p**3 - 108 - 756*p.
-4*(7*p + 3)**3
Let k(v) be the first derivative of v**6/6 - 3*v**5/5 - 5*v**4/4 + v**3 + 2*v**2 - 41. Factor k(m).
m*(m - 4)*(m - 1)*(m + 1)**2
Suppose 105/2*u**3 - 51*u - 27/2*u**4 - 3/2*u**5 - 45/2*u**2 + 36 = 0. Calculate u.
-12, -1, 1, 2
Let b be (3/5)/(4/10). Let p = -14430 + 14432. Factor -b*k + 1/2*k**p + 0.
k*(k - 3)/2
Let l be ((-14 - -5) + 3)*(-10)/12. Let y(r) be the second derivative of 0*r**2 + 7*r + 3/4*r**3 + 0 + 3/40*r**l + 1/2*r**4. Factor y(u).
3*u*(u + 1)*(u + 3)/2
Let c be (-2028)/(-169) - 5*2. Let h(x) be the first derivative of 0*x + 2/21*x**3 - 1/7*x**c + 9. Solve h(q) = 0 for q.
0, 1
Let o(u) be the second derivative of u**6/30 + 113*u**5/20 - 19*u**4/2 + 2*u + 5. Factor o(y).
y**2*(y - 1)*(y + 114)
Let q(m) be the first derivative of m**5/140 - m**4/21 - m**3/42 + 2*m**2/7 - 13*m + 17. Let d(a) be the first derivative of q(a). Factor d(b).
(b - 4)*(b - 1)*(b + 1)/7
Let 2/5*a**2 - 22/5*a + 4 = 0. Calculate a.
1, 10
Let i(o) = 16*o - 14*o**4 + 14 - 40*o - 14*o**3 + 34*o**3 - 10*o**5. Let k(z) = 2*z**5 + 3*z**4 - 4*z**3 + 5*z - 3. Let s(t) = 3*i(t) + 14*k(t). Factor s(g).
-2*g*(g - 1)**2*(g + 1)**2
Let d(w) = -7*w**2 + 30*w - 14. Let k(n) = 7*n**2 - 30*n + 13. Suppose 19 = i + 5*o, -3*o = 2*i + 1 - 4. Let b(f) = i*k(f) - 5*d(f). Factor b(u).
-(u - 4)*(7*u - 2)
Let j(n) be the third derivative of n**6/900 + n**5/300 - n**4/30 + n**3 + 21*n**2. Let a(w) be the first derivative of j(w). Let a(c) = 0. What is c?
-2, 1
What is j in -12 + 4 - 3*j**3 + 3*j**2 + j**2 + j**4 - 6*j**2 + 6*j + 6*j = 0?
-2, 1, 2
Let w(b) be the second derivative of 3*b**5/100 + 3*b**4/10 - 27*b**3/10 + 228*b. Factor w(f).
3*f*(f - 3)*(f + 9)/5
Let h(y) = 9*y**5 + 9*y**4 + 21*y**3 + 21*y + 21. Let d = -42 - -63. Let q(w) = -w**5 - w**4 - 2*w**3 - 2*w - 2. Let j(m) = d*q(m) + 2*h(m). Factor j(o).
-3*o**4*(o + 1)
Solve -30 + 5/6*a**3 + 95/6*a**2 + 40/3*a = 0.
-18, -2, 1
Let m = -457 + 457. Let j(f) be the third derivative of 1/360*f**6 + m*f + 3*f**2 + 4/9*f**3 + 0 - 1/90*f**5 - 1/18*f**4. Suppose j(r) = 0. Calculate r.
-2, 2
What is k in -1/3*k**3 - 5/3*k - 2*k**2 + 0 = 0?
-5, -1, 0
Factor -410 + 35 - 5*z**2 + 2944*z - 3069*z + z**3.
(z - 15)*(z + 5)**2
Let m(l) = l**2 - 12*l + 12. Let g be (-10)/(-5) + -1 + (2 - 1). Let b(z) = -3*z**2 + 48*z - 48. Let k(f) = g*b(f) + 9*m(f). Factor k(w).
3*(w - 2)**2
Let q(s) be the second derivative of 1/7*s**4 + 4/7*s**2 + 0 + 6/7*s**3 - 4/35*s**5 - 6*s. Factor q(h).
-4*(h - 2)*(h + 1)*(4*h + 1)/7
Let w(p) be the first derivative of 5*p**4/4 - 80*p**3/3 - 175*p**2/2 - 90*p + 24. Factor w(f).
5*(f - 18)*(f + 1)**2
Let t(u) be the third derivative of u**7/350 + 3*u**6/100 + 11*u**5/100 + 3*u**4/20 + u**2 + 49. Factor t(d).
