5, 2/3, 4
Let d be 1/(-2) - (-10)/4. Let v(s) be the first derivative of 1/3*s**3 + s**d - 1 + s. Determine l so that v(l) = 0.
-1
Let y be 18/5 - (-4)/10. Let c be y/(-16) - 63/(-12). Factor 2/9 - 22/9*u**4 - 4/3*u**2 - 2/3*u**c + 2/9*u - 28/9*u**3.
-2*(u + 1)**4*(3*u - 1)/9
Let r = -806 + 169261/210. Let w(i) be the third derivative of 0*i + r*i**5 + 0*i**3 + 0 - 3*i**2 + 1/42*i**4. Factor w(q).
2*q*(q + 2)/7
Let k(r) be the first derivative of r**3/24 + r**2/2 + 2*r + 51. Determine n, given that k(n) = 0.
-4
Let x = -1/1196 - -5383/1196. Factor -6*z + 2*z**3 - x - 1/2*z**4 + z**2.
-(z - 3)**2*(z + 1)**2/2
Let i(o) = -o**5 - o**3 + o**2 + 1. Let y(k) = 6*k**5 - 8*k**4 + 10*k**3 + 4*k**2 - 8*k - 4. Let h(d) = 4*i(d) + y(d). Factor h(n).
2*n*(n - 2)**2*(n - 1)*(n + 1)
Let v(h) = -h**3 + 4*h**2 + h - 2. Let a be v(4). Factor 0*s**3 - 4*s**2 - 2*s**3 + 2*s**2 + 4*s**a.
-2*s**2*(s - 1)
Let z(s) = -3*s + 21. Let c be z(7). Factor 2/9*g + c - 2/9*g**2 + 2/9*g**4 - 2/9*g**3.
2*g*(g - 1)**2*(g + 1)/9
Let m(i) be the second derivative of 3*i - 1/189*i**7 + 1/54*i**4 + 0*i**2 - 1/30*i**5 + 0 + 0*i**3 + 1/45*i**6. Factor m(r).
-2*r**2*(r - 1)**3/9
Let o = -23/3 + 25/3. Factor 0*s**3 + 2/3 - 4/3*s**2 + o*s**4 + 0*s.
2*(s - 1)**2*(s + 1)**2/3
Suppose 0 = -18*i + 14*i. Factor i + 0*g + 1/2*g**2 - 1/2*g**3 - 1/2*g**4 + 1/2*g**5.
g**2*(g - 1)**2*(g + 1)/2
Let i(b) be the third derivative of -b**5/540 - b**4/108 - b**3/54 + 6*b**2. Determine c, given that i(c) = 0.
-1
Let z(j) = j**2 - 8*j - 15. Let y = -11 - -12. Let b(u) = u**2 + 1. Let h(f) = y*z(f) + 3*b(f). Factor h(q).
4*(q - 3)*(q + 1)
Suppose 0*p = 5*k + p - 296, -5*k - 2*p + 292 = 0. Let a be (-9)/(-2)*10/k. Solve -3/4*b**2 - a*b**3 + 0 + 0*b = 0.
-1, 0
Let b(i) be the second derivative of -1/60*i**5 + 0 - 5/18*i**3 + 1/9*i**4 - i + 1/3*i**2. Find g such that b(g) = 0.
1, 2
Suppose -11*s - 6*s + 68 = 0. Let g(k) be the first derivative of 2/11*k**3 - 3 - 4/11*k**2 - 8/11*k - 2/55*k**5 + 1/11*k**s. Let g(z) = 0. What is z?
-1, 2
Let x be 23/(-8) + 0 + 3/1. Let s(v) be the second derivative of -2*v + 1/16*v**4 - x*v**3 - 1/80*v**5 + 1/8*v**2 + 0. Find y such that s(y) = 0.
1
Let x = 27/25 - -19/75. Factor 5/3*l + 1/3*l**2 + x.
(l + 1)*(l + 4)/3
Solve -3/8*c**2 - 3/4*c + 0 = 0.
-2, 0
Let p = -3 - -5. Suppose -p*l + 12 = 2*s, 4*s = s - l + 10. Let -1/3 - 1/3*n**s - 2/3*n = 0. Calculate n.
-1
Let g(p) = -2*p - 2. Let h be g(-2). Let v = 5 + 0. Factor -4/5*d**4 + 0 + 0*d**h + 2/5*d**v + 2/5*d**3 + 0*d.
2*d**3*(d - 1)**2/5
Let a(d) = d**2 - 2*d - 1. Let o be a(3). Let s = 1 - -2. Factor -k**2 + 2*k**o + 4*k**3 - s*k**3.
k**2*(k + 1)
Let t(v) be the first derivative of v**3/9 + v**2/6 - 2*v/3 - 10. Solve t(q) = 0.
