et z be n(-133). Factor 6/7 - 9/7*l**2 + 3/7*l**4 + 3/7*l - 3/7*l**z.
3*(l - 2)*(l - 1)*(l + 1)**2/7
Let p(g) be the third derivative of -g**5/35 - 29*g**4/56 - 15*g**3/7 + 217*g**2. Factor p(r).
-3*(r + 6)*(4*r + 5)/7
Let d(b) be the second derivative of 0*b**3 + 17*b + 0*b**2 + 0 - 2/15*b**6 + 0*b**4 + 0*b**5. Factor d(y).
-4*y**4
Let l be -4*(-2)/24*18. Suppose -2*r = -s - 0 - 8, -l = r - 3*s. Factor r*q + 18*q**2 + 61 - 30*q - 52 - 3*q**4.
-3*(q - 1)**3*(q + 3)
Let b(h) be the third derivative of 26*h**2 + 0 + 0*h**3 + 1/672*h**8 + 1/80*h**6 + 0*h**5 + 1/105*h**7 + 0*h + 0*h**4. Let b(u) = 0. Calculate u.
-3, -1, 0
Let a(x) be the third derivative of 0*x + 3*x**2 + 0 + 5/36*x**4 - 1/90*x**5 + 2/3*x**3. Determine c, given that a(c) = 0.
-1, 6
Suppose 5*p = 4*c - 591, -21*c - p = -17*c - 621. Let i = -152 + c. What is n in -1/4*n**3 + 9/2 - 21/4*n + i*n**2 = 0?
2, 3
Let r be (-174)/(-87) + 2/(-3). Let g(p) be the first derivative of -9/2*p**2 - 3 - 2*p - r*p**3. Factor g(v).
-(v + 2)*(4*v + 1)
Let x(c) be the first derivative of -c**8/504 + 2*c**7/105 - c**6/15 + c**5/9 - c**4/12 - 3*c**2 + 6. Let v(h) be the second derivative of x(h). Factor v(z).
-2*z*(z - 3)*(z - 1)**3/3
Let k(b) = 3*b**3 + 101*b**2 - 2*b + 4. Let y(z) = 9*z**3 + 304*z**2 - 7*z + 14. Let r(q) = 7*k(q) - 2*y(q). Solve r(c) = 0 for c.
-33, 0
Let m(t) be the second derivative of 4*t**4/3 + 50*t**3/3 - 42*t**2 + 8*t - 12. Factor m(j).
4*(j + 7)*(4*j - 3)
Let x(t) be the first derivative of t**6/2 - 3*t**5 + 9*t**4/2 + 335. Factor x(s).
3*s**3*(s - 3)*(s - 2)
Let m be (((-5358)/(-133))/(-47))/((-10)/7). Factor -6/5*j - 3/5*j**2 - m.
-3*(j + 1)**2/5
Let g(j) = 2*j**2 - j - 2. Let u be g(2). Let v = u + 0. Factor 15*f**3 - v*f**2 + 0*f**2 - 6*f + f**2 - 6*f**4.
-3*f*(f - 2)*(f - 1)*(2*f + 1)
Let d(y) be the second derivative of 0*y**2 + 2/15*y**6 + 0 + 2/3*y**3 + y**4 + 3/5*y**5 - 9*y. Let d(u) = 0. What is u?
-1, 0
Let j(t) be the third derivative of -t**8/144 - 17*t**7/210 + 7*t**6/18 + 4*t**5/3 - 56*t**4/9 - 8*t**3 + 13*t**2. What is d in j(d) = 0?
-9, -2, -2/7, 2
Let f(p) be the third derivative of p**5/30 - 19*p**4/108 + 10*p**3/27 - 397*p**2. Find q, given that f(q) = 0.
1, 10/9
Let u(q) be the first derivative of -15 - 3/2*q + 1/2*q**3 + 3/8*q**2 - 3/16*q**4. Suppose u(t) = 0. What is t?
-1, 1, 2
Let k = 1094 - 4375/4. Let i be (-2)/(-24) - 6/(-36). Factor 0*u - 1/4*u**4 + 0 + 1/4*u**2 + i*u**5 - k*u**3.
u**2*(u - 1)**2*(u + 1)/4
Let h = 14547 + -14547. What is p in 12/5*p**3 + 0*p - 8/5*p**2 + h - 4/5*p**4 = 0?
0, 1, 2
Let u(h) = h + 4. Let k be u(0). Let -3*x**2 + 12*x**3 - 3*x**2 - k*x**4 - 3*x**2 + x**2 = 0. What is x?
0, 1, 2
Let s(f) be the third derivative of f**5/210 + f**4/3 + 28*f**3/3 + 62*f**2 - 2. Factor s(b).
