 first derivative of g(r). Factor w(m).
2*(m + 1)**2/25
Let v be (-3)/(-2) + (-260)/8. Let x = v + 33. Solve -2/3*o**3 + 2*o**x + 0*o - 8/3 = 0 for o.
-1, 2
Factor -1/3*k**2 - 2*k - 1/3*k**4 + 4/3*k**3 + 0.
-k*(k - 3)*(k - 2)*(k + 1)/3
Let u(r) = r**3 - 4*r - 6. Let p(h) = -6*h**3 + h**2 + 24*h + 34. Let b = -31 - -25. Let n(o) = b*p(o) - 34*u(o). Determine l, given that n(l) = 0.
-1, 0, 4
Factor 8/3*f - 2/3*f**2 + 10/3.
-2*(f - 5)*(f + 1)/3
Let r(b) = -b**3 - 8*b**2 - 9*b - 8. Suppose -a + 3*a = -14. Let n be r(a). Determine j, given that -n - 2*j**2 + 4*j + 9*j - 5*j = 0.
1, 3
Let y(h) be the second derivative of -1/130*h**5 - 1 + 7*h - 1/13*h**3 - 2/39*h**4 + 0*h**2. Determine m, given that y(m) = 0.
-3, -1, 0
Let j(u) be the first derivative of 7*u**4/2 + 74*u**3/3 + 38*u**2 + 16*u - 429. Solve j(t) = 0 for t.
-4, -1, -2/7
Let b(q) = -441*q + 443. Let u be b(1). Solve 1/2 - 1/2*m**3 + 3/2*m**u - 3/2*m = 0 for m.
1
Let h = -2/4051 - -12163/20255. Factor 6/5*y**3 + 0*y + 0 - h*y**2 - 3/5*y**4.
-3*y**2*(y - 1)**2/5
Suppose 12 = 3*d + d. Let o = d - 0. Factor 5*k**2 - 2*k**4 - 3*k**3 + o*k - k**4 - 2*k**2.
-3*k*(k - 1)*(k + 1)**2
Let c(o) be the second derivative of 2*o - 1/3*o**6 + 0*o**5 - 5/42*o**7 + 5/6*o**4 + 5/6*o**3 + 0*o**2 + 0. Factor c(u).
-5*u*(u - 1)*(u + 1)**3
Let w be (146/(-365))/(-11*2/70). Solve 12/11*l - w + 2/11*l**2 = 0.
-7, 1
Let p = -13 + 11. Let x be 9/10 + p + (-16)/(-10). Factor -x*s**4 - 7/4*s + 1/2 - 1/2*s**3 + 1/4*s**5 + 2*s**2.
(s - 1)**4*(s + 2)/4
Let c(f) be the first derivative of 5*f**4 + 25*f**3/3 - 35*f**2/2 - 10*f + 44. Factor c(d).
5*(d - 1)*(d + 2)*(4*d + 1)
Suppose 3*x - 2*n = -10, 3 = x - 2*n + 17. Determine q so that -7/11*q**3 + 2/11*q**x - 8/11 + 12/11*q + 1/11*q**5 + 0*q**4 = 0.
-2, 1, 2
Suppose 12*b - 14*b + 14*b = -18*b. Factor 0*w**3 + b + 1/3*w**2 - 1/3*w**4 + 0*w.
-w**2*(w - 1)*(w + 1)/3
Suppose -80 = 4*u + 128. Let k(s) = -44*s**3 - 8*s - 26. Let b(l) = -5*l**3 - l - 3. Let w(y) = u*b(y) + 6*k(y). Solve w(i) = 0 for i.
-1, 0, 1
Let o(x) be the third derivative of x**9/20160 - x**8/6720 - x**7/420 + x**6/60 - 4*x**5/15 + 7*x**2. Let g(n) be the third derivative of o(n). Factor g(d).
3*(d - 2)*(d - 1)*(d + 2)
Factor -8 + 35 + 388*y**3 + 35*y - 403*y**3 - 70*y**2 + 23.
-5*(y - 1)*(y + 5)*(3*y + 2)
Let i(d) be the first derivative of -d**6/105 - d**5/35 + 2*d**3/21 + d**2/7 + 40*d - 34. Let t(b) be the first derivative of i(b). Factor t(h).
-2*(h - 1)*(h + 1)**3/7
Let c(w) be the second derivative of w**6/30 + w**5/4 + 2*w**4/3 + 2*w**3/3 + 4*w + 3. Suppose c(s) = 0. Calculate s.
-2, -1, 0
Let j = -100876/15 - -6726. Determine m, given that 0*m - j*m**4 + 0 - 2/15*m**5 - 2*m**3 - 6/5*m**2 = 0.
