 1/48*a**6 + 0*a + 1/1344*a**8 - 7*a**2 + 1/24*a**5. Find j, given that v(j) = 0.
-1
Let f = 1/1943 + 3881/9715. Suppose -6/5*z - f*z**2 + 0 = 0. What is z?
-3, 0
Let w = -49 - -42. Let h be 55/21 + (-1)/(w/(-2)). Let q**3 - h*q**5 + 0 - 16/3*q**2 + 16/3*q**4 + 4/3*q = 0. What is q?
-1, 0, 2/7, 1, 2
Let c = 7643/4 + -1907. Factor 3/4*g**3 + 27/4 + 9/4*g - c*g**2.
3*(g - 3)**2*(g + 1)/4
Let w = 3/1037 - -20713/9333. Determine s, given that -w*s - 50/9 - 2/9*s**2 = 0.
-5
Let z(o) be the second derivative of -5/36*o**4 + 0 + 2/3*o**2 + 1/90*o**6 - 1/126*o**7 - 2/9*o**3 + 13*o + 1/12*o**5. Let z(k) = 0. What is k?
-2, -1, 1, 2
Let z be 3/(6/(-8)) + 6. Let h(d) be the first derivative of -d**z + 0*d - d**4 + 1/5*d**5 + 5/3*d**3 + 2. Factor h(l).
l*(l - 2)*(l - 1)**2
Let j(l) be the first derivative of 4/3*l**3 + 0*l + 31 - 1/2*l**2. Solve j(c) = 0 for c.
0, 1/4
Let m = 139 + -134. Let k be (m/(-9))/(30/(-36)). Factor 2/3*a**2 - 5/3*a + k.
(a - 2)*(2*a - 1)/3
Let v(x) = -x**3 - 2*x**2 - 8*x - 4. Let f(z) = 8 - 10*z - 7*z**2 + 2*z**3 + 26*z + 12*z**2. Let g(p) = -3*f(p) - 5*v(p). Factor g(i).
-(i + 1)*(i + 2)**2
Let a(y) be the third derivative of -2/3*y**3 + 0 + 13/36*y**4 - 6*y + 1/18*y**5 - 2*y**2. Factor a(o).
2*(o + 3)*(5*o - 2)/3
Suppose -5*n + 3*n - 8 = 3*c, -n + 6 = -c. Let v(w) = -w**2 - 4*w - 3. Let d be v(-3). Determine i, given that -4*i - n*i**2 + d*i**2 - 2*i**2 = 0.
-1, 0
Suppose 4*s = 7*u - 4*u - 3, 21 = 3*u + 2*s. Let l(r) be the first derivative of -1/2*r**6 - 4 + 0*r**3 + 0*r**2 + 1/5*r**u + 1/2*r**4 + 0*r. Factor l(o).
-o**3*(o - 1)*(3*o + 2)
Let b(u) be the first derivative of -u**3/12 - 39*u**2/4 - 1521*u/4 - 152. Solve b(c) = 0.
-39
Let g(q) = -4*q - 60. Let d be g(-20). Suppose 2*v - 6*a = -a + d, -4*v - 2*a - 8 = 0. Factor 1/2*m**3 + v*m**2 - 1/2*m + 0.
m*(m - 1)*(m + 1)/2
Let q(u) = u**3 - u**2 - u - 10. Let z be q(3). Factor -z*c**2 + 4 - 24*c + c**2 + 24.
-4*(c - 1)*(c + 7)
Suppose -14 = 2*f - 22. Solve -3*z**5 - 30*z**3 - z - f*z - 20*z**4 - 20*z**2 + 0*z - 2*z**5 = 0 for z.
-1, 0
Let w(b) = 28*b**3 + 64*b**2 + 44*b - 4. Let g(n) = -n**4 - 28*n**3 - 64*n**2 - 45*n + 3. Let o(v) = 4*g(v) + 3*w(v). Factor o(x).
-4*x*(x + 2)**2*(x + 3)
Suppose 0 = -3*t - u - 112, -2*t - 71 = -3*u - 0*u. Let v = t - -37. Let 3*d**2 + v + 3/2*d**3 + 0*d = 0. What is d?
-2, 0
Solve 26*p**3 + 8104*p**2 - 16928 + 342*p**3 - 368*p + 258*p**2 + 2*p**4 + 8564*p**2 = 0 for p.
-92, -1, 1
Let i(n) = 4*n**3 + n**2 - 2. Let k be i(1). Suppose -g + 12 = 3*g - 4*b, -g - k = b. Solve g*q**2 + 0*q + 6/7*q**4 + 3/7*q**3 + 0 + 3/7*q**5 = 0 for q.