-2, 1
Factor 4/9*j - 4/9*j**3 + 2/9*j**4 - 2/9*j**2 + 0.
2*j*(j - 2)*(j - 1)*(j + 1)/9
Let k(s) be the third derivative of 1/30*s**5 - 4*s**2 + 1/240*s**6 + 0*s**3 + 0 + 1/12*s**4 + 0*s. Factor k(i).
i*(i + 2)**2/2
Let l be 22/99 + (-2 - 102/(-27)). Let 12/5*y**l - 3/5*y**3 - 3*y + 6/5 = 0. Calculate y.
1, 2
Let j(v) = -6*v**3 + 10*v**2 + 24*v + 6. Let b(f) = -12*f**3 + 20*f**2 + 49*f + 12. Let i = 2 + -4. Let w(n) = i*b(n) + 5*j(n). Factor w(z).
-2*(z - 3)*(z + 1)*(3*z + 1)
Solve -9*a**2 + a**3 + a**3 + 0*a + a**3 + 6*a = 0 for a.
0, 1, 2
Let q(p) = p**3 + 11*p**2 - 13*p + 6. Let i be q(-12). Let w be i/(-30) - (-26)/10. Suppose 0 - 1/2*o**w + 1/2*o = 0. Calculate o.
0, 1
Let n = -3/1244 + 35111/115692. Let u = n + 1/31. Suppose 0*b**2 - 1/3*b**5 + u*b**4 + 0*b**3 + 0 + 0*b = 0. What is b?
0, 1
Let u(v) be the third derivative of -v**8/35280 + v**7/2940 - v**6/630 + v**5/6 + 8*v**2. Let k(y) be the third derivative of u(y). Factor k(z).
-4*(z - 2)*(z - 1)/7
Let 6/7*y**3 - 6/7*y - 2/7*y**4 + 4/7 - 2/7*y**2 = 0. Calculate y.
-1, 1, 2
Factor 9*l**2 - 11*l**2 - 4*l**3 - 2*l**2 + 4*l**4 + 4*l.
4*l*(l - 1)**2*(l + 1)
Suppose 0*u + 4*z = 3*u - 4, -z = 4*u + 20. Let f be (u/3)/(5/(-15)). Factor 0 - 2*s**5 + 0*s**2 + 2/3*s**3 + 0*s - 4/3*s**f.
-2*s**3*(s + 1)*(3*s - 1)/3
Let w = 91 + -89. Let z(g) be the second derivative of 1/2*g**4 + 0 - g**3 + g**w - g - 1/10*g**5. Suppose z(p) = 0. Calculate p.
1
Let j(a) = -a**2 - 6*a + 4. Let h be j(-6). Let b = h + 4. Let 6*n + b + 18*n**2 + 3*n + 15*n = 0. What is n?
-2/3
Let c be (-10)/((1 - 2)*2). Let g = c - 4. Let l(x) = x + 1. Let v(r) = r**2 - 1. Let i(b) = g*v(b) + 3*l(b). Solve i(h) = 0 for h.
-2, -1
Let u = 135 - 3106/23. Let b = u + 49/69. Let 4/3*o**2 - 4/3 - b*o**3 + 2/3*o = 0. Calculate o.
-1, 1, 2
Let b = 38 + -60. Let g = 25 + b. Determine m, given that 15/2*m**4 + 9/2*m**2 + 0 - 9*m**g - 9/4*m**5 - 3/4*m = 0.
0, 1/3, 1
Let k(z) = 4*z**2 + 9*z + 7. Let u be k(-1). Let -2/3*i**5 - 2/3*i**3 + 0*i**u - 4/3*i**4 + 0*i + 0 = 0. What is i?
-1, 0
Find k such that 2/9*k**2 + 2/9 - 4/9*k = 0.
1
Factor -3/2*i - 1/6*i**3 + 0 + i**2.
-i*(i - 3)**2/6
Suppose 3*n - 3 = 6. Let 0 + 4*d**n - 3*d**3 + 0 - d = 0. What is d?
-1, 0, 1
Let f = 950 - 945. Let -1/3*c**f - 5/3*c - 1/3 - 10/3*c**3 - 5/3*c**4 - 10/3*c**2 = 0. What is c?
-1
Factor 2/19*s**2 - 10/19*s + 8/19.
2*(s - 4)*(s - 1)/19
Let c be ((-2)/(-6)*0)/(2 - 4). Factor -2/13*l + 2/13*l**2 + c.
2*l*(l - 1)/13
Let j(k) be the second derivative of -1/2*k**2 - 1/30*k**6 - 2/3*k**3 + 2*k - 1/2*k**4 - 1/5*k**5 + 0. Let j(g) = 0. What is g?
-1
Let b = 0 - -6/7. Let 0 + 2/7*i + 6/7*i**2 + b*i**3 + 2/7*i**4 = 0. Calculate i.
