e f*p = -2*p + 21. Factor 0*j + 3/2*j**p + j**4 + 0 + 1/2*j**2.
j**2*(j + 1)*(2*j + 1)/2
Let y(p) = -2*p**4 + 4*p**3 - 2*p**2 + 3. Let v(n) = 4*n**4 - 8*n**3 + 4*n**2 - 5. Let r(g) = 3*v(g) + 5*y(g). Factor r(x).
2*x**2*(x - 1)**2
Suppose 5*a - 6*a = 0. Let q(o) be the first derivative of a*o - 1 + 1/12*o**4 + 1/6*o**2 - 2/9*o**3. Factor q(x).
x*(x - 1)**2/3
Let v(a) = -9*a**2 - a + 3. Let k(t) = -5*t**2 - t + 2. Suppose o - 4 = -0*o. Let x(m) = o*v(m) - 7*k(m). Find i such that x(i) = 0.
1, 2
Let h(q) be the first derivative of 41/3*q**3 - 2 - 21/4*q**4 - 12*q**2 + 4*q. Solve h(p) = 0 for p.
2/7, 2/3, 1
Let r be 5/(-10) - 10/(-4). Solve 4*g - 4*g + 24*g - 12*g**2 + 60*g**r + 3 = 0 for g.
-1/4
Let o(g) be the third derivative of 0 - 1/60*g**4 + 1/75*g**5 + 0*g - 5*g**2 - 2/15*g**3 + 1/300*g**6. Solve o(l) = 0 for l.
-2, -1, 1
Let 12/5*p**2 + 0 + 4/5*p**5 - 8/5*p - 12/5*p**4 + 4/5*p**3 = 0. Calculate p.
-1, 0, 1, 2
Let n be ((-8)/(-32))/((-5)/(-2) + -2). Determine s so that -n*s**2 + 0 + 0*s + 1/2*s**5 - 1/2*s**3 + 1/2*s**4 = 0.
-1, 0, 1
Let r(m) be the third derivative of -m**7/420 - m**6/120 + m**5/40 + m**4/6 + m**3/3 - 10*m**2. Factor r(o).
-(o - 2)*(o + 1)**2*(o + 2)/2
Let m be (32/(-3))/((-4)/(-10)). Let c = -26 - m. Factor 2/9*k**4 - 4/9 + 2/9*k**3 - c*k**2 - 10/9*k.
2*(k - 2)*(k + 1)**3/9
Suppose 0 = 4*u - 12, -3*f + 4*u = 1539 + 111. Let k be f/(-490) - 4/(-14). Factor -k*t - 3/5*t**2 - 2/5.
-(t + 2)*(3*t + 1)/5
Factor -1/3*s**2 + 1 - 2/3*s.
-(s - 1)*(s + 3)/3
Let k(l) be the first derivative of -10/27*l**3 + 0*l + 2/9*l**4 - 2/45*l**5 + 2/9*l**2 + 1. Find n, given that k(n) = 0.
0, 1, 2
Let v(i) be the first derivative of 5 + 0*i**3 + 1/4*i**4 + 0*i**2 + 0*i + 1/5*i**5. Find q, given that v(q) = 0.
-1, 0
Let q(i) = 7*i**2 - 7*i. Let t(p) = 8*p**2 - 8*p. Let w(m) = 3*q(m) - 2*t(m). Suppose w(n) = 0. What is n?
0, 1
Let h(y) be the first derivative of y**7/420 - y**6/90 + y**5/60 + y**3/3 + 2. Let p(z) be the third derivative of h(z). Factor p(u).
2*u*(u - 1)**2
Let s = -20 + 11. Let n be (24/s)/(-1) + -2. Let 0 + n*m - 2/3*m**3 + 2/3*m**2 - 2/3*m**4 = 0. What is m?
-1, 0, 1
Let h(v) = 4*v**3 - 7*v**2 + 3*v + 5. Let w(g) = -2*g**3 + 4*g**2 - 2*g - 2. Let l(c) = -2*h(c) - 5*w(c). Factor l(a).
2*a*(a - 2)*(a - 1)
Let o(p) be the third derivative of p**7/105 + p**6/30 - 3*p**2. Factor o(v).
2*v**3*(v + 2)
Suppose 1 = g - 0. Suppose -2*l = -7 - g. Factor 4/7*n**l + 2/7*n + 8/7*n**2 + 0 + 10/7*n**3.
2*n*(n + 1)**2*(2*n + 1)/7
Suppose -30 + 6 = -r. Let u = -21 + r. Determine h so that 56/5*h - 46/5*h**u - 12/5*h**2 - 14/5*h**4 + 16/5 = 0.
-2, -2/7, 1
Let p(i) = i**3 - 14*i**2 - 14*i - 12. Let s = 2 - -13. Let r be p(s). Find b such that 0 - 5/3*b**r + 4/3*b**5 - b**4 + 1/3*b + b**2 = 0.
