x(c) be the first derivative of b(c). Factor x(f).
f**2*(f - 1)*(f + 1)
Let v(b) = -b**3 + 36*b**2 - 72*b + 53. Let o(j) = -18*j**2 - 9*j + 16*j - 27 + 29*j. Let m(x) = 5*o(x) + 3*v(x). Suppose m(g) = 0. Calculate g.
2
Let x be (-2 - (-61)/12) + -3. Let t(q) be the second derivative of -1/48*q**4 + q - 1/8*q**2 + 0 - x*q**3. Factor t(m).
-(m + 1)**2/4
Let h(p) be the third derivative of -p**8/336 - p**7/210 + p**6/120 + p**5/60 + 29*p**2. Suppose h(y) = 0. What is y?
-1, 0, 1
Let y be 143/26*(-2)/3. Let g = y - -13/3. Factor 0*j - g*j**2 + 0 + 4/3*j**3.
2*j**2*(2*j - 1)/3
Solve -2*o**2 + 3 + 0*o**2 + 3*o + o**2 - o = 0.
-1, 3
Let m be (-27)/(-54) + 1 + 10/4. Let j(w) be the second derivative of 3*w + 0*w**2 + 0 + 1/6*w**m + 0*w**3. Let j(a) = 0. Calculate a.
0
Let h(u) be the second derivative of -u**8/1680 + u**7/840 + u**3/6 + u. Let n(d) be the second derivative of h(d). Let n(a) = 0. Calculate a.
0, 1
Let u be ((-1)/(-2))/(6/(-36)). Let a = u - -5. Find x, given that -2*x**5 + 0*x**4 + 6*x - 4*x**2 - 4*x**3 + 6*x**4 + 0*x**4 - a = 0.
-1, 1
Let t = -1317 - -4027/3. Solve t*m + 8/3 + 361/3*m**3 + 254/3*m**2 + 224/3*m**4 + 49/3*m**5 = 0.
-2, -1, -2/7
Let z(n) be the first derivative of 0*n + 1/3*n**2 - 1/6*n**4 + 1/9*n**3 - 1/15*n**5 - 3. Factor z(g).
-g*(g - 1)*(g + 1)*(g + 2)/3
Suppose 5*i + 0 + 5 = 0. Let q be -3 - 40/(-12) - i. Factor 0*j**2 - q*j**3 + 0*j - 2*j**4 + 0.
-2*j**3*(3*j + 2)/3
Let h be (-6 - 63/(-33))/(6/(-4)). Find k such that -18/11*k**4 + h*k**3 + 2/11*k - 14/11*k**2 + 0 = 0.
0, 1/3, 1
Factor -1/6*g**2 + 0 + 1/6*g.
-g*(g - 1)/6
Let x be (-1)/(((-15)/12)/5*14). Factor -x + 4/7*a - 2/7*a**2.
-2*(a - 1)**2/7
Let d(u) be the third derivative of -u**5/12 - 5*u**4/8 + 64*u**2. Factor d(v).
-5*v*(v + 3)
Let j(z) be the first derivative of 1/12*z**4 - 1/3*z - 1/3*z**3 + 2 + 1/2*z**2. Let j(r) = 0. What is r?
1
Let l(f) be the second derivative of 5/2*f**5 + 8*f - 12*f**2 - 56/3*f**3 - 55/6*f**4 + 0. Factor l(i).
2*(i - 3)*(5*i + 2)**2
Let q be ((-28)/210)/(6/(-10)). Find f, given that -2/3*f**3 + 0 - q*f + 2/3*f**2 + 2/9*f**4 = 0.
0, 1
Let k = -1/53 + 55/106. Let y(u) be the first derivative of 1/10*u**5 - 1 - k*u**2 + 1/4*u**4 + 0*u**3 - 1/2*u. Let y(a) = 0. Calculate a.
-1, 1
Let m(f) = f - 1. Let g(j) = j**2 - 4*j + 3. Let t(y) = 3*g(y) + 6*m(y). Factor t(h).
3*(h - 1)**2
Let p(g) = g**2. Let o be p(2). Let m(r) be the second derivative of 0*r**2 + 2*r - 1/75*r**6 + 0*r**5 + 0 + 1/30*r**o + 0*r**3. Factor m(a).
-2*a**2*(a - 1)*(a + 1)/5
Let l(n) be the first derivative of n**9/4536 - n**8/1260 + n**6/270 - n**5/180 - n**3 - 3. Let k(g) be the third derivative of l(g). Factor k(q).
2*q*(q - 1)**3*(q + 1)/3
Let g(x) = -11*x**2 + 6*x - 8. Let s(r) = 12*r**2 - 7*r + 6. Let u(q) = 3*g(q) + 4*s(q). Factor u(l).