3*d*(d + 1)*(d + 2)*(d + 3)/5
Let d(b) be the third derivative of 0*b + 1/250*b**6 + 0 - 3/250*b**5 - 1/2625*b**7 + 1/75*b**4 + 0*b**3 + 17*b**2. Factor d(m).
-2*m*(m - 4)*(m - 1)**2/25
Let i(p) be the second derivative of p**5/35 - p**4/3 - 16*p**3/21 + 13*p. Let i(s) = 0. Calculate s.
-1, 0, 8
Suppose -4*j + 3*j = 6*j. Let m(d) be the second derivative of -d + j - 109/12*d**4 + 63/10*d**5 - 2*d**2 + 6*d**3 - 49/30*d**6. Factor m(o).
-(o - 1)**2*(7*o - 2)**2
Let u = -2/4159 + 8324/12477. Determine i, given that 0*i + u*i**5 - 4/3*i**4 + 2/3*i**3 + 0 + 0*i**2 = 0.
0, 1
Let j(t) be the first derivative of -45*t**4/4 - 91*t**3/3 - 27*t**2 - 8*t + 151. Factor j(f).
-(f + 1)*(5*f + 4)*(9*f + 2)
Let u be ((-14)/28)/((-1)/8). Suppose -5*z + 3*n + 6 = 1, 2*z + n = 13. Suppose u*d**z + 1 + d**3 - 4*d**4 - 2*d + d**3 - d**4 = 0. What is d?
-1, 1
Let g(o) be the third derivative of o**7/18900 - o**6/1350 + o**5/225 + 9*o**4/8 - 17*o**2. Let r(w) be the second derivative of g(w). Factor r(d).
2*(d - 2)**2/15
Let n be ((-2)/6)/((-143)/78 - (-2 + 1)). Let n*k**3 + 1/5*k**4 + 1/5*k**2 + 0 + 0*k = 0. Calculate k.
-1, 0
Let d(h) be the first derivative of -3*h**4/2 + h**3 - 3*h - 14. Let y(u) = 5*u**3 - 4*u**2 + 2. Let o(v) = -2*d(v) - 3*y(v). Find l, given that o(l) = 0.
0, 2
Let x = -9425/7 - -1347. Factor 2/7*s**4 + 8/7*s**3 + 0 + x*s + 10/7*s**2.
2*s*(s + 1)**2*(s + 2)/7
Let f(u) be the third derivative of -u**6/120 + 5*u**5/4 - 481*u**4/8 + 1369*u**3/6 + 296*u**2. Factor f(t).
-(t - 37)**2*(t - 1)
Factor 4/7*w**2 + 22500/7 - 600/7*w.
4*(w - 75)**2/7
Let n(l) be the third derivative of 1/24*l**5 + 1/252*l**7 + 5/144*l**4 + 16*l**2 + 0*l**3 + 0 + 1/48*l**6 + 0*l. Factor n(r).
5*r*(r + 1)**3/6
Let m = 137901/100 - 1379. Let c(g) be the third derivative of 0*g - m*g**5 + 0*g**4 - 4*g**2 + 0 + 0*g**3. Let c(l) = 0. Calculate l.
0
Suppose 6 = -10*f + 16*f. Let d(g) = 1. Let s(j) = -128*j**5 + 416*j**4 - 504*j**3 + 270*j**2 - 54*j - 2. Let c(b) = f*s(b) + 2*d(b). Factor c(z).
-2*z*(z - 1)*(4*z - 3)**3
Let j(x) be the second derivative of x**7/147 - 4*x**6/105 + 2*x**5/35 - x + 13. Let j(v) = 0. What is v?
0, 2
Suppose 31*d + 892 - 985 = 0. Let 0*s - 4/7*s**d + 0 + 8/7*s**2 = 0. Calculate s.
0, 2
Suppose 0 = -2*h + 100 - 90, 0 = -2*p + 4*h - 16. Suppose -1/4*z**p - 9/4 - 3/2*z = 0. What is z?
-3
Let n(m) be the first derivative of 2*m**4/9 + 6*m**3 + 164*m**2/9 + 8*m - 279. Solve n(z) = 0 for z.
-18, -2, -1/4
Let d(f) be the third derivative of f**8/10080 + f**7/630 + 31*f**5/60 + 2*f**2. Let y(c) be the third derivative of d(c). Factor y(g).
2*g*(g + 4)
Let i(l) be the third derivative of l**8/1344 + l**7/420 + l**6/480 - 3*l**2 - 79. Suppose i(h) = 0. Calculate h.
-1, 0
Let z(g) = -12*g**2 - 14*g + 16. Let l = -26 - -16. Let s(p) = p**2 + p - 1. Let x(n) = l*s(n) - z(n). What is y in x(y) = 0?