-1, -1/4, 0, 1
Let a(k) be the third derivative of 0*k - 3*k**2 + 0*k**3 + 1/20*k**6 - 1/10*k**5 - 1/105*k**7 + 0 + 1/12*k**4. Solve a(r) = 0 for r.
0, 1
Factor 0 + 18/5*b**2 + 2/5*b**4 + 8/5*b + 12/5*b**3.
2*b*(b + 1)**2*(b + 4)/5
Suppose 0 = -2*n - 2 + 6. Let p(o) be the second derivative of 1/2*o**3 - 1/4*o**4 + 3*o**n + 0 - 4*o. Determine d so that p(d) = 0.
-1, 2
Let m(u) = -2*u**2 + 24*u + 26. Let d be m(13). Let q(j) be the third derivative of 0*j**3 - 1/30*j**5 + d + 0*j - 1/24*j**4 + j**2. Let q(x) = 0. Calculate x.
-1/2, 0
Let r = 3 - -5. Let f = r - 6. Solve 10/3*s**f + 8/3 + 16/3*s + 2/3*s**3 = 0.
-2, -1
Let d(b) = b**3 + 5*b**2 + 3*b. Let t be d(-4). Suppose -3*k - 2*x = -t*x + 8, -8 = -4*k - 2*x. Factor z**4 + z - z**2 - 3*z**3 + k*z**2 + 2*z**3.
z*(z - 1)**2*(z + 1)
Let l = 8 - 5. Suppose -13 = -5*g - 3*s - 1, -10 = -2*g + 4*s. Factor 2*h + 0*h**3 + h**g - h**2 - 2*h**l.
-h*(h - 1)*(h + 2)
Let d(q) = 2*q**4 - q**3 - q**2 + q - 1. Let h(f) = -f**4 + 20*f**3 - 40*f**2 - 8*f + 53. Let w(a) = d(a) - h(a). Factor w(v).
3*(v - 3)**2*(v - 2)*(v + 1)
Let s(d) be the third derivative of d**2 + 0*d**6 - 1/21*d**3 + 0*d**4 + 0*d + 1/105*d**5 - 1/735*d**7 + 0. Factor s(i).
-2*(i - 1)**2*(i + 1)**2/7
Let h = -3 + 0. Let p = -8 - h. Let n(q) = -q**2 + 2*q + 1. Let i(j) = -3*j**2 + 5*j + 3. Let x(o) = p*n(o) + 2*i(o). Factor x(y).
-(y - 1)*(y + 1)
Let v(n) = -5*n**5 - 11*n**4 - 5*n**3 + n**2 + 7*n + 1. Let g(d) = -16*d**5 - 34*d**4 - 14*d**3 + 2*d**2 + 20*d + 2. Let x(a) = -6*g(a) + 20*v(a). Factor x(l).
-4*(l - 1)*(l + 1)**3*(l + 2)
Let o(v) = -v - 4. Let k be o(-7). Factor -2*y**4 - 4*y**2 + y**5 + y**3 + y**4 - 2*y**k + 5*y**2.
y**2*(y - 1)**2*(y + 1)
Let i = 11 + -8. Solve i*s**2 - s - 2*s**2 - s**2 - s**2 = 0 for s.
-1, 0
Suppose -64*b = -63*b - 5. Let h(r) be the first derivative of r**b + 0*r**2 + 1/3*r**3 + 1/3*r**6 + 0*r + r**4 - 1. What is p in h(p) = 0?
-1, -1/2, 0
Let x(l) = 16*l**2 - l - 6. Let s = 3 + -5. Suppose -5*t = 5*r - 65, 0*t - 5 = -r + 3*t. Let p(a) = 3*a**2 - 1. Let c(b) = r*p(b) + s*x(b). Factor c(k).
(k + 1)**2
Let v(x) be the first derivative of -16*x**3/3 - 6*x**2 + 4*x - 11. Factor v(z).
-4*(z + 1)*(4*z - 1)
Let i = 29 + -16. Let -35*l**2 - 18*l**4 - 11*l - 6 - i*l**2 - 16*l - 42*l**3 - 3*l**5 = 0. What is l?
-2, -1
Let d(b) be the second derivative of b**5/60 + b**4/24 - 5*b**2/2 - 4*b. Let z(y) be the first derivative of d(y). Solve z(g) = 0 for g.
-1, 0
Let w(t) be the second derivative of t**5/60 - 29*t. Factor w(l).
l**3/3
Let v(w) be the first derivative of -w**3/9 - w**2/3 + 5. Factor v(i).
-i*(i + 2)/3
Let t(i) be the second derivative of -i**9/9072 + i**8/2520 - i**6/540 + i**5/360 + i**3/3 + 2*i. Let q(k) be the second derivative of t(k). Factor q(s).