5*l*(3*l - 2)
Let s(r) = 8*r**2 - 8*r - 7. Let g(l) = l**2 - l - 1. Let t(w) = 28*g(w) - 4*s(w). What is d in t(d) = 0?
0, 1
Let x(s) be the first derivative of -s**5/25 + s**4/10 - s**3/15 - 7. Suppose x(i) = 0. What is i?
0, 1
Factor 2/7*z + 2/7 - 2/7*z**2 - 2/7*z**3.
-2*(z - 1)*(z + 1)**2/7
Let b = 24545/53361 - -2/5929. Let c = b - 1/63. Solve -c + 2/3*p - 2/9*p**2 = 0 for p.
1, 2
Let x(k) be the first derivative of -k**4/18 - k**3/9 + 8*k - 8. Let t(g) be the first derivative of x(g). Suppose t(r) = 0. What is r?
-1, 0
Let i be (-40)/16*2/(-1). Factor 2*h**4 - 9*h**2 - 4*h**3 + 2*h**4 + 4*h**i + 5*h**2.
4*h**2*(h - 1)*(h + 1)**2
Let g = 2 + -1. Let h = -4 + 6. Determine x so that -2 + h*x - g + 2*x**2 - 1 = 0.
-2, 1
Let k be (-62)/(-14) + 6/(-14). Let r = k + -5/2. Determine v so that 5/2*v**2 - v**5 - 3/2*v**4 + 5/2*v**3 - 1 - r*v = 0.
-2, -1, -1/2, 1
Let k(g) be the third derivative of 1/24*g**3 + 1/80*g**5 - 1/480*g**6 + 0*g + g**2 - 1/32*g**4 + 0. Solve k(v) = 0.
1
Let a(g) be the second derivative of -g**5/120 + g**4/48 - g**2 + 4*g. Let z(h) be the first derivative of a(h). Determine y, given that z(y) = 0.
0, 1
Factor 4/3*z**2 + 2/9 - 8/9*z**3 - 8/9*z + 2/9*z**4.
2*(z - 1)**4/9
Let f(b) be the first derivative of -4*b**5/5 - 4*b**4/3 - 4*b**3/9 + 2. What is w in f(w) = 0?
-1, -1/3, 0
Let a(m) be the first derivative of -m**5/5 - m**4/4 + 2*m**3/3 - 17. Factor a(y).
-y**2*(y - 1)*(y + 2)
Let z(y) = 3*y**2 + 2 - 4*y**2 + 2*y + 0*y**2 + 4*y. Let d be z(6). Factor 4/3*p**d - p - 1/3.
(p - 1)*(4*p + 1)/3
Let l(k) be the second derivative of -k**6/1440 - k**5/480 + k**4/48 - 2*k**3/3 + 3*k. Let b(a) be the second derivative of l(a). Suppose b(v) = 0. What is v?
-2, 1
Let r = 31 - 31. Suppose r + 4/3*i + 2/3*i**2 = 0. Calculate i.
-2, 0
Determine c, given that -60*c + 45*c**5 + 118*c**2 + 4 + 4*c**5 + 4 - 126*c**4 + 11*c**3 = 0.
-1, 2/7, 1, 2
Let b(p) be the second derivative of -p**2 + 0 + 1/150*p**5 - p + 1/15*p**3 - 1/30*p**4. Let a(r) be the first derivative of b(r). Find m such that a(m) = 0.
1
Factor 1/4*a + 1/4*a**3 + 0 - 1/2*a**2.
a*(a - 1)**2/4
Solve 2/11*u**4 - 2/11*u + 2/11*u**3 - 2/11*u**2 + 0 = 0 for u.
-1, 0, 1
Let c(q) be the first derivative of 1/4*q**2 - 5 + 1/12*q**3 - 3/4*q. Factor c(w).
(w - 1)*(w + 3)/4
Factor 2/9 - 2/3*k**4 - 2/3*k + 2/9*k**5 + 4/9*k**3 + 4/9*k**2.
2*(k - 1)**4*(k + 1)/9
Let w(k) be the second derivative of 1/18*k**4 - 2/27*k**3 + 0*k**2 + 3*k + 0 - 1/90*k**5. Factor w(g).
-2*g*(g - 2)*(g - 1)/9
Let y be -4*3*4/(-72). Factor 0*x**2 + 0 - 2/3*x**3 + y*x.
-2*x*(x - 1)*(x + 1)/3
Let y(f) be the second derivative of -3*f**7/8 + 9*f**6/10 - f**5/4 - 5*f**4/8 + f**3/8 + f**2/4 + 15*f. Let y(p) = 0. What is p?
