Let g(c) = -4*c**5 - 15*c**4 - 7*c**3 + 12*c**2 + 11*c. Let s(k) = -16*g(k) + 3*x(k). Factor s(t).
4*t*(t - 1)*(t + 1)**2*(t + 2)
Let b be (-5)/(180/(-152)) + -4. Let x(a) be the first derivative of -a**2 - b*a**3 - 1 - 4/3*a. Find v such that x(v) = 0.
-2, -1
Let b(s) = -9*s**3 - 13*s**2 - s + 13. Let z(r) = 4*r**3 + 6*r**2 - 6. Let i(c) = 2*b(c) + 5*z(c). Suppose i(t) = 0. Calculate t.
-2, -1, 1
Let -1/2*d**3 + 1/2 + 3/2*d**2 - 3/2*d = 0. Calculate d.
1
Let 6454*a**4 + 24 - 2*a**2 - 12*a - 40*a**2 - 6445*a**4 + 3*a**3 = 0. Calculate a.
-2, -1, 2/3, 2
Let p be (-4)/(-2) + 8 + -5. Let l(c) be the second derivative of 0*c**2 + c - 2/5*c**p + 0 - 1/3*c**3 + 2/3*c**4. Solve l(y) = 0 for y.
0, 1/2
Let b(o) be the second derivative of o**6/150 - o**5/25 + o**4/12 - o**3/15 - 27*o. Find a such that b(a) = 0.
0, 1, 2
Factor -20*l - 4 + 0 - 77*l**2 + 101*l**2.
4*(l - 1)*(6*l + 1)
Let r(f) be the first derivative of f**7/210 - f**6/50 + 3*f**5/100 - f**4/60 - f + 3. Let m(k) be the first derivative of r(k). Factor m(x).
x**2*(x - 1)**3/5
Let g = 2885/7 - 411. Let -g - 2/7*j**2 - 8/7*j = 0. What is j?
-2
Let j = 9 - 9. Let u(x) be the second derivative of j - 8/3*x**3 - x + 5/4*x**5 + 2*x**2 + 5/12*x**4. Factor u(b).
(b + 1)*(5*b - 2)**2
Let z(f) be the first derivative of -f**3/4 - 3*f**2/4 + 4. Factor z(s).
-3*s*(s + 2)/4
Suppose 16 - 4 = 4*t. Let n(x) be the second derivative of x - 1/6*x**4 + 4/3*x**2 + 1/15*x**5 + 1/45*x**6 + 0 - 4/9*x**t. Find c, given that n(c) = 0.
-2, 1
Let l(x) be the third derivative of -x**10/30240 - x**9/7560 + x**7/1260 + x**6/720 + x**4/8 + 2*x**2. Let v(p) be the second derivative of l(p). Factor v(w).
-w*(w - 1)*(w + 1)**3
Let y be (144/480)/((-6)/(-8) - 0). Factor 0*a + 2/5*a**3 - y*a**2 + 0.
2*a**2*(a - 1)/5
Let o be 79/9 + (-4)/(-18). Let y be 0/(-1)*o/18. Determine f so that 8/7*f + 2/7*f**3 - 8/7*f**2 + y = 0.
0, 2
Let s = -310 - -313. Factor 0*d**2 + d**s + 0*d + 7/2*d**5 + 9/2*d**4 + 0.
d**3*(d + 1)*(7*d + 2)/2
Suppose 4*w + 4 + 8 = 0. Let c be w - (-1 + (1 - 3)). Factor c + 0*v + 2/5*v**3 + 2/5*v**2.
2*v**2*(v + 1)/5
Let n be (-46)/8 - -3 - -3. Let s(i) be the first derivative of 1/8*i**4 - 1/20*i**5 + 0*i**3 + 1 - n*i**2 + 1/4*i. Factor s(h).
-(h - 1)**3*(h + 1)/4
Let j(s) = 7*s**3 + s. Let z(i) = -57*i**3 - 9*i. Let d(o) = 33*j(o) + 4*z(o). Factor d(b).
3*b*(b - 1)*(b + 1)
Let u(z) = -6*z**2 + 8*z. Let j(t) = 7*t - 1 + 1 - 2*t**2 - 3*t**2. Let y(c) = -c**2 + 8*c - 3. Let b be y(7). Let i(l) = b*j(l) - 3*u(l). Factor i(f).
-2*f*(f - 2)
Suppose -3*w + r - 5 = w, -3*w = r - 5. Factor -2/3*i**3 - 2/3*i**4 + w + 4/3*i**2 + 0*i.
-2*i**2*(i - 1)*(i + 2)/3
Let -2/3*t - 4/3*t**2 + 0*t**3 + 2/3*t**5 + 4/3*t**4 + 0 = 0. What is t?