-s*(s - 1)**3*(s + 1)/3
Let w be 5 + -6 - (3 + -1). Let i = 6 + w. Find m, given that m**i + 0*m**4 + 0*m**4 - 3*m**3 + 2*m**4 = 0.
0, 1
Suppose 0 = -5*l + 27 - 17. Factor -2/7*t**l - 8/7 - 8/7*t.
-2*(t + 2)**2/7
Let d(t) be the second derivative of t**7/84 - t**6/20 + t**5/20 - 7*t. Factor d(s).
s**3*(s - 2)*(s - 1)/2
Let k(b) be the third derivative of -b**6/960 - b**5/480 + b**4/96 - 2*b**2. What is y in k(y) = 0?
-2, 0, 1
Suppose -56/11*t**2 + 2/11*t**3 + 0 + 392/11*t = 0. What is t?
0, 14
Let b(z) be the first derivative of -2*z**3/57 + z**2/19 + 4*z/19 + 4. Find s such that b(s) = 0.
-1, 2
Let q(k) be the second derivative of -k**7/21 + k**6/15 + k**5/5 - k**4/3 - k**3/3 + k**2 - 3*k. Factor q(j).
-2*(j - 1)**3*(j + 1)**2
Let i(c) = c**2 - 11*c - 57. Let t be i(15). Suppose 18/7*s**4 + 144/7*s - 48/7*s**2 - 24/7*s**t - 96/7 - 3/7*s**5 = 0. What is s?
-2, 2
Suppose 7/5 + 1/5*f**2 + 8/5*f = 0. What is f?
-7, -1
Let y = -13/4 + 47/12. Factor 0*q**2 + 0 - 2/3*q + y*q**3.
2*q*(q - 1)*(q + 1)/3
Let f(u) be the third derivative of 25*u**8/336 - u**7/7 - 61*u**6/120 + 11*u**5/30 + 3*u**4/2 + 4*u**3/3 - 10*u**2. Find o, given that f(o) = 0.
-1, -2/5, 1, 2
Let r(u) = -7*u**4 - 15*u**3 - 3*u**2 + 13*u + 8. Let l(m) = -15*m**4 - 30*m**3 - 5*m**2 + 25*m + 15. Let i(t) = 2*l(t) - 5*r(t). Factor i(x).
5*(x - 1)*(x + 1)**2*(x + 2)
Factor -1/4*p**3 - 1/4*p**2 + 1/4*p + 1/4.
-(p - 1)*(p + 1)**2/4
Let b(j) = j**2 + j - 2. Let n(r) = 7*r**2 + 22*r - 64. Let d(u) = 2*b(u) - n(u). Suppose d(i) = 0. What is i?
-6, 2
Let z(y) be the second derivative of -y**8/560 + y**7/105 - y**6/60 + y**4/24 + y**3/2 - 2*y. Let r(x) be the second derivative of z(x). Solve r(h) = 0.
-1/3, 1
Let a(b) = 4*b**3 + 3*b - b**4 - 5 + b + 0*b**4 - 6*b**2. Let j(h) = 2*h**4 - 8*h**3 + 12*h**2 - 8*h + 11. Let k(c) = -9*a(c) - 4*j(c). Let k(p) = 0. What is p?
1
Suppose -1/5*q**2 + 3/5 + 2/5*q = 0. What is q?
-1, 3
Let j(f) = f**2 - 2. Let v be j(-2). Let y be (-7 - -1)/((-18)/12). Factor 0*u**v + y*u + 4*u + 2*u**2 + 8.
2*(u + 2)**2
Let f be (-142)/360 + 16/40. Let h(i) be the third derivative of 0*i + 2*i**2 + f*i**5 + 0 + 1/24*i**4 + 1/9*i**3. Factor h(t).
(t + 1)*(t + 2)/3
Determine y so that -12*y + 3*y + 6*y**4 + 3*y**2 + 9*y**3 - 3*y**4 - 6 = 0.
-2, -1, 1
Suppose 0 = w, -2*w = -3*a + w - 6*w. Factor -14/13*o**3 + a*o + 6/13*o**4 + 4/13*o**2 + 0.
2*o**2*(o - 2)*(3*o - 1)/13
Suppose 2*b + 3*b + 3 = x, -5*b - 5*x = -15. Factor d**3 - 1 + b*d**2 - 3*d**2 + 35*d - 32*d.
(d - 1)**3
Let u(o) be the first derivative of 11*o**3/3 - 31*o**2/2 - 6*o - 34. Let u(y) = 0. What is y?
-2/11, 3
Let x(h) be the third derivative of -h**6/300 - 2*h**5/75 + h**4/60 + 4*h**3/15 + 40*h**2. Solve x(v) = 0 for v.
-4, -1, 1
Let x(a) 