 = 3*i - 9. What is l in 0 + 0*l + 0*l**f + 1/5*l**2 - q*l**4 = 0?
-1, 0, 1
Let m(n) be the third derivative of -n**7/630 + 2*n**6/45 - 8*n**5/15 + 9*n**4/8 - 13*n**2. Let p(b) be the second derivative of m(b). Factor p(d).
-4*(d - 4)**2
Let v = -1685 - -1685. Solve 0*b + 1/2*b**2 + v = 0.
0
Let r(f) = f**3 - 9*f**2 + 3*f - 12. Let h be r(9). Let v be (-52)/(-20) - (-6)/h. Factor -12*s - 9/2*s**2 + 27/2*s**v + 6.
3*(s + 1)*(3*s - 2)**2/2
Let a(r) be the second derivative of 0*r**2 + 0 + 1/21*r**7 - r - 1/5*r**5 + 0*r**4 + 1/3*r**3 + 0*r**6. Suppose a(u) = 0. Calculate u.
-1, 0, 1
Factor -3*n**4 - 3*n**2 + 20*n + n**2 + 37*n**2 + 0*n**4 - 2*n**4 + 10*n**3.
-5*n*(n - 4)*(n + 1)**2
Factor 4*z**2 - 13*z - 31*z + 8*z.
4*z*(z - 9)
Let w(l) = l**3 - 4*l**2 + 2*l + 2. Let p be w(3). Let f be (p/4)/((21/6)/(-7)). Solve f*r**2 + 0*r + 0 = 0.
0
Let c(v) = v**2 - 8*v - 9. Let j be c(10). Let l be j/24 + (-7)/21. Factor -1/8*x + l + 1/8*x**3 - 1/8*x**2.
(x - 1)**2*(x + 1)/8
Let z(i) be the first derivative of i**4/8 + 5*i**3/18 + i**2/12 - i/6 + 58. What is r in z(r) = 0?
-1, 1/3
Let g(o) = -20*o**3 + 28*o**2 - 32*o. Let x(a) = 13*a**3 - 19*a**2 + 21*a. Let s(c) = -5*g(c) - 8*x(c). Factor s(m).
-4*m*(m - 2)*(m - 1)
Let z be (-113600)/11088 - 4/(-22). Let s = 72/7 + z. Let 2/9*h**2 + s + 4/9*h = 0. Calculate h.
-1
Let w(r) be the first derivative of r**8/84 - r**7/24 + r**6/36 + r**5/24 - 8*r**3 - 2. Let v(s) be the third derivative of w(s). Factor v(j).
5*j*(j - 1)**2*(4*j + 1)
Suppose 122*z**3 - 45 + 2*z - 121*z**3 - 11*z**2 + 61*z - 8*z**2 = 0. Calculate z.
1, 3, 15
Let o(q) be the third derivative of -1/4*q**4 + 0 - 3/70*q**7 + 0*q - 1/5*q**6 - q**2 - 7/20*q**5 + 0*q**3. Find s, given that o(s) = 0.
-1, -2/3, 0
Determine v, given that -5/3*v**2 - v**3 + 0 + 0*v = 0.
-5/3, 0
Let k be 34/14 - 57/133. Let x(p) be the third derivative of 0 + 0*p + 1/3*p**3 + k*p**2 - 1/20*p**5 + 1/10*p**7 + 3/8*p**4 - 29/120*p**6. Factor x(q).
(q - 1)**2*(3*q + 1)*(7*q + 2)
Let o(k) = k**2 - 2*k - 5. Let s be o(4). Find p, given that p**3 + s*p + 4*p**3 - 3*p**2 - p**3 - 7*p**3 + 3 = 0.
-1, 1
Let i(k) be the first derivative of -5*k**4/4 + 135*k**3 + 825*k**2/2 + 415*k + 744. Suppose i(c) = 0. What is c?
-1, 83
Factor -47 - 36*y**2 + 28*y**3 + 4*y - 30*y + 63 - 22*y.
4*(y - 2)*(y + 1)*(7*y - 2)
Let v(r) be the first derivative of -2/9*r**3 - 12 - 1/9*r**4 - 8/9*r + 8/9*r**2 + 2/45*r**5. Factor v(p).
2*(p - 2)*(p - 1)**2*(p + 2)/9
Let r(w) = 38*w**2 + 152*w + 2. Let d be r(-4). What is b in 0 + 2/3*b**d - 1/3*b**3 - 1/3*b = 0?
0, 1
Let x = 83/120 - 1/40. Let r(d) = -d**3 + 12*d**2 - 8*d - 33. Let a be r(11). Factor 2/3 + a*w - x*w**2.
-2*(w - 1)*(w + 1)/3
Let k(c) be the second derivative of -31*c + 0 + 3/32*c**4 - 3/16*c**2 - 1/8*c**3. Factor k(r).