-1, 0, 1
Let n be (-2)/(-9) - 32/(-18). Let f(i) = 19*i**3 - 2*i + 2*i - 18*i**3. Let z(d) = -6*d**3 - 2*d**2 + 4*d + 2. Let w(t) = n*f(t) + z(t). Factor w(k).
-2*(k - 1)*(k + 1)*(2*k + 1)
Let c = 29 + -18. Suppose -13 = -4*n - m + 2*m, -3*n + c = -m. Factor 4*h**3 + 2*h**4 - n*h**3 + 2*h**2 - 3*h**2 - 3*h**4.
-h**2*(h - 1)**2
Determine f, given that -3/2*f + 0 - 1/4*f**4 + f**3 - 1/4*f**2 = 0.
-1, 0, 2, 3
Suppose 3*k = o - 0*k - 84, 5*o - 420 = 4*k. Solve 8*t + 25*t - 123*t**3 + o*t**4 + 0*t**2 + 6 + 0*t**2 = 0.
-2/7, -1/4, 1
Let g(j) = -j - 1. Let x be g(-5). Suppose 2*r - x*a - 12 = 0, 0*r = -2*r - 2*a - 6. Factor 2/9*o**2 + 0*o + r + 2/9*o**3.
2*o**2*(o + 1)/9
Let g(v) be the second derivative of v**6/600 - v**5/150 + v**4/120 - v**2 - 2*v. Let x(m) be the first derivative of g(m). Factor x(t).
t*(t - 1)**2/5
Let v = -114 + 114. Let h(x) be the third derivative of 0*x**3 + 1/210*x**5 - 3*x**2 + 0*x + v - 1/84*x**4. Determine w, given that h(w) = 0.
0, 1
Let k(j) be the third derivative of 0*j - j**2 + 0 + 2/9*j**3 + 1/36*j**4 - 1/90*j**5. Factor k(c).
-2*(c - 2)*(c + 1)/3
Let p be (1 + (-6 - -6))*(-3)/(-9). Factor p*q**2 - q + 2/3.
(q - 2)*(q - 1)/3
Suppose 0 - 4/9*t + 8/9*t**3 + 14/9*t**2 = 0. What is t?
-2, 0, 1/4
Let n(c) be the second derivative of c**6/60 + c**5/40 - c**4/6 - c**3/3 + 31*c. Suppose n(m) = 0. Calculate m.
-2, -1, 0, 2
Let g be 21 + -17 - ((-8)/(-5) - -2). Factor -8/5 - g*v**2 + 8/5*v.
-2*(v - 2)**2/5
Let y(a) be the first derivative of -a**5/30 - a**4/24 + a**3/18 + a**2/12 - 10. Let y(c) = 0. Calculate c.
-1, 0, 1
Let l(u) be the first derivative of -4 - 4/15*u**3 + 2/5*u + 1/5*u**2. Factor l(i).
-2*(i - 1)*(2*i + 1)/5
Let a = 805/3 + -11171/42. Let r = -1/42 + a. Let -1/3 - r*q**2 + q**3 + 5/3*q = 0. Calculate q.
1/3, 1
Suppose 2*h - 5 = 1. Let g(i) be the second derivative of 1/60*i**4 - 1/30*i**3 + 0*i**2 + h*i + 0. Factor g(q).
q*(q - 1)/5
Let m(a) be the first derivative of -3*a**4/4 - a**3 + 6*a**2 + 12*a + 39. Suppose m(x) = 0. What is x?
-2, -1, 2
Solve 2*t - 6*t**2 + 13*t**4 + 3*t**3 - 4*t**4 + t**2 - t = 0 for t.
-1, 0, 1/3
Factor -36/7*z**3 - 162/7*z**2 + 0 + 0*z - 2/7*z**4.
-2*z**2*(z + 9)**2/7
Let o(p) = -2*p**5 + 9*p**4 - 5*p**3 - 2*p**2 - 7*p - 7. Let r(k) = -k**5 + 5*k**4 - 3*k**3 - k**2 - 4*k - 4. Let t(s) = -4*o(s) + 7*r(s). Factor t(v).
v**2*(v - 1)**2*(v + 1)
Let g be 2/(-18)*-4 - 12/36. Let x(z) be the second derivative of -4/45*z**5 + 1/9*z**4 + 0 + z - g*z**2 + 0*z**3 + 1/45*z**6. Solve x(w) = 0 for w.
-1/3, 1
Let u(y) be the third derivative of y**7/3780 + y**6/270 + y**5/60 + y**4/8 + y**2. Let g(h) be the second derivative of u(h). Factor g(c).
2*(c + 1)*(c + 3)/3
Let t(a) = -a**2 - 31*a - 195. Let c be t(-22). Solve 0 + 0*n - 1/4*n**c - 1/4*n**2 = 0 for n.