2*(b + 14)**2/7
Let h = -654 - -654. Let l(i) be the second derivative of 0 + 1/50*i**5 + 1/30*i**4 + 0*i**2 - 12*i + h*i**3. Solve l(x) = 0 for x.
-1, 0
Suppose -10952/3 + 296/3*x - 2/3*x**2 = 0. Calculate x.
74
Factor -2/7*l + 2/7*l**3 + 0*l**2 + 0.
2*l*(l - 1)*(l + 1)/7
Let u(c) be the third derivative of 17*c**6/120 + 8*c**5/15 - c**4/6 - 12*c**2 + 7*c. Solve u(f) = 0 for f.
-2, 0, 2/17
Let j = 2983 + -2981. Find r, given that -1/5*r**2 - j*r - 5 = 0.
-5
Let u be ((-19)/(-38))/(2/(-18)*(-8 + 6)). Suppose -3*n**2 + 3*n**4 - 3/2*n**3 - 3/4*n**5 + u*n + 0 = 0. What is n?
-1, 0, 1, 3
Let z(c) = 50*c**2 + 146*c - 34. Let x(v) = 17*v**2 + 49*v - 11. Let u be (3 + -2)/(3/42). Let g(k) = u*x(k) - 5*z(k). Let g(w) = 0. What is w?
-4, 1/3
Factor -2/3*d**3 - 188/3 - 64*d**2 - 126*d.
-2*(d + 1)**2*(d + 94)/3
Determine o so that 11*o - 25*o**2 - 4*o + 5*o**4 - 15*o**3 + 8*o + 65 - 45 = 0.
-1, 1, 4
Find k such that 0 + 0*k - 14/11*k**2 + 2/11*k**4 - 12/11*k**3 = 0.
-1, 0, 7
Let -879/2*s**2 + 7203/2 - 21315/2*s - 9/2*s**3 = 0. Calculate s.
-49, 1/3
Factor 31*z - 34*z + 16*z**2 - 21 + 3*z**3 + 5*z**2.
3*(z - 1)*(z + 1)*(z + 7)
Let i = -51 + 63. Factor -10*b - 5*b - i - 23*b**2 + 9*b**2 + 11*b**2.
-3*(b + 1)*(b + 4)
Let i(m) be the second derivative of -6*m**2 - 1 + 0*m**5 - 2*m**4 + 2/15*m**6 - 24*m + 16/3*m**3. Factor i(c).
4*(c - 1)**3*(c + 3)
Let f(h) be the second derivative of 1/4*h**4 - 1/60*h**5 + 2/3*h**2 + 20*h + 0 - 11/18*h**3 - 1/90*h**6. Factor f(o).
-(o - 1)**3*(o + 4)/3
Suppose 4*s + 68 = 2*f, -7*f + 3*f - 3*s + 169 = 0. Determine b so that -5*b**5 + 10*b**5 - 30*b**4 + f*b**3 + 6 + 14 + 10*b**2 + 0*b**4 - 45*b = 0.
-1, 1, 4
Let h(d) = -d**2 - d. Let r(y) = -18*y**2 - 36*y + 2*y**2 + 20*y. Let z(s) = -36*h(s) + 2*r(s). Suppose z(i) = 0. Calculate i.
-1, 0
Suppose -2750*j = -2716*j - 68. Factor -2/3*f**j + 0*f + 0 + 4/3*f**3 - 2/3*f**4.
-2*f**2*(f - 1)**2/3
Let m = -1 - 1. Let v(h) = h**4 - h**3 - 3*h**2 + 3*h. Let t(o) = 3*o**2 - 3*o. Let g(r) = m*t(r) - 3*v(r). Suppose g(x) = 0. Calculate x.
-1, 0, 1
Let k(g) = 2*g**2 + 3*g - 11. Let x be k(-4). Factor 3 - 7*i**2 - 3*i - 3*i**5 + 15*i**3 + 3*i**4 + i**2 - x*i**3.
-3*(i - 1)**3*(i + 1)**2
Let v(a) = -2*a**2 + 18*a + 103. Let g be v(19). Let l = 279 + g. Suppose -1/4*j**l + 0 - 3/4*j = 0. What is j?
-3, 0
Let q(o) be the first derivative of 5*o**3/3 - 15*o**2/2 - 200*o - 46. Factor q(d).
5*(d - 8)*(d + 5)
Let l(p) be the first derivative of p**4/18 - p**3/3 + 2*p**2/3 + 4*p - 1. Let d(x) be the first derivative of l(x). Factor d(a).
2*(a - 2)*(a - 1)/3
Let u(g) be the third derivative of -g**6/600 + g**5/30 - 17*g**4/120 + 4*g**3/15 - 73*g**2. Factor u(m).
-(m - 8)*(m - 1)**2/5
Let l = 144320 + -37523257/260. Let u = 2/65 - l. Factor -3/4*q**2 + 0 - u*q**3 - 1/2*q.