-3, -1, 0
Let y(b) be the second derivative of 1/4*b**3 + 0*b**2 + 0*b**4 + 0*b**6 + 0 + 26*b - 3/20*b**5 + 1/28*b**7. Find u, given that y(u) = 0.
-1, 0, 1
Suppose 5*c = -5*g + 5, 2*g + 16 = 48*c - 47*c. Let j be (-1)/(-5) + 57/15. Suppose 2/3*m + 8/3*m**j + 22/3*m**3 - 2/3 + c*m**2 = 0. What is m?
-1, 1/4
Let t(o) be the first derivative of o**4/8 + 2*o**3/3 + 3*o**2/4 - 82. Let t(b) = 0. What is b?
-3, -1, 0
Suppose -3 = 2*x - 17. Factor 14*m**2 - 2*m**2 + 65*m**2 - 12*m - 147*m**3 + x*m**2.
-3*m*(7*m - 2)**2
Suppose -60 = -9*u - 42. Let b(d) be the first derivative of 2/21*d**3 + 2 - 8/7*d + 0*d**u. Let b(f) = 0. Calculate f.
-2, 2
Let k(v) = -v**5 - v**4 - v**3 - 1. Let a(p) = -8*p**5 - 172*p**4 - 2356*p**3 - 10976*p**2 - 4. Let t(w) = a(w) - 4*k(w). Solve t(x) = 0.
-14, 0
Let a(v) be the second derivative of -2/15*v**6 + 3/5*v**5 + 0 - 4*v + 0*v**2 - 2/3*v**4 + 0*v**3. Solve a(z) = 0.
0, 1, 2
Let n = 13 - 9. Let a be (-1 + -14)*((-2)/(-3))/(-2). Let 15*k**3 - 5 + n + 0 - 3*k**2 + 9*k**4 - a - 15*k = 0. What is k?
-1, -2/3, 1
Let q(a) be the third derivative of a**8/3024 - 13*a**7/630 + a**6/3 + 20*a**5/27 + 249*a**2. Factor q(t).
t**2*(t - 20)**2*(t + 1)/9
Let l(r) be the third derivative of r**6/48 - 5*r**5/24 + 5*r**4/16 + 15*r**3/4 + 54*r**2 + 2. Factor l(i).
5*(i - 3)**2*(i + 1)/2
Let k(s) be the third derivative of 0*s + 1/588*s**8 + 22*s**2 - 2/105*s**5 + 0*s**6 + 0*s**3 - 1/42*s**4 + 0 + 4/735*s**7. Factor k(l).
4*l*(l - 1)*(l + 1)**3/7
Suppose -15*n = -20*n + 65. Factor 9*t**2 + 1 + 4*t**2 - n*t**2 + 2*t + t**2.
(t + 1)**2
Let q be 0 + 2120/2090 + 85/95 + -1. Factor -8/11*a + 0 - q*a**2.
-2*a*(5*a + 4)/11
Let v(b) be the second derivative of 0 + 1/18*b**3 - 1/72*b**4 + 14*b - 1/12*b**2. Solve v(a) = 0.
1
Let z = -1/33 + 15/11. Let g(n) = n**3 + n**2 - 20*n - 33. Let b be g(-2). Factor -y - 1/3*y**b + z*y**2 + 0.
-y*(y - 3)*(y - 1)/3
Suppose -2*o - 5*o + 21 = 0. Suppose 4*j - 2*w - w - 19 = 0, 4*j = 4*w + 24. Factor -6*n + 3*n + o*n**2 - j - 5.
3*(n - 2)*(n + 1)
Let t = -133 - -142. Let v be 104/117*t/6. Solve -2/3*r - 2/3*r**2 + v = 0 for r.
-2, 1
Find d, given that 13852815/8*d - 465/8*d**4 + 14415/4*d**3 - 446865/4*d**2 - 85887453/8 + 3/8*d**5 = 0.
31
Let z(r) = 6*r**2 + 7*r + 8. Let c(w) = 2 - 6*w + 0 - 5*w**2 - 9. Let o be (-1)/(-1) + 1 + 2 + 2. Let h(q) = o*z(q) + 7*c(q). Suppose h(t) = 0. Calculate t.
-1, 1
Let m(k) = -2*k**4 - 28*k**3 - 54*k**2 + 72*k + 6. Let t(g) = 2*g**4 + 26*g**3 + 52*g**2 - 72*g - 4. Let r(o) = -2*m(o) - 3*t(o). Factor r(l).
-2*l*(l - 1)*(l + 6)**2
Let j(w) be the first derivative of -2/3*w**3 + 13 - 4*w + 3*w**2. Solve j(m) = 0 for m.
1, 2
Let h(a) = 6*a**2 + 14. Let i(z) = 4*z**2 + z + 12. Let o(f) = 3*h(f) - 4*i(f). Factor o(k).
