40 + s**4/6 - 25*s. Let z(g) be the third derivative of m(g). Factor z(w).
w**2*(w - 2)*(w + 1)/4
Let n(r) be the third derivative of 0 - 1/336*r**7 - 1/2688*r**8 - 1/96*r**4 - 7/480*r**5 + 0*r + 0*r**3 - 3/320*r**6 - 2*r**2. Factor n(d).
-d*(d + 1)**3*(d + 2)/8
Factor -2*m**3 + 203/3*m**2 + 34/3*m + 0.
-m*(m - 34)*(6*m + 1)/3
Factor -1/6*u**2 - 7/6 + 4/3*u.
-(u - 7)*(u - 1)/6
Factor -24/11 + 280/11*q - 46/11*q**2.
-2*(q - 6)*(23*q - 2)/11
Let v = -25 - -18. Let m be (-1)/1 + (-21)/v. Factor 2*i**2 - 6*i**4 + 6*i**4 - m*i**4.
-2*i**2*(i - 1)*(i + 1)
Factor 10*h**2 - 1/2*h**3 - 50*h + 0.
-h*(h - 10)**2/2
Factor 5/6*j**2 - 25/6*j - 5.
5*(j - 6)*(j + 1)/6
Let r = -1023 - -1026. Let 0*y**r + 0*y - 5/3*y**2 + 4/3 + 1/3*y**4 = 0. Calculate y.
-2, -1, 1, 2
Let d(f) be the second derivative of 3/10*f**3 - 3/50*f**5 - 24*f + 1/20*f**4 + 0 + 0*f**2. Factor d(o).
-3*o*(o + 1)*(2*o - 3)/5
Let t(q) be the third derivative of q**8/336 - 2*q**7/21 - q**6/120 + q**5/3 - 85*q**2. Factor t(a).
a**2*(a - 20)*(a - 1)*(a + 1)
Let k(b) be the third derivative of 25*b**2 + 0*b**4 - 1/12*b**5 + 1/12*b**6 - 1/42*b**7 + 0*b**3 + 0 + 0*b. Determine x, given that k(x) = 0.
0, 1
Let g(i) be the first derivative of 1/2*i**2 - 1 + 3/2*i**4 + 1/6*i**6 + 4/5*i**5 + 0*i + 4/3*i**3. Determine t, given that g(t) = 0.
-1, 0
Let f(l) be the third derivative of -1/4*l**4 - 8 + 0*l**3 - l**2 + 0*l + 1/15*l**5 + 1/60*l**6. Factor f(w).
2*w*(w - 1)*(w + 3)
Let w = 5277/4 - 1319. Factor -1/4*u - w*u**2 + 0.
-u*(u + 1)/4
Solve 125*z**4 + 26*z - 1416*z - 165 + 1428*z**2 - 3558*z**2 - 35 - 1025*z**3 + 210*z = 0 for z.
-1, -2/5, 10
Let x(q) be the second derivative of q**7/56 + 7*q**6/40 + 27*q**5/40 + 11*q**4/8 + 13*q**3/8 + 9*q**2/8 - 109*q. Suppose x(p) = 0. Calculate p.
-3, -1
Let d(j) be the second derivative of j**6/20 - 3*j**5/10 + 5*j**4/8 - j**3/2 + 88*j. Factor d(i).
3*i*(i - 2)*(i - 1)**2/2
Let v(p) = -3*p - 9. Let b be v(-4). Determine j so that 0*j**3 + 0*j**b + 8*j - 2*j**3 = 0.
-2, 0, 2
Let x(u) be the third derivative of u**7/735 + u**6/140 + u**5/105 + 401*u**2 + 1. Determine t, given that x(t) = 0.
-2, -1, 0
Suppose -14*n - 20 = -24*n. Let v(i) be the third derivative of 0 - 1/30*i**3 + 1/60*i**4 + i**n + 0*i - 1/300*i**5. Factor v(t).
-(t - 1)**2/5
Let m(s) be the first derivative of -s**4/72 + 5*s**3/36 + 47*s - 37. Let p(g) be the first derivative of m(g). Determine u so that p(u) = 0.
0, 5
Let p = 124 + -115. Suppose p*n = 5*n. Let -1/3*c - 1/3*c**2 + n = 0. Calculate c.
-1, 0
Let c be (-8 - -2)/(-5 + 3). Let v(g) be the first derivative of 9*g - 4*g**2 + g**c - 1 - 2*g**2 + 7. Let v(a) = 0. What is a?
1, 3
Let 1/4*y**3 - 49/4*y - 1/4*y**2 + 49/4 = 0. Calculate y.
-7, 1, 7
Suppose 0*p + p - 8 = 0. Suppose p = -2*j + 4*y, j - 4*y = 3*j - 16. Factor -4*k**j + 0*k**2 + k + k**3 + 2*k + k**2 - 1.