-1/3, -2/7, 1/3, 1
Let l(k) = -k**2 + 2*k - 7. Let p(d) = -6*d**2 + 10*d - 36. Let y(f) = 16*l(f) - 3*p(f). Suppose y(g) = 0. What is g?
-2, 1
Let k(r) be the second derivative of r**6/90 - r**5/30 - r**4/36 + r**3/9 + 30*r. Factor k(x).
x*(x - 2)*(x - 1)*(x + 1)/3
Let l be 0 - (-2 - (-118)/60). Let j(b) be the second derivative of 0 + 0*b**2 - l*b**4 + b - 1/15*b**3. Factor j(s).
-2*s*(s + 1)/5
Let o(n) be the third derivative of -n**5/12 + 25*n**4/24 - 5*n**2. Factor o(f).
-5*f*(f - 5)
Let j = -12 - -17. Suppose -3*q + 24 = 5*r, j*r - 3*q + 2 = 8. Let -4*g + 3*g**4 - 2*g**2 - 1 + r*g**3 + g - g**3 + g**5 = 0. What is g?
-1, 1
Let w = 3 + -1. Solve h + 4 + 2*h**w - 7*h + 0*h**2 + 0*h**2 = 0 for h.
1, 2
Let g(c) be the first derivative of 3/5*c**5 - 3/2*c**2 - 9/4*c**4 + 3*c**3 - 3 + 0*c. Solve g(b) = 0.
0, 1
Factor 0*a - 8/5*a**2 + 4/5*a**3 + 0 + 4/5*a**4.
4*a**2*(a - 1)*(a + 2)/5
Let m(v) be the first derivative of -v**3/6 + 2*v**2 - 8*v + 2. Factor m(j).
-(j - 4)**2/2
Let h = -33 + 33. Let p(d) be the second derivative of 0*d**5 + 1/10*d**4 + 2/15*d**3 + h - 1/75*d**6 - 3*d + 0*d**2. Factor p(w).
-2*w*(w - 2)*(w + 1)**2/5
Let m(o) = 2*o**2 - 7*o + 23. Let p = 11 + -15. Let a(y) = -2*y**2 + 8*y - 22. Let x(s) = p*m(s) - 5*a(s). Find l such that x(l) = 0.
3
Let x = 4 - 1. Suppose -x*p - 2*p = -10. Let 1/4*m**p + 1/2*m + 1/4 = 0. Calculate m.
-1
Let r(q) be the third derivative of q**5/60 - q**4/24 - q**3/3 + 6*q**2. Factor r(h).
(h - 2)*(h + 1)
Factor 0 - 24/5*m**3 - 3*m**2 - 2/5*m - 11/5*m**4.
-m*(m + 1)**2*(11*m + 2)/5
Let r(i) = 2852*i**4 - 836*i**3 - 916*i**2 - 172*i - 28. Let f(q) = 317*q**4 - 93*q**3 - 102*q**2 - 19*q - 3. Let t(x) = -28*f(x) + 3*r(x). Factor t(k).
-4*k*(4*k + 1)**2*(5*k - 4)
Suppose 0*k = z - k - 11, -5*k = 5. Factor 3*d**4 + 7*d**5 + 4 - z*d**5 - 4.
-3*d**4*(d - 1)
Let v(f) be the first derivative of 5 + 2*f**6 + 9/5*f**5 - 15/4*f**4 + 0*f - 3*f**3 + 3/2*f**2. What is h in v(h) = 0?
-1, 0, 1/4, 1
Find u, given that -5/2*u**2 + 0*u**3 + 5/2*u**4 + 0 + 0*u = 0.
-1, 0, 1
Let o(n) be the first derivative of 7*n**6/6 + 2*n**5/5 - 10. Factor o(p).
p**4*(7*p + 2)
Let r be 10/(-60) + (-2)/(-8). Let t(w) be the first derivative of -1/16*w**4 - 1/20*w**5 + 0*w + 1/8*w**2 + r*w**3 + 3. Solve t(v) = 0.
-1, 0, 1
Let v(u) = u**4 - u**3 - u**2 + u - 6. Let g(h) = 1. Let o(w) = 6*g(w) + v(w). Factor o(r).
r*(r - 1)**2*(r + 1)
Let 3/4*w**2 + 0 - 9/4*w - 3/4*w**4 + 9/4*w**3 = 0. What is w?
-1, 0, 1, 3
Let t(v) be the third derivative of -v**5/20 + v**4/8 + v**3 - 2*v**2. Suppose t(n) = 0. What is n?
-1, 2
Suppose -15 = -5*q + 5*a, -2*q + 4*a = -6*q + 12. Factor 0*d**3 - d - 2*d**q + 2*d**2 + d.
-2*d**2*(d - 1)
Let z(k) be the first derivative of 1/36*k**4 + 0*k**2 + 1 + 1