3*(r - 1)*(3*r + 1)/8
Let g(c) be the third derivative of c**9/20160 - c**8/280 + 4*c**7/35 - 32*c**6/15 + 9*c**5/20 - 2*c**2. Let q(a) be the third derivative of g(a). Factor q(b).
3*(b - 8)**3
Let u be (-13)/182*238/(-85). Suppose 0 - u*g**5 - 1/5*g**2 - 3/5*g**3 + 0*g - 3/5*g**4 = 0. What is g?
-1, 0
Let -92*z**2 + 4*z + 4 + 96*z**2 - 12 = 0. What is z?
-2, 1
Let r be -2*(-1 + 2) - -1 - (-6 - -5). Factor -4/9*n**2 + r - 2/9*n**3 + 0*n.
-2*n**2*(n + 2)/9
Suppose 9*c - 4 = 7*c - 2*n, -3*n + 18 = 5*c. Let p(u) be the second derivative of 5/6*u**2 + 0 + c*u - 5/9*u**3 + 5/36*u**4. Factor p(r).
5*(r - 1)**2/3
Find g, given that 2*g**2 + 13*g**2 - 10*g**2 - 2*g**2 + 3*g**4 - 6*g**3 = 0.
0, 1
Let v(i) = -i**3 + i**2. Let k(s) = 16*s**3 - 46*s**2 + 154*s - 196. Let t(m) = -k(m) - 14*v(m). Factor t(o).
-2*(o - 7)**2*(o - 2)
Suppose 3*i = -67 - 176. Let s be (-76 - i)*((-2)/(-1) + -1). Factor 4*w - s*w**2 - 4/5.
-(5*w - 2)**2/5
Let a(s) be the second derivative of -2*s**6/105 + 6*s**5/35 - 3*s**4/7 + 8*s**3/21 - 293*s. Factor a(z).
-4*z*(z - 4)*(z - 1)**2/7
Let i(z) be the second derivative of 5*z**6/39 - 42*z**5/13 + 512*z**4/39 - 16*z**3 + 112*z**2/13 + 74*z + 2. Find m such that i(m) = 0.
2/5, 2, 14
Let s(i) be the third derivative of -1/60*i**6 + 0*i + 0*i**3 + 0 + 1/6*i**4 - 1/30*i**5 - 11*i**2. Suppose s(w) = 0. Calculate w.
-2, 0, 1
Let a(g) = -8*g**3 - 24*g**2 + 44*g + 50. Let k(b) = -8*b**3 - 25*b**2 + 40*b + 51. Let z(t) = -6*a(t) + 4*k(t). Factor z(w).
4*(w - 2)*(w + 4)*(4*w + 3)
Let q(o) be the first derivative of -7 - 20/9*o**2 + 5/2*o**4 + 0*o**5 - 16/9*o - o**6 + 20/27*o**3. Determine n so that q(n) = 0.
-2/3, 1
Let z be 6*(-4)/(-8) - -6. Let k(a) = 2*a**4 + 6*a**3 + 4*a**2. Let y(l) = 5*l**4 + 13*l**3 + 9*l**2. Let c(g) = z*k(g) - 4*y(g). Factor c(j).
-2*j**3*(j - 1)
Suppose 0 = 2*y - d + 4 - 2, 4*y - 4*d = -4. Let f(x) = 10*x**3 + 10*x**2 - 10*x - 16. Let z(o) = -o**3 + o**2 + o. Let c(k) = y*f(k) - 6*z(k). Factor c(s).
-4*(s - 1)*(s + 1)*(s + 4)
Let b(j) be the second derivative of -5*j**7/168 - 5*j**6/24 + 5*j**5/16 + 75*j**4/16 - 135*j**2/2 - 449*j. Factor b(y).
-5*(y - 2)**2*(y + 3)**3/4
Let a(i) be the third derivative of -50*i**2 + 0*i**3 + 0 - 1/90*i**5 - 1/108*i**6 + 0*i + 1/54*i**4. Let a(k) = 0. What is k?
-1, 0, 2/5
Let j(r) = 4*r**2 - 40. Let z(h) = -4*h**2 + 41. Let n = 2 + 3. Let w(v) = n*j(v) + 4*z(v). Factor w(a).
4*(a - 3)*(a + 3)
Suppose -7/6*l**3 - 13/6*l - 5/2*l**2 - 2/3 - 1/6*l**4 = 0. Calculate l.
-4, -1
Factor -5/2*r**3 - 325/2*r - 35*r**2 - 250.
-5*(r + 4)*(r + 5)**2/2
Let h = -1 - -17. What is g in 0*g**3 - h*g - 4*g**2 + 24*g**3 - 94 + 90 = 0?