-1, 0
Let w(p) be the third derivative of -p**7/105 - 7*p**6/10 + 179*p**5/30 - 19*p**4 + 92*p**3/3 + 37*p**2 + 2*p. Factor w(i).
-2*(i - 2)*(i - 1)**2*(i + 46)
Let m = -298 + 300. Let t(o) be the first derivative of 6*o + o**3 + 9/2*o**m - 8. Factor t(a).
3*(a + 1)*(a + 2)
Let l(t) be the third derivative of -5*t**6/228 + 4*t**5/57 - 4*t**4/57 - 211*t**2. Factor l(n).
-2*n*(5*n - 4)**2/19
Let t(p) be the second derivative of p**7/1260 - p**6/45 + 4*p**5/15 + 2*p**4/3 - 2*p. Let b(i) be the third derivative of t(i). Factor b(m).
2*(m - 4)**2
Let g(o) be the third derivative of -o**8/672 - o**7/42 - o**6/16 + o**5/12 + o**4/3 - 45*o**2. What is y in g(y) = 0?
-8, -2, -1, 0, 1
Let f be (-6 - (-1 - 2))/(15/(-20)). Let b(k) be the third derivative of 0*k - 11/10*k**f + 2/5*k**3 + 0 + 121/100*k**5 - 3*k**2. Suppose b(y) = 0. Calculate y.
2/11
Let b(l) = -6*l - 34. Let q be b(-6). Solve -6*u - 3/2*u**q - 6 = 0 for u.
-2
Let t(c) be the second derivative of c**7/1260 + c**6/720 - c**5/360 - c**4/144 + 4*c**2 + 9*c. Let v(u) be the first derivative of t(u). Factor v(i).
i*(i - 1)*(i + 1)**2/6
Find a such that 50*a - 102*a**3 - 4*a**4 + 22*a**3 + 4*a**2 + 30*a + 0*a**2 = 0.
-20, -1, 0, 1
Let c = 520/2981 - -2/271. Let w be 2/17 + ((-282)/374 - -1). Solve 0 - w*m + c*m**2 = 0.
0, 2
Let l(g) be the first derivative of g**6/2 - 9*g**5/5 - 15*g**4/4 + 27*g**3 - 48*g**2 + 36*g + 109. Let l(z) = 0. What is z?
-3, 1, 2
Let n(r) be the third derivative of 0*r - 6*r**2 + 3/20*r**5 - 1/12*r**4 + 0*r**3 + 0 + 11/120*r**6. Solve n(y) = 0 for y.
-1, 0, 2/11
Let v(b) be the first derivative of 5*b**3 - 8 + 1/3*b**5 - 25/12*b**4 - 35/6*b**2 + 10/3*b. Let v(l) = 0. What is l?
1, 2
Let z(t) = 3*t**2 + 7*t - 13. Let u(h) = h**2 + 4*h - 7. Let v be -2 + (7 - 3 - 17). Let f(l) = v*u(l) + 6*z(l). Solve f(g) = 0.
3
Factor -192/7*n - 80/7*n**2 + 256/7 + 12/7*n**3 + 4/7*n**4.
4*(n - 4)*(n - 1)*(n + 4)**2/7
Let p be 4/(-15)*(-15)/10. Let c = -27/20 + 7/4. Solve 4/5 - p*o**2 + c*o = 0.
-1, 2
Let b(a) be the third derivative of -a**7/420 + a**6/240 + a**5/30 - a**4/12 - 623*a**2. Factor b(v).
-v*(v - 2)*(v - 1)*(v + 2)/2
Determine i, given that 3*i**2 + 4*i**3 + 3*i**4 + 0*i**3 - 6*i**4 - 18*i + 4*i**4 - 2*i**4 = 0.
-2, 0, 3
Let a(h) be the second derivative of -h**6/39 + 23*h**5/390 - h**4/26 + 11*h**2/2 - 9*h. Let x(v) be the first derivative of a(v). Solve x(z) = 0 for z.
0, 2/5, 3/4
Suppose 5*h + 2*v = 15, 6 = 2*h + 3*v - 8*v. Let b(a) = 2*a**2 + a + 3. Let f(u) = 2*u**2 - u + 1. Let n(q) = h*f(q) - b(q). Factor n(s).
4*s*(s - 1)
Let f = 2061 - 20607/10. Let x(g) be the second derivative of 12/5*g**2 - 3/20*g**5 - 1/50*g**6 - 12*g - f*g**4 + 2/5*g**3 + 0. What is v in x(v) = 0?
-2, 1
Let y(c) be the second derivative of c**4/132 - 4*c**3/33 - 10*c**2/11 + 2*c + 219. Determine o, given that y(o) = 0.
-2, 10
Factor 3176/7*v**2 + 15488/7 - 2112*v + 24*v**3 + 2/7*v**4.