-3, 1
Let n = -1/232 - -469/1160. Let u(k) be the first derivative of 3/25*k**5 - 1/10*k**6 - n*k**3 + 3/10*k**4 + 3/5*k - 5 - 3/10*k**2. Factor u(c).
-3*(c - 1)**3*(c + 1)**2/5
Let x(a) be the third derivative of a**8/336 - 4*a**7/525 - a**6/50 + 7*a**5/150 + 7*a**4/120 - a**3/5 + 2*a**2 - 110. Determine u, given that x(u) = 0.
-1, 3/5, 1, 2
Let p = 4848 - 4848. Factor p*u - 8/3 + 2/3*u**2.
2*(u - 2)*(u + 2)/3
Let u(m) be the first derivative of -m**6/2520 - m**5/140 - 9*m**3 + 40. Let p(h) be the third derivative of u(h). Let p(o) = 0. What is o?
-6, 0
Suppose -15 = 3*r + c + 4*c, -23 = 2*r - c. Let g be r/42 + 10/15. What is m in -g*m**3 - 3/7 - 9/7*m - 9/7*m**2 = 0?
-1
Suppose -10*s - 1404 = -4*s. Let j be 42/s - 1/(-3). Determine f so that 0 - 2/13*f + 0*f**2 + j*f**3 = 0.
-1, 0, 1
Suppose 5*z + 118 = 443. Let r = z + -63. Factor -2/7*u**3 + 4/7*u**r + 0*u + 0.
-2*u**2*(u - 2)/7
Factor -118*f**2 + 13924*f - 1643032/3 + 1/3*f**3.
(f - 118)**3/3
Suppose 5*b - 9 = 21. Suppose b = c + c - 4*y, -c - 5*y + 3 = 0. What is k in 0 + 0*k**c + 6/7*k**4 - 6/7*k**2 + 3/7*k - 3/7*k**5 = 0?
-1, 0, 1
Suppose 4*y = 11 + 37. Let p be (-2)/(-11) + 20/11. Factor 5*c**p + c**2 - y*c**2 - 3*c - 3*c**3.
-3*c*(c + 1)**2
Let g = 96/19 - 269/57. Let 0*l + 4*l**3 + 0 + 2*l**4 + 8/3*l**2 + g*l**5 = 0. What is l?
-2, 0
Find z, given that 243845*z - 4*z**2 - 243879*z + 35 + 3*z**2 = 0.
-35, 1
Determine p, given that -172*p + 82*p - 3*p**2 + 84*p + 3*p**4 + 6*p**3 = 0.
-2, -1, 0, 1
Let y(t) be the third derivative of t**9/45360 - t**8/3024 - t**7/630 - t**5/15 - t**4/12 + 2*t**2 - 2. Let u(m) be the third derivative of y(m). Factor u(h).
4*h*(h - 6)*(h + 1)/3
Determine s so that -24*s - 2*s**2 - s - 9*s - 40*s + 15 + 61 = 0.
-38, 1
Let x be (4 - 44/33) + (-2)/(-6). Let 7/3*a**2 + 0 - x*a**3 + 2/3*a = 0. Calculate a.
-2/9, 0, 1
Suppose 5*i + 79 - 74 = 0. Let m = i - -3/2. Factor 1/2*r**2 - m*r**3 + 0 + 0*r.
-r**2*(r - 1)/2
Let p(q) be the second derivative of 5*q**7/168 + 3*q**6/8 + 7*q**5/16 - 15*q**4/16 - 5*q**3/3 + q + 29. Let p(m) = 0. What is m?
-8, -1, 0, 1
Let q(l) be the second derivative of 0 + 1/18*l**4 - 4*l**2 - 25*l + 4/9*l**3. Let q(w) = 0. Calculate w.
-6, 2
Let t(o) = 9*o**5 + 84*o**4 + 108*o**3 + 54*o**2 - 9*o. Let u(l) = -7*l**5 - 85*l**4 - 109*l**3 - 55*l**2 + 10*l - 1. Let f(j) = 7*t(j) + 6*u(j). Factor f(y).
3*(y + 1)**4*(7*y - 2)
Let v(d) be the second derivative of d**6/120 - d**5/60 - 5*d**2 - 2*d. Let r(z) be the first derivative of v(z). Factor r(j).
j**2*(j - 1)
Let c = -486/25 + 496/25. Factor 0*j - c*j**3 + 0*j**4 + 2/5*j**5 + 0 + 0*j**2.
2*j**3*(j - 1)*(j + 1)/5
Suppose 0 = -5*l - 5*j + 61 + 39, 3*