-1/2, -1/3, 1
Let s(z) be the third derivative of -z**5/330 + z**4/11 - 35*z**3/33 + z**2 - 342. Solve s(n) = 0.
5, 7
Let h(i) be the first derivative of -16 - 3/5*i**5 + 0*i**3 + 0*i**2 + 0*i**4 + 0*i. Factor h(v).
-3*v**4
Suppose 3*b - 52 = -5*q + 2*b, b = -3*q + 32. Suppose -12*v + 4 = -q*v. Solve 0*n**2 - 12 + 3 - 6*n + 0*n**v - n**2 = 0.
-3
Let n(c) = 7*c**3 + c**2 - 26*c + 36. Let y(v) = 2*v**3 + 2*v**2 - v. Let d(r) = -n(r) + 2*y(r). Solve d(w) = 0 for w.
-3, 2
Let p be -1 - (2/(-6) + (-49)/6). Solve p*c**3 - 3/2*c**5 + 3/2*c**4 - 6 - 12*c - 3/2*c**2 = 0 for c.
-1, 2
Let t = 261 + -256. Let r(o) be the third derivative of 1/12*o**4 - 7*o**2 + 0*o + 1/60*o**t - 1/2*o**3 + 0. Suppose r(c) = 0. What is c?
-3, 1
Suppose 0 = 126313*z - 126317*z + 8. Factor -75/2 + 5*r - 1/6*r**z.
-(r - 15)**2/6
Factor -19/2 - 37/4*d + 1/4*d**2.
(d - 38)*(d + 1)/4
Let k(o) be the third derivative of 1/3*o**3 + 28*o**2 + 0*o + 0 + 1/72*o**6 + 11/90*o**5 + 23/72*o**4. Suppose k(f) = 0. What is f?
-3, -1, -2/5
Let f(j) be the first derivative of -6 + 1/2*j**2 + 2/15*j**3 + 2/5*j. Suppose f(l) = 0. What is l?
-2, -1/2
Let f(t) be the third derivative of -t**7/2415 - 13*t**6/345 + 53*t**5/690 - 45*t**2 - 2. Factor f(w).
-2*w**2*(w - 1)*(w + 53)/23
Let h(o) be the third derivative of o**6/60 + 11*o**5/5 + 363*o**4/4 + 32*o**2. Determine y so that h(y) = 0.
-33, 0
Suppose 56*f = 58*f - 6. Let u(w) be the second derivative of -24/25*w**5 - w - 1/15*w**f - 64/75*w**6 + 0 - 2/5*w**4 + 0*w**2. Factor u(h).
-2*h*(4*h + 1)**3/5
Solve 84/5 + 1/5*h**2 - 17*h = 0.
1, 84
Suppose 2*g + 33 = 6*g + 5*i, i = 5. What is a in -a + 1 + 1/4*a**g = 0?
2
Let c(u) be the first derivative of -u**4/15 - 2*u**3/15 + 21*u + 16. Let s(h) be the first derivative of c(h). Let s(q) = 0. Calculate q.
-1, 0
Let v(l) be the second derivative of -l**7/21 + l**6/5 + 21*l**5/5 + 49*l**4/3 + 29*l**3 + 27*l**2 - 77*l + 2. Factor v(s).
-2*(s - 9)*(s + 1)**3*(s + 3)
Let h(t) be the second derivative of -t**4/24 + 65*t**3/6 - 4225*t**2/4 - t + 59. Determine k so that h(k) = 0.
65
Suppose -13*v + 20*v = 0. Suppose -2 - 2 = 2*c, a - 3*c - 6 = v. Solve a*d**2 - 1/2*d + 1/2*d**3 + 0 = 0 for d.
-1, 0, 1
Let n be 3/(-1 - (2 + (0 - 4))). Let 3*u - 3*u + 3*u**n = 0. Calculate u.
0
Let s = 295/9 - 1171/36. Let 54 + 27*x + s*x**3 + 9/2*x**2 = 0. Calculate x.
-6
Determine a so that 0 - 22/9*a**2 + 16/9*a**3 + 2/3*a = 0.
0, 3/8, 1
Let n(z) be the second derivative of 0 + 5/6*z**4 - 16*z + 0*z**3 - 1/15*z**6 + 0*z**5 - 4*z**2. Suppose n(d) = 0. Calculate d.
-2, -1, 1, 2
Let f be (1/(-3))/(15/(-180)). Solve 0 + 4/9*l**f - 8/9*l**3 - 4/3*l**2 + 0*l = 0.
-1, 0, 3
Let v be ((-33)/(-12))/(17/(-748)). Let h = v - -124. Solve -1/3*i**4 + 0 - 4/3*i**2 + 0*i + 4/3*i**h = 0 for i.
0, 2
Factor 17*f**3 + 100 + 85*f + f**5 + 41*f**3 - 13