et p(l) = -7*l**5 - 9*l**4 + 2*l**3 + 4*l**2 + 5*l. Let x(y) = 4*y**5 + 5*y**4 - y**3 - 2*y**2 - 3*y. Let r(g) = 3*p(g) + 5*x(g). Factor r(n).
-n**2*(n - 1)*(n + 1)*(n + 2)
Let j(u) be the first derivative of -2*u**8/105 - 8*u**7/525 - u**6/300 + 5*u**2/2 - 6. Let v(f) be the second derivative of j(f). Factor v(k).
-2*k**3*(4*k + 1)**2/5
Let y(a) be the third derivative of a**5/75 + a**4/5 + 16*a**3/15 + 2*a**2 + 13*a. Factor y(b).
4*(b + 2)*(b + 4)/5
Let s(n) = -29*n**4 - 29*n**3 + 60*n**2 + 11*n - 40. Let l(b) = 7*b**4 + 7*b**3 - 15*b**2 - 3*b + 10. Let k(d) = -9*l(d) - 2*s(d). Let k(q) = 0. What is q?
-2, -1, 1
Suppose 82*t**2 - 8*t**3 + 15 + 33*t**3 + 55*t - 17*t**2 = 0. Calculate t.
-1, -3/5
Suppose 8 + 2 = 5*q. Factor 2*x + q*x**4 - 6*x + 7*x**3 - 3*x**3 - 2.
2*(x - 1)*(x + 1)**3
Let g(y) be the first derivative of y**3/7 - 3*y/7 - 10. Suppose g(z) = 0. Calculate z.
-1, 1
Suppose 0 = 5*q - 6 - 4. Let t(o) be the first derivative of -1/6*o**4 + 0*o + 1/3*o**2 + q + 0*o**3. What is c in t(c) = 0?
-1, 0, 1
Let f(x) be the third derivative of 1/30*x**5 + 0 + 1/9*x**3 + 1/180*x**6 + 0*x + 1/12*x**4 - 3*x**2. Let f(u) = 0. Calculate u.
-1
Let o(q) be the second derivative of -q**7/560 + q**6/135 - q**5/144 - q**4/72 + q**3 - 6*q. Let s(x) be the second derivative of o(x). Factor s(u).
-(u - 1)**2*(9*u + 2)/6
Let o(u) be the second derivative of 2*u**6/15 - 7*u**5/10 + u**4/2 + 10*u. Factor o(h).
2*h**2*(h - 3)*(2*h - 1)
Let u(x) be the first derivative of 1/12*x**3 - 8 + 4*x + x**2. Factor u(z).
(z + 4)**2/4
Let -1/2 - 1/2*j**2 + j = 0. What is j?
1
Let v(n) be the first derivative of -n**3/6 + n**2/4 + n + 12. Suppose v(c) = 0. What is c?
-1, 2
Factor -15/7*z + 3/7*z**2 + 6/7*z**3 + 6/7.
3*(z - 1)*(z + 2)*(2*z - 1)/7
Let z(t) = -3*t**3 + 2*t + 1. Let i be z(-1). Find b, given that 1 + 2*b - 3*b**4 + b**3 - 3*b**3 + i*b**4 = 0.
-1, 1
Suppose 3*w = 4*q - 23, q + 6 = 2. Let y(r) = 9*r**3 - 13*r - 2. Let l(a) = 18*a**3 - 27*a - 4. Let o(u) = w*y(u) + 6*l(u). Factor o(p).
-(p - 1)*(3*p + 1)*(3*p + 2)
Let t(n) be the third derivative of -n**7/42 - n**6/6 + 10*n**4/3 + 40*n**3/3 - 64*n**2. Let t(i) = 0. What is i?
-2, 2
Let k(d) be the third derivative of d**5/390 - d**4/156 - 2*d**2. Factor k(o).
2*o*(o - 1)/13
Let f = -2/135 + 92/135. Let u(d) be the second derivative of 0 + 1/18*d**4 + f*d**2 + 1/3*d**3 + d. Factor u(x).
2*(x + 1)*(x + 2)/3
Suppose -3*n - 2*i = -8, 3*i - 5 = -4*n + 6. Let g(k) be the first derivative of 2 - 6*k + k**3 + 3/2*k**n. Factor g(c).
3*(c - 1)*(c + 2)
Let m be 10/4 - (-1)/2. Let i be 7/3 + (-2)/6. Let -2/3*a**m - 2/3*a**i + 0 + 0*a = 0. Calculate a.
-1, 0
Let h(w) be the second derivative of w**4/6 + w**3/3 - 2*w**2 - 2*w + 10. Determine l, given that h(l) = 0.
-2, 1
Let x be (-1)/6 - 11/(-33). Let t(i) be the second derivative of 2*i + i**2 - x*i**4 - 1/10*i**5 + 0 + 1/3*i**3. Let t(d) = 0. What is d?