-q*(q + 1)*(q + 2)/4
Let k(j) be the third derivative of 0 + 1/120*j**5 + 0*j + j**2 + 0*j**4 + 0*j**3. Let k(o) = 0. What is o?
0
Factor 1669*n**2 - 4*n**3 - 37 - 1709*n**2 + 208*n - 187.
-4*(n - 2)**2*(n + 14)
Let u = -97455/7 - -13923. Factor 2/7*o**3 + 4/7*o**2 - u*o + 0.
2*o*(o - 1)*(o + 3)/7
Let u(x) = -x**3 - 24*x**2 - x - 27. Let v be u(-24). Let i be 10*4/32 - (v - -4). Suppose -1/8*y**4 - 9/8 - 1/2*y**3 + 3/2*y + i*y**2 = 0. Calculate y.
-3, 1
Determine g so that 342/5 + 3/5*g**2 - 123/5*g = 0.
3, 38
Let u(y) be the second derivative of y**6/50 + 4*y**5/25 - 29*y**4/20 + 52*y**3/15 - 18*y**2/5 - 414*y. Find b such that u(b) = 0.
-9, 2/3, 1, 2
Let -8 + 22*h - 15 - 3*h**2 - 4 + 6 + 2*h**2 = 0. What is h?
1, 21
Let w = 134011/19 + -7053. Factor 0 + 10/19*o**2 + w*o.
2*o*(5*o + 2)/19
Let s(d) = -2*d**3 + 28*d**2 + 36*d - 88. Let h be s(15). Find l, given that 2/5*l**h + 0*l + 2/5*l**5 - 3/5*l**3 - 3/5*l**4 + 0 = 0.
-1, 0, 1/2, 2
Let n(q) = -4*q**4 + q**3 + 8*q**2 + 18*q. Let m(v) = v**4 - 2*v**3 - 2*v. Let u(g) = -12*m(g) - 4*n(g). Factor u(a).
4*a*(a - 2)*(a + 1)*(a + 6)
Let h(c) be the second derivative of -c**8/2520 + c**7/1260 + c**6/270 - 7*c**3/2 + 19*c. Let y(u) be the second derivative of h(u). Let y(n) = 0. Calculate n.
-1, 0, 2
Let x = -45 + 81. Factor 4*a**3 + a**2 - x*a + 7*a**2 + 4*a**2 + 20.
4*(a - 1)**2*(a + 5)
Let l be -2 - -14 - 3250/273. Let l + 0*a - 2/21*a**2 = 0. What is a?
-1, 1
Let s(q) be the third derivative of -1/336*q**8 - 1/105*q**7 - 19*q**2 + 0 + 0*q + 0*q**3 + 1/30*q**5 + 1/120*q**6 + 0*q**4. Suppose s(d) = 0. What is d?
-2, -1, 0, 1
Suppose -21*q - 11 - 10 = 0. Let n be (q - -2)/(-4 + 76/16). Factor -2/3*a**2 - n*a - 2/3.
-2*(a + 1)**2/3
Let k(i) = 18*i - 481. Let a be k(27). Factor 324/5*r**a + 0 - 128/5*r**3 + 0*r - 16/5*r**2 - 36*r**4.
4*r**2*(r - 1)*(9*r + 2)**2/5
Let c(g) = -3*g**5 + 6*g**4 - 12*g**3 + 3*g**2 + 3*g - 3. Let y(u) = 3*u**5 - 7*u**4 + 11*u**3 - 3*u**2 - 2*u + 2. Let o(l) = 2*c(l) + 3*y(l). Factor o(x).
3*x**2*(x - 1)**3
Let f(u) be the third derivative of u**9/90720 + u**8/20160 + 5*u**4/12 - u**3/3 - 36*u**2. Let v(n) be the second derivative of f(n). Factor v(j).
j**3*(j + 2)/6
Let f = 449 + -448. Let p(s) be the first derivative of 0*s - 8/3*s**3 + 0*s**2 - 10/3*s**6 - f + 32/5*s**5 - s**4. Find o such that p(o) = 0.
-2/5, 0, 1
Factor -2048/13 - 128/13*c - 2/13*c**2.
-2*(c + 32)**2/13
Let f(q) be the second derivative of -1/18*q**4 + 0 + 1/9*q**3 + 10*q + 1/120*q**5 + 0*q**2. Find l, given that f(l) = 0.
0, 2
Let u(y) = y**4 + y**3 + y + 1. Let x be (4 - 8 - -3)/((-2)/(-10)). Let p(b) = b**5 + 7*b**4 + 8*b**3 + 8*b + 8. Let c(a) = x*p(a) + 40*u(a). Factor c(h).
-5*h**4*(h - 1)