2*(k - 3)*(k + 1)
Let i = 776/3 - 258. Suppose -4*z + 2*t + 14 = 0, -z + 14 = t - 5*t. Determine w so that -i*w**z - 1/3*w**3 + 2/3 + 1/3*w = 0.
-2, -1, 1
Let j(o) be the first derivative of -o**5/12 + 5*o**4/12 - 5*o**3/6 - 9*o**2/2 + 5. Let g(u) be the second derivative of j(u). Factor g(s).
-5*(s - 1)**2
Let t(a) be the first derivative of 0*a + 1 - 1/3*a**2 + 0*a**3 + 1/6*a**4. Suppose t(r) = 0. Calculate r.
-1, 0, 1
Factor -10/3*m**2 + 10 + 25/3*m - 5/3*m**3.
-5*(m - 2)*(m + 1)*(m + 3)/3
Let c(t) be the third derivative of t**8/560 - 3*t**7/175 - 2*t**6/25 - t**5/50 + 3*t**4/8 + 4*t**3/5 - 2*t**2 + 182*t. Find m, given that c(m) = 0.
-1, 1, 8
Suppose 110 = -0*r + 5*r. Suppose -5*k - 1 - 4 = -3*a, -4*a + r = k. Factor u**k - 8*u - 4*u**2 - 8 + u**2.
-2*(u + 2)**2
Suppose -5*f + 6*f + w = 21, -3*f + 61 = w. Suppose -2*p = -12*p + f. Factor 16/3*l - 4/3*l**3 + 2/3*l**4 - 2*l**p - 8/3.
2*(l - 2)*(l - 1)**2*(l + 2)/3
Let j(k) = -2*k**3 + 3*k**2 - 4*k + 3. Let y be j(2). Let f = 11 + y. Factor 0*t + 2*t**f - t**4 - 2*t + 2*t - 1.
-(t - 1)**2*(t + 1)**2
Let o(c) be the second derivative of -c**5/20 + 7*c**4 - 392*c**3 + 10976*c**2 + 3*c - 16. Solve o(k) = 0.
28
Solve 0 - 40/7*h**2 - h**3 + 1/7*h**4 - 44/7*h = 0 for h.
-2, 0, 11
Let g(a) = -5*a**3 - 58*a**2 + 8*a + 49. Let l(k) = -19*k**3 - 230*k**2 + 30*k + 197. Let r(s) = 22*g(s) - 6*l(s). Factor r(i).
4*(i - 1)*(i + 1)*(i + 26)
Find s, given that -9/2*s**2 - 24*s**3 + 21*s**5 + 0 + 9/2*s**4 + 3*s = 0.
-1, -1/2, 0, 2/7, 1
Let s(d) be the second derivative of -3*d**5/20 - d**4 - 5*d**3/2 - 3*d**2 + 346*d. Factor s(g).
-3*(g + 1)**2*(g + 2)
Let q(f) be the third derivative of -f**5/15 - f**4/3 + 2*f**3 + 39*f**2 - f. Solve q(t) = 0.
-3, 1
Suppose -1766*n - 51 = -1783*n. Determine w so that -4/7*w**4 - 8/7 - 20/7*w**n - 4*w - 36/7*w**2 = 0.
-2, -1
Let m(j) be the third derivative of -32/105*j**7 + 0*j + 0*j**3 + 0 + 2/3*j**4 - 22*j**2 + 1/10*j**6 + 16/15*j**5 - 1/12*j**8. Solve m(g) = 0.
-2, -1, -2/7, 0, 1
Let s(y) be the first derivative of -y**5/10 + 3*y**4/4 + 7*y**3/6 + 27. Find m, given that s(m) = 0.
-1, 0, 7
Let g(r) be the second derivative of -r**4/6 + 98*r**3/3 - 2401*r**2 - 515*r. Let g(w) = 0. Calculate w.
49
Let u = -4 + 8. Let g(i) be the first derivative of 0*i**3 - 5*i - 2*i - i + u*i**3 - 2*i**2 - 2. Find d such that g(d) = 0.
-2/3, 1
Factor -14*m + 26 - 8*m**2 + 3*m**2 + 94 - 11*m.
-5*(m - 3)*(m + 8)
Let y(u) = -2*u + 38. Let n be y(0). Let j = n - 151/4. Factor 1/2*k**2 + j*k - 1/2 - 1/4*k**3.
-(k - 2)*(k - 1)*(k + 1)/4
Let m(v) be the second derivative of 5*v**4/24 + 11*v**3/12 - 3*v**2 - 7*v + 15. Factor m(g).
(g + 3)*(5*g - 4)/2
Let l be 2 + 0 - 0/(-1). Let t = -23194 - -23198. Determine i so that -4/3*i**t + 2/3*i**5 + 0*i**3 + 0*i**l + 0 + 0*i = 0.
0, 2
Let w(y) be