-1, 1
Let i be -4 - (15/(-3) + -3 + 2). Factor -2/5*g**i + 0 + 4/5*g.
-2*g*(g - 2)/5
Let c be -6 + (-184)/(-18) + -4. Factor -c*s + 2/3*s**2 + 0 + 2/9*s**4 - 2/3*s**3.
2*s*(s - 1)**3/9
Let d(k) = k**2 + 5*k + 4. Let b be d(-4). Let m = 3 - b. Factor -2 + 0 + n - n**m + 1 + 2 - n**2.
-(n - 1)*(n + 1)**2
Let v(f) be the first derivative of -4*f**3/9 + 10*f**2/3 - 16*f/3 + 26. Factor v(n).
-4*(n - 4)*(n - 1)/3
Let b(x) be the second derivative of -x**6/10 - 3*x**5/10 + x**3 + 3*x**2/2 + 9*x. Factor b(k).
-3*(k - 1)*(k + 1)**3
Suppose -36/5 - 24/5*n - 4/5*n**2 = 0. What is n?
-3
Determine r, given that -308*r**5 - 20*r + 7*r**4 + 313*r**5 - 4 - 39*r**2 + 8*r**2 - 13*r**3 = 0.
-1, -2/5, 2
Suppose -4*i + 3*u = i - 22, 4*u = -2*i + 14. Let s = i + -23/5. Factor -s*w + 1/5*w**2 + 0 + 1/5*w**3.
w*(w - 1)*(w + 2)/5
Factor 9*c**4 + c - 2*c + c - 3*c**3.
3*c**3*(3*c - 1)
Let t(y) be the third derivative of -y**9/30240 - y**8/13440 + 5*y**4/24 - 2*y**2. Let c(k) be the second derivative of t(k). Factor c(f).
-f**3*(f + 1)/2
Let -2/3*l**4 + 7/3*l + 2/3*l**3 + 8/3*l**2 + 2/3 - 1/3*l**5 = 0. Calculate l.
-1, 2
Let f(p) = -p**2 - p. Let d(m) = -m**3 - 3*m - 4. Let r(s) = -d(s) - 5*f(s). Factor r(n).
(n + 1)*(n + 2)**2
Let r(l) = -33*l**3 + 15*l**2 + 3*l + 5. Let b(u) = 16*u**3 - 8*u**2 - 2*u - 2. Let f(m) = 5*b(m) + 2*r(m). Factor f(x).
2*x*(x - 1)*(7*x + 2)
Let h(a) be the first derivative of -4*a**2 - 2/3*a**3 - 2 - 8*a. Let h(c) = 0. What is c?
-2
Let c(a) be the first derivative of 0*a - a**2 + 0*a**3 - 1 - 1/72*a**4 + 1/180*a**5. Let r(h) be the second derivative of c(h). Let r(b) = 0. Calculate b.
0, 1
Suppose 4*p + 2 - 2*p**2 + 1 + 2 - 7 = 0. Calculate p.
1
Let i be 3 + ((-3)/(-3) - 2). Suppose 27 = v - 5*n, -2*v - i*n = 3*n + 21. Factor -4/5*b + 2/5*b**v + 0.
2*b*(b - 2)/5
Solve 32/5*d + 2/5*d**4 + 0 + 18/5*d**3 + 48/5*d**2 = 0.
-4, -1, 0
Solve 6*f**3 + 0*f**4 - 3*f - 5*f + f**4 + f**4 = 0.
-2, 0, 1
Let z(j) be the first derivative of -6 - 6/7*j + 2/21*j**3 - 2/7*j**2. What is f in z(f) = 0?
-1, 3
Let l(j) = -j**3 + 11*j**2 - 9*j - 8. Let i be l(10). Let g be (-5 + i)*(-5)/30. Factor 3/2*a + 1/2*a**3 + g + 3/2*a**2.
(a + 1)**3/2
Suppose 0*t - 1 = t. Let r(a) = -3*a + 1. Let s be r(t). Factor 1 - s*b**2 + 2*b**2 - 2*b + 3.
-2*(b - 1)*(b + 2)
Factor -20/7*i**3 + 0*i - 4/7*i**5 - 16/7*i**4 + 0 - 8/7*i**2.
-4*i**2*(i + 1)**2*(i + 2)/7
Let m = 22 - 18. Solve t**3 - 2*t**4 - 3*t**3 - 4 + m*t**2 + 2*t**2 + 3*t - t = 0.
-2, -1, 1
Solve 4/7 - 18/7*c**3 - 26/7*c + 40/7*c**2 = 0.
2/9, 1
Let f be ((1 - 3) + 2)/(1 - -1). Factor 1/2*u**4 + 1/2*u**3 - 1/2*u**2 - 1/2*u**5 + f*u + 0.