2*(v - 2)**2*(v + 44)**2/7
Let a(q) be the second derivative of -1/3*q**6 + 10*q + 25/21*q**7 - 12*q**2 - 80/3*q**3 - 179/6*q**4 - 141/10*q**5 + 0. Solve a(v) = 0 for v.
-1, -2/5, 3
Let o(t) be the first derivative of -t**6/3 + 54*t**5/5 - 49*t**4 + 284*t**3/3 - 93*t**2 + 46*t - 484. Factor o(u).
-2*(u - 23)*(u - 1)**4
Let v = -5 - -11. Let l = v - 3. Determine n so that l*n - 3*n + 3*n**2 = 0.
0
Let c be (((-1352)/65)/26)/((-6)/5). Factor 4/3*w + 0 + c*w**3 - 2*w**2.
2*w*(w - 2)*(w - 1)/3
Let b = -11703 - -58551/5. Factor 64/5*s - b*s**3 - 16/5*s**2 - 11/5*s**4 + 0 - 1/5*s**5.
-s*(s - 1)*(s + 4)**3/5
Let a(s) = s**4 + 8*s**3 + 11*s**2 + 4*s + 1. Suppose 4*u - 10 = -u. Let f(g) = 0 + g**2 + 1 + g**4 - u*g**4. Let i(l) = -a(l) + f(l). Factor i(q).
-2*q*(q + 1)**2*(q + 2)
Suppose w + 72 = -3*w. Let d = -16 - w. Solve -d*x**4 + 5*x**3 + 16*x**2 + 4*x + 0*x - 5*x**4 - 18*x**4 = 0 for x.
-2/5, 0, 1
Factor -2*d**3 + 5*d**2 + 4 + 2*d - 7*d**2 - 2*d**2.
-2*(d - 1)*(d + 1)*(d + 2)
Suppose 2*b + 62 = -68. Let v be (-361)/b + (8 - 636/78). Let 3/5*w**2 + 18/5*w + v = 0. Calculate w.
-3
Let m(j) = j**5 + 2*j**4 + j**3 + j**2 + 1. Let b(y) = -3*y**5 - 9*y**4 - 18*y**3 - 18*y**2 - 6. Let s(c) = b(c) + 6*m(c). Find a such that s(a) = 0.
-2, -1, 0, 2
Let g = -7336 - -51355/7. Factor 18/7 - g*a**3 + 12/7*a**2 + 33/7*a.
-3*(a - 6)*(a + 1)**2/7
Let m(z) be the third derivative of -z**5/30 - 5*z**4/4 + 53*z**2. Factor m(x).
-2*x*(x + 15)
Let l = 2394 - 7175/3. Factor -l*c**3 + 2/3 + 16/3*c**2 - 11/3*c.
-(c - 1)**2*(7*c - 2)/3
Let l(v) = v**3 - 3*v**2 - 2*v + 4. Let g be l(3). Let j be g + (6 - (-1 - -1)). Let 2*n**j + 7*n**3 - n**3 - 4*n**3 = 0. What is n?
-1, 0
Let m be 770/33 + (-2)/(-3). Suppose -19*w = -m*w + 10. Factor 2/5 + 1/5*j - 1/5*j**w.
-(j - 2)*(j + 1)/5
Let q = 809/4 + -202. Let l(j) be the first derivative of -1/4*j - 1/12*j**3 + 2 + q*j**2. Factor l(g).
-(g - 1)**2/4
Let o be (-58)/(-87)*(-3)/(-4). Let y(v) be the first derivative of -2/5*v**5 + v**2 + 3 + 2/3*v**3 + 0*v - o*v**4. Find r, given that y(r) = 0.
-1, 0, 1
Let s(g) = g**3 + 1. Suppose 3*z + z - 8 = 0. Let i(a) = -2*a**4 + 6*a**3 - 10*a**2 + 4*a - 2. Let w(t) = z*s(t) + i(t). Solve w(m) = 0.
0, 1, 2
Let a(q) = q**2. Let x(v) = -69*v**3 - 23*v**2. Let r(i) = -5*a(i) - x(i). Factor r(h).
3*h**2*(23*h + 6)
Let s(b) be the third derivative of b**8/1008 + b**7/315 - b**6/120 - 2*b**5/45 - b**4/18 + 4*b**2 - 3. Factor s(a).
a*(a - 2)*(a + 1)**2*(a + 2)/3
Let d(s) be the second derivative of s**5/240 - s**4/8 - 13*s**3/24 + 22*s**2 - 2*s + 1. Let u(j) be the first derivative of d(j). Factor u(t).
(t - 13)*(t + 1)/4
Let g(y) be the first derivative of y**7/420 + y**6/180 - y**5/30 - 14*y**3/3 + 24. Let i(s) be the third derivative of g