(k - 1)**3
Let t be (-6)/14 + 575/35. Suppose -5*g + 14 = -t. Factor -5*u - 18 - g*u - u - 2*u**2.
-2*(u + 3)**2
Let u be (-16)/((-4)/(12/18*1)). What is i in -2/3 + u*i**2 + 2*i = 0?
-1, 1/4
Find v, given that -8*v + 11*v**3 - 170*v**4 + 8*v**2 - 14*v**2 + 173*v**4 = 0.
-4, -2/3, 0, 1
Suppose 261 - 48 = 71*p. Solve 3/4*j - 3/2*j**2 + 3/4*j**p + 0 = 0.
0, 1
Let z be 1/(-15) + 110/450*3. Suppose -16/3 + 2*c**5 - 8/3*c - 20/3*c**4 + 12*c**2 + z*c**3 = 0. Calculate c.
-1, -2/3, 1, 2
Let i be (42/(-9) - -4)*(202/(-10) - 5). Determine j so that -196/5*j**2 - i*j - 9/5 = 0.
-3/14
Let d = -2076 + 18722/9. Determine p so that -d*p**3 + 26/9*p**2 - 14/9*p**4 - 4/3 + 38/9*p = 0.
-3, -1, 2/7, 1
Let d be (26 - 27)/(18/48 + 7/(-8)). Factor -3/5*u**d - 1/5*u**3 + 4/5*u + 0.
-u*(u - 1)*(u + 4)/5
Let n(q) be the third derivative of q**5/120 + 67*q**4/48 - 17*q**3/3 - q**2 - 10. Factor n(k).
(k - 1)*(k + 68)/2
Suppose 3*l - 130 = 4*y, 2*l - 2*y = -0*y + 90. Let r be (-170)/(-3)*180/l. Let 94*b**2 - 56*b + 8 + 64*b**3 + 50*b**4 - r*b**3 + 44*b**2 = 0. Calculate b.
2/5, 1
Let w(k) be the first derivative of k**5/35 - 10*k**4/7 + 400*k**3/21 + 31. Factor w(c).
c**2*(c - 20)**2/7
Let v(a) be the first derivative of -7*a**6/6 + a**5/2 - 17*a - 14. Let u(s) be the first derivative of v(s). Factor u(k).
-5*k**3*(7*k - 2)
Suppose -36*z**3 - 3*z**4 - z**5 - 48*z + 4229*z**2 - 4145*z**2 + 4*z**5 = 0. What is z?
-4, 0, 1, 2
Let o(w) be the third derivative of -14*w**2 + 121/1008*w**8 + 0*w**5 + 0 + 0*w + 0*w**4 + 1/90*w**6 + 22/315*w**7 + 0*w**3. Factor o(b).
b**3*(11*b + 2)**2/3
Let d be 3/(-6) + 49/14. Suppose -4*r = -4, n = 3*n - d*r + 3. Determine b, given that 2/5*b**5 + 0*b**3 + 0*b + 0*b**2 + 2/5*b**4 + n = 0.
-1, 0
Let o = 4660 - 13975/3. Factor -8/3*t**2 + 0 + t + o*t**3.
t*(t - 1)*(5*t - 3)/3
Factor -42*k - 153*k - 224*k - 161*k + 16820 + 4*k**2 + k**2.
5*(k - 58)**2
Determine q so that 577/6*q + 32 + 1/2*q**2 = 0.
-192, -1/3
Let x(k) be the first derivative of k**3/3 + 5*k**2/2 - 19*k + 12. Let g be x(-8). Solve -33/8*m**4 - 3/8*m**3 + 15/8*m - 3/4 - 3/2*m**g + 39/8*m**2 = 0.
-2, -1, 1/4, 1
Let t(s) be the first derivative of s**4 - 8*s**3/3 - 8*s**2 + 32*s + 269. Factor t(b).
4*(b - 2)**2*(b + 2)
Suppose 0 = 4*w - 3*w - 37. Factor w*n**3 - 21*n**3 + 4*n**4 - 64*n - 72 + 8.
4*(n - 2)*(n + 2)**3
Let f(s) be the second derivative of s**6/420 - 2*s**5/105 - s**4/28 + 6*s**3/7 + 5*s**2/2 - s. Let t(v) be the first derivative of f(v). Factor t(q).
2*(q - 3)**2*(q + 2)/7
Suppose 2*j - 3 = 19. What is f in -6*f + 3 + 4*f + 8*f**2 + 2*f**3 - j = 0?
-4, -1, 1
Let r(b) be the second derivative of b**8/560 + 3*b**7/280 - b**6/120 - 3*b**5/40 - b**3 + 10*b. Let o(c) be the second derivative of r(c). Factor o(z).