-u**2*(u - 1)**2*(u + 1)/2
Let f(y) = -2*y**2 - 4*y**2 + 2*y**2 + 4 + 2*y**2. Let d(k) = 3*k**2 - 7. Let x(h) = 4*d(h) + 7*f(h). Factor x(j).
-2*j**2
Let r(y) be the first derivative of -2/3*y**3 - 3 - 4*y**2 - 8*y. Factor r(f).
-2*(f + 2)**2
Factor -5*r**2 + 3*r + 9 + 3*r + 2*r**2.
-3*(r - 3)*(r + 1)
Let -3/4*f**4 + 3*f**3 + 0 - 9/4*f**2 + 0*f = 0. Calculate f.
0, 1, 3
Let d(y) be the first derivative of -10 + 12/5*y**5 + 0*y + 1/2*y**6 + 9/2*y**4 + 3/2*y**2 + 4*y**3. Factor d(m).
3*m*(m + 1)**4
Let v(o) be the first derivative of -5*o**3/3 + 20*o - 25. Factor v(f).
-5*(f - 2)*(f + 2)
Let 9/2*x**2 - 7/2*x + 1/2*x**4 + 1 - 5/2*x**3 = 0. What is x?
1, 2
Let c(g) be the third derivative of -1/48*g**4 - 2*g**2 + 0*g**5 + 0*g + 1/240*g**6 + 0 + 0*g**3. Factor c(f).
f*(f - 1)*(f + 1)/2
Factor -26/11*z + 2/11*z**3 - 24/11*z**2 + 0.
2*z*(z - 13)*(z + 1)/11
Let u be 954/265 + (-4)/(-10). Factor 0*y**2 + 0*y + 1/2*y**u + 1/2*y**3 + 0.
y**3*(y + 1)/2
Let u(r) be the second derivative of r**6/15 - r**4/2 - 2*r**3/3 + 5*r. Factor u(x).
2*x*(x - 2)*(x + 1)**2
Let d = 802/597 + -2/199. Find j, given that d*j**2 + 40/9*j - 26/9*j**3 - 16/9 - 10/9*j**4 = 0.
-2, 2/5, 1
Let w = 0 - 0. Let m(f) = -f**2 - 7*f + 10. Let d be m(-8). Determine g, given that 2*g**d - 2*g + w*g + 4*g = 0.
-1, 0
Let u(q) be the third derivative of q**6/1200 - q**4/240 + 3*q**2. Factor u(t).
t*(t - 1)*(t + 1)/10
Let f be 1 + -2 + (1 - 2). Let p(k) = -1. Let h(u) = -5*u + 6*u + 2*u - 4*u + u**2 + 5. Let r(g) = f*h(g) - 10*p(g). Suppose r(x) = 0. Calculate x.
0, 1
Let f(n) = n**2 + n - 1. Let c(x) = 14*x**2 + 14*x + 1. Let z(d) = -c(d) + 2*f(d). Factor z(i).
-3*(2*i + 1)**2
Solve -16*b - b + 16 + 6*b - b - 4*b**2 = 0.
-4, 1
Determine t so that -2/3*t + 2*t**2 - 2*t**3 + 2/3*t**4 + 0 = 0.
0, 1
Factor 28*q**2 + 8*q**3 - 28*q**4 - 8*q - 21 + 21.
-4*q*(q - 1)*(q + 1)*(7*q - 2)
Let x(q) be the first derivative of q**5/4 - 5*q**4/8 + 5*q**2/4 - 5*q/4 - 6. Find v, given that x(v) = 0.
-1, 1
Let f(i) = -i**3 - 1. Let g(n) = -2*n**5 - 20*n**4 - 42*n**3 - 44*n**2 - 14*n + 6. Let j(t) = -12*f(t) - 2*g(t). Let j(v) = 0. What is v?
-7, -1, 0
Factor -32/5*y + 12*y**2 - 64/5 + 4/5*y**4 + 32/5*y**3.
4*(y - 1)*(y + 1)*(y + 4)**2/5
Let t(g) = g - 9. Let p be t(9). Factor -16*n**2 + 27*n + p*n - 7*n - 8 + 4*n**3.
4*(n - 2)*(n - 1)**2
Let k(t) be the first derivative of -5*t**6/6 + 11*t**5 - 115*t**4/2 + 150*t**3 - 405*t**2/2 + 135*t - 46. Determine s so that k(s) = 0.
1, 3
Let d(s) be the second derivative of s**9/30240 + s**8/13440 - s**4/4 - 5*s. Let w(z) be the third derivative of d(z). Suppose w(x) = 0. Calculate x.
-1, 0
Let p(i) be the third derivative of 1/16*i**4 + 0 + 1/70*i**7 - 3/80*i**6 + 0*i**5 - 2*i**2 + 0*i + 0*i