-1, 0
Suppose 3 = w + 3*g - 4, -4*w = -2*g + 14. Let p be (w/(-4))/(4/16). Suppose 2/3*u + 2/9 + 2/3*u**p + 2/9*u**3 = 0. What is u?
-1
Let g(d) be the third derivative of 0 + 0*d + 2*d**2 + 1/24*d**3 + 1/240*d**6 - 1/80*d**5 + 0*d**4. Find l such that g(l) = 0.
-1/2, 1
Suppose 0 = -5*s + 9 - 9. Let s + 2/3*k**3 + 2*k - 8/3*k**2 = 0. What is k?
0, 1, 3
Let j(b) be the third derivative of -1/45*b**5 + 0*b**3 + 0 + 1/60*b**6 - 5*b**2 + 0*b**4 + 0*b - 1/315*b**7. Solve j(u) = 0.
0, 1, 2
Factor 18*d**2 - 7*d**2 - 5*d**2 - 5*d**2.
d**2
Let y(n) = 3*n**3 + n**2 - 2*n. Let x be y(1). Let o(s) be the first derivative of -3*s**x + 3 + 0*s**3 + 1/2*s**4 + 4*s. Find h such that o(h) = 0.
-2, 1
Let w(m) be the second derivative of -1/45*m**6 + 0 - 1/6*m**4 - 1/9*m**3 - 1/10*m**5 + 2*m + 0*m**2. Factor w(n).
-2*n*(n + 1)**3/3
Let c(p) be the second derivative of -p**7/49 - p**6/105 + 9*p**5/70 - p**4/14 - 2*p**3/21 + 12*p. Suppose c(l) = 0. What is l?
-2, -1/3, 0, 1
Let n(p) be the second derivative of -p**7/98 + p**6/70 + 3*p**5/140 - p**4/28 - 3*p. Factor n(a).
-3*a**2*(a - 1)**2*(a + 1)/7
Let b(y) be the first derivative of -y**5/5 + 2*y**4/3 - 10*y - 2. Let d(q) be the first derivative of b(q). Determine v, given that d(v) = 0.
0, 2
Let n(d) = d + 10. Let k be n(-8). Let t(o) be the second derivative of -1/30*o**5 + 2/9*o**4 + 0 - k*o - 5/9*o**3 + 2/3*o**2. Find u such that t(u) = 0.
1, 2
Factor -6/7 - 4/7*m + 2/7*m**2.
2*(m - 3)*(m + 1)/7
Let g(w) be the second derivative of -4*w**6/15 - 3*w**5/5 + 8*w**4/3 - 2*w**3 + 52*w. Suppose g(z) = 0. Calculate z.
-3, 0, 1/2, 1
Let d be (-1)/(-36) + (12/(-27))/(-2). Factor d*m - 1/4*m**3 + 1/4 - 1/4*m**2.
-(m - 1)*(m + 1)**2/4
Let n(k) = k**5 - k**4 - k**3 + k**2 - k - 1. Let m(g) = g**4 - g**3 - g**2 - 1. Let x(d) = -3*m(d) + 3*n(d). Let x(f) = 0. What is f?
-1, 0, 1
Suppose w - 5*u = 2*w - 28, -8 = -2*w + 2*u. Let k be (-36)/w*1/(-1). Solve -7/2*a**3 + a**4 + 1/2 - 5/2*a + k*a**2 = 0 for a.
1/2, 1
Let z(b) be the second derivative of b**4/66 + b**3/33 - 2*b**2/11 + 5*b. Factor z(k).
2*(k - 1)*(k + 2)/11
Let p(q) = 8*q**3 + 16*q**2 + 4*q - 20. Let c(y) = 9*y**3 + 17*y**2 + 5*y - 21. Let a(x) = -4*c(x) + 5*p(x). Suppose a(z) = 0. What is z?
-2, 1
Let j be 452/10 + (-9)/15. Let c = 45 - j. Find k, given that c*k**3 + 6/5*k**2 - 8/5 + 0*k = 0.
-2, 1
Let k be -1*(-3)/1 + 0. Let g = -63/2 - -90. Factor g*s**2 - 20*s - 81/2*s**k + 2.
-(s - 1)*(9*s - 2)**2/2
Let b(v) = v**3 - 10*v**2 - 9*v + 4. Let r be b(11). Factor -13*y**3 - 10*y - 8 + 15*y**3 + r*y - 10*y**2.
2*(y - 2)**2*(y - 1)
Find a such that a**2 + 7*a**2 + 24*a + 2*a**3 + 4*a**2 + 16 = 0.
-2
Let l(g) be the third derivative of g**10/75600 - g**9/10080 + g**8/3360 - g**7/2520 + g**5/20 - 6*g**2. Let r(x) be the third derivative of l(x). Factor r(j).
2*j*(j - 1)**3
Let l(r) be the first derivative of r**3/3 + 5*