 0*x - 1/3*x**3 - 5/3*x**4 = 0. Calculate x.
-1, 0, 1/3
Let j(d) = -d - 5*d + 7*d. Let b be j(3). Factor 1/5*m**b + 0 + 2/5*m**2 + 1/5*m.
m*(m + 1)**2/5
Let a(t) be the first derivative of -t**3/21 - t**2/7 - 4. Factor a(g).
-g*(g + 2)/7
Suppose -4*f**3 + f**2 - 3*f**2 - 2*f**2 = 0. What is f?
-1, 0
Let z(c) = -c**2 + 4*c. Suppose 5*b + 2*y - 23 = 0, -5*y + 8 = -3*b - b. Let f be z(b). Factor v**2 - 3*v**4 + v**5 + 5*v**4 + 0*v**4 - f*v**4 - v**3.
v**2*(v - 1)**2*(v + 1)
Let w(y) be the third derivative of -y**9/151200 - y**8/8400 - y**7/1050 - y**6/225 - y**5/30 + 2*y**2. Let x(n) be the third derivative of w(n). Factor x(o).
-2*(o + 2)**3/5
Let q(y) be the second derivative of 0*y**2 - 1/6*y**3 + y + 0 + 1/12*y**4. Find w such that q(w) = 0.
0, 1
Find v, given that 2/7*v**4 + 2/7*v**5 - 6/7*v**3 - 2/7*v**2 + 0 + 4/7*v = 0.
-2, -1, 0, 1
Let h(s) be the first derivative of s**6/75 - s**5/50 - s**4/10 + s**3/3 - 2*s**2/5 - 4*s - 2. Let v(a) be the first derivative of h(a). Factor v(c).
2*(c - 1)**3*(c + 2)/5
Suppose -h - 1 + 6 = 0. Let l(q) be the second derivative of -1/2*q**2 + 1/20*q**h - 1/4*q**4 + 0 + 1/2*q**3 - q. Factor l(b).
(b - 1)**3
Let r(g) = -g**2 + 0*g**2 - 10*g + 0*g**2 + 13*g. Let m(x) = 1. Let k(n) = -6*m(n) + 3*r(n). Let k(u) = 0. Calculate u.
1, 2
Let r(i) be the first derivative of -4/5*i - 2 - 1/5*i**2 + 2/15*i**3. Factor r(j).
2*(j - 2)*(j + 1)/5
Let o(i) be the first derivative of -9*i**4/8 - 7*i**3/6 + i**2/2 - 36. Factor o(d).
-d*(d + 1)*(9*d - 2)/2
Let j = 1559/86340 - 2/1439. Let d(n) be the second derivative of -1/150*n**6 + n + 0*n**5 + 0*n**2 + j*n**4 + 0 + 0*n**3. Determine u so that d(u) = 0.
-1, 0, 1
Suppose s + 42 = -s. Let b be (1/(-6))/(7/s). Factor -1/2*g**2 - b*g + 0.
-g*(g + 1)/2
Let h(n) = 2*n**2 - 4*n + 4. Let u be h(1). Let q(d) be the second derivative of -1/15*d**3 + 0 + 0*d**u - 1/60*d**4 + 2*d. Let q(s) = 0. Calculate s.
-2, 0
Let y(d) be the second derivative of 3*d**5/5 + d**4/4 - 4*d. Factor y(f).
3*f**2*(4*f + 1)