3*z*(z - 1)*(z + 1)*(z + 3)
Suppose 0 = a + 2*k - 34, 115 = 5*a - k - 0*k. Let q = -21 + a. Solve -2/11*v - 2/11*v**5 - 12/11*v**q + 8/11*v**2 + 8/11*v**4 + 0 = 0 for v.
0, 1
Let x(n) be the second derivative of -n**4/6 - 5*n**3 - 36*n**2 + 219*n. Factor x(y).
-2*(y + 3)*(y + 12)
Let n be (-2)/6*54/6. Let g be -1*n/1 - 0. Determine f, given that -134*f**3 - 42*f**2 + 100*f**g + f - 8*f**4 + 17*f + 2*f**4 = 0.
-3, 0, 1/3
Suppose 14*u = 5*u. Let x(w) be the third derivative of 0*w**5 + 1/630*w**7 + 1/120*w**6 + 0 + u*w**3 - w**2 - 1/18*w**4 + 0*w. Factor x(d).
d*(d - 1)*(d + 2)**2/3
Suppose 0 = -0*p + 3*p - 30. Suppose 11 = -p*x + 31. Solve -4/17*s**3 - 6/17*s**4 + 2/17 - 2/17*s**5 + 6/17*s + 4/17*s**x = 0.
-1, 1
Let s(g) be the first derivative of -g**4/2 - 10*g**3/3 - 4*g**2 + 55. What is p in s(p) = 0?
-4, -1, 0
Let g be 5 + (-764)/(-12) + (-2)/3. Let s be (-256)/g + 0 + 4. Factor 4/17*q**2 - 2/17*q - 2/17*q**4 - 2/17*q**5 - 2/17 + s*q**3.
-2*(q - 1)**2*(q + 1)**3/17
Let q(a) = 16*a**4 - 5*a**3 - 4*a**2 - 4*a - 3. Let f(c) = 96*c**4 - 31*c**3 - 25*c**2 - 23*c - 17. Let d(n) = 6*f(n) - 34*q(n). Factor d(p).
2*p*(p - 1)*(4*p + 1)**2
Solve 0*q - 8/3*q**4 + 2/3*q**3 + 0 + 8/3*q**2 - 2/3*q**5 = 0.
-4, -1, 0, 1
Let a be ((-7)/(-98))/(18/21). Let t(x) be the second derivative of 0*x**3 + 1/60*x**6 - a*x**4 - x + 0 + 0*x**5 + 1/4*x**2. Factor t(s).
(s - 1)**2*(s + 1)**2/2
Factor 13/6*p + 5/6*p**2 + 1.
(p + 2)*(5*p + 3)/6
Suppose -3*z + 5*o - 17 + 3 = 0, 4*o - 18 = -z. Factor 5*h**z - 56 - 64*h - 6*h + 301.
5*(h - 7)**2
Let l(n) = -8*n**3 - 121*n**2 - 199*n + 362. Let t(g) = -3*g**3 - 39*g**2 - 66*g + 120. Let b(x) = -6*l(x) + 17*t(x). Factor b(p).
-3*(p - 22)*(p - 1)*(p + 2)
Solve -1/4*d + 1/4*d**2 - 1/4 + 1/4*d**3 = 0.
-1, 1
Let p(m) = m**2 + 3*m - 1. Suppose 8*l = -0*l - 32. Let h be p(l). Determine a, given that 15*a**2 + 5*a**3 + 27*a + 2*a**h + 3*a**2 - 4*a**3 = 0.
-3, 0
Let g(x) be the third derivative of -x**5/4 - 43*x**4/8 + 9*x**3 - 37*x**2. Solve g(r) = 0 for r.
-9, 2/5
Let a be -6 - (-140)/21 - 30/(-36). Solve -19/4*i - 1/4*i**3 - a + 3/4*i**4 - 17/4*i**2 = 0 for i.
-1, -2/3, 3
Suppose -370 - 280 = -26*p. Let j(i) be the first derivative of 2 + 15*i**2 + 4*i + 12*i**5 + p*i**4 + 80/3*i**3 + 7/3*i**6. Factor j(z).
2*(z + 1)**4*(7*z + 2)
Suppose 4*n - 3*v = 11, -3*n + v + 6 + 1 = 0. Let m(s) be the third derivative of -s**n + 0 + 7/12*s**5 + 0*s + 1/6*s**4 - 2/3*s**3. Let m(p) = 0. What is p?
-2/5, 2/7
Suppose 0 = 8*f - 18*f + 360. Solve -8*w + 52*w**3 + 4*w**4 + f*w**3 + 20*w**2 - 104*w**3 = 0 for w.
0, 1, 2
Solve -99/2*r**3 + 0*r - 12*r**4 + 0*r**2 + 3/2*r**5 + 0 = 0 for r.
-3, 0, 11
Suppose