-1, 0
Let b(r) be the second derivative of -1/63*r**7 + 0*r**3 + 1/30*r**5 + 6*r + 0 + 1/45*r**6 - 1/18*r**4 + 0*r**2. Factor b(s).
-2*s**2*(s - 1)**2*(s + 1)/3
Let v = -199 + 598/3. Determine u, given that 2/3*u**2 - u + v = 0.
1/2, 1
Factor -3 - 31*i + 15*i + 12*i - i**2.
-(i + 1)*(i + 3)
Let s(q) be the second derivative of -q**4/2 - 3*q**3/2 - 3*q**2/2 + 25*q. Factor s(x).
-3*(x + 1)*(2*x + 1)
Let z(h) = 25*h**3 - 30*h**2 + 15*h + 20. Let d(x) = -x**3 + x**2 - 1. Let n(u) = 30*d(u) + z(u). Solve n(y) = 0 for y.
-2, 1
Let c(g) be the third derivative of -g**6/120 + g**4/24 - 8*g**2. Factor c(j).
-j*(j - 1)*(j + 1)
Suppose -3*f - 2*b = 4, 4*b = 2*b - 4. Let x be (-1)/(-1) - 10/14. Factor x*v**3 + f*v**2 + 0*v**4 + 0 + 0*v - 2/7*v**5.
-2*v**3*(v - 1)*(v + 1)/7
Let y(u) be the first derivative of -u**7/1155 - 2*u**2 - 2. Let m(f) be the second derivative of y(f). Find o, given that m(o) = 0.
0
Let u be 1 + 2/(-72) - 130/585. Factor 0*w - u + 3/4*w**2.
3*(w - 1)*(w + 1)/4
Let q(h) be the second derivative of h**4/18 - 4*h**3/3 + 12*h**2 + 13*h. Solve q(w) = 0 for w.
6
Let q(k) be the second derivative of -4*k**7/119 + 47*k**6/255 - 23*k**5/170 - 41*k**4/102 + 35*k**3/51 - 6*k**2/17 + 22*k. Let q(r) = 0. Calculate r.
-1, 1/4, 2/3, 1, 3
Let d = 26 + -16. Factor -2*k**3 - 7*k - d + 8 + k + 4 + 6*k**2.
-2*(k - 1)**3
Let u(i) be the first derivative of -1/16*i**4 + 2 + 2*i + 3/8*i**3 - 3/4*i**2. Let y(n) be the first derivative of u(n). Factor y(f).
-3*(f - 2)*(f - 1)/4
Let v(w) = -w**3 + 2*w**2 + w + 1. Let t be v(2). Let -3*h**4 - 6/5*h**5 + 0*h + 0 - 3/5*h**2 - 12/5*h**t = 0. Calculate h.
-1, -1/2, 0
Let t(l) be the second derivative of l**5/80 - l**3/24 + l. Let t(k) = 0. Calculate k.
-1, 0, 1
Let i(l) be the third derivative of 0*l + 0*l**3 + 2/45*l**5 + 1/90*l**6 - 1/315*l**7 + 0 + 6*l**2 - 2/9*l**4. Find w such that i(w) = 0.
-2, 0, 2
Let t(j) = -6*j - 7. Let f be t(5). Let h = 112/3 + f. Solve -32/3 + 80/3*i + 40/3*i**3 - 10/3*i**4 - 80/3*i**2 + h*i**5 = 0.
2
Let a(r) = 1 - 2 - 2*r + 2 - 3. Let o be a(-2). Factor 4/7 + 2/7*q - 2/7*q**o.
-2*(q - 2)*(q + 1)/7
Let w be 39/30 + 5/(-10). Let 2/5*a + 0 + 2/5*a**3 - w*a**2 = 0. What is a?
0, 1
Factor 0 - f + 7*f**3 - 10*f**3 - f**4 - 3*f**2 + 0.
-f*(f + 1)**3
Let s(t) be the third derivative of -t**7/525 - t**6/75 - t**5/75 + t**4/15 + t**3/5 - 12*t**2. Let s(k) = 0. Calculate k.
-3, -1, 1
Let g be (-1)/(-2) + 24/16. Let 7*u**g + 0*u**4 - u**5 + 4*u**5 - 4*u**2 - 3*u**3 - 3*u**4 = 0. What is u?
-1, 0, 1
Factor 14 - 6 - 7 + 0*p - p**2 - 2*p + 2*p**3.
(p - 1)*(p + 1)*(2*p - 1)
Let s(c) = -50*c**2 - 135*c - 5. Let r(f) = f**3 + 50*f**2 + 133*f + 4. Let d(l) = -5*r(l) - 4*s(l). Solve d(y) = 0.
-5, 0
Find s, given that 2*s**2 - 6*s - 41 + 41 = 0