**8/3360 - w**7/420 + w**6/120 - w**5/60 + 5*w**4/12 + 22*w. Let m(n) be the third derivative of s(n). Solve m(u) = 0.
1
Factor -153/5 + 12*n - 3/5*n**2.
-3*(n - 17)*(n - 3)/5
Let k(f) be the first derivative of -2*f**3 - 4*f**2 + 30*f + 100. Solve k(a) = 0 for a.
-3, 5/3
Let a(z) = -7*z**2 - 119*z - 2. Let p(x) = 8*x**2 + 121*x + 3. Let o(u) = -3*a(u) - 2*p(u). Factor o(r).
5*r*(r + 23)
Suppose -4*b = 3*a - 2*b - 30, -4*a + 4*b + 60 = 0. Let p be (-5)/((-80)/(-12)) + 9/a. Factor 4/5*g - 2/5*g**4 + 6/5*g**2 + p + 0*g**3.
-2*g*(g - 2)*(g + 1)**2/5
Suppose -4*a - 11 = 3*x, -x - 4*x - 3 = -a. Let f be x/9 + 690/54. Find w, given that 50/3*w**2 - 46/3*w**4 - f*w**3 - 4/3 - 2/3*w + 40/3*w**5 = 0.
-1, -1/4, 2/5, 1
Let r(a) be the third derivative of -1/180*a**6 + 0*a**3 + 1/45*a**5 + 0*a - 1/36*a**4 - 4*a**2 + 0. Factor r(q).
-2*q*(q - 1)**2/3
Let g = 15716/17 + -924. Factor -14/17*d**2 + 6/17 + g*d.
-2*(d - 1)*(7*d + 3)/17
Suppose 2*x = r + 5, 2*x = -x + 4*r. Find k such that 2*k**x + 0*k**5 + 8*k**2 - 5*k**4 - 5*k**4 + 4*k - 4*k**5 = 0.
-1, 0, 1
Let u(s) = 3*s**3 + 27*s**2 - 66*s + 54. Let q(c) = -2*c**3 - c**2 + c. Let o(f) = 3*q(f) + u(f). Factor o(i).
-3*(i - 3)**2*(i - 2)
Let f = -2 + 5. Let g(u) be the second derivative of 1/6*u**4 + 6*u + 0*u**2 + 0 + 0*u**f. Factor g(l).
2*l**2
Let v(y) be the second derivative of -y**4/54 - 38*y**3/27 + 13*y**2/3 + 60*y. What is p in v(p) = 0?
-39, 1
Let x(k) = k**3 + 2*k**2 - 7*k - 11. Let y be x(-2). Let r(m) be the second derivative of -y*m - 1/20*m**5 + 1/6*m**4 + 0*m**2 + 0*m**3 + 0. Factor r(b).
-b**2*(b - 2)
Suppose 13*u = 16*u - 555. Solve u*l - 16*l**4 + 30 + 69*l**3 - 29*l**4 + 235*l**2 - 34*l**3 = 0.
-1, -2/9, 3
Let b(u) be the third derivative of -14*u**2 - 3/32*u**4 + 0 + 1/60*u**5 + 0*u + 1/12*u**3. Determine j, given that b(j) = 0.
1/4, 2
Let p(v) be the first derivative of -v**4/16 - 13*v**3/3 + 195. Solve p(l) = 0 for l.
-52, 0
Let t = 194 - 197. Let l be ((-15)/6 - -2)*t/9. Suppose 2/3*p**2 + 0 + l*p**3 + 2/3*p = 0. What is p?
-2, 0
Let c(s) be the first derivative of s**6/900 - s**5/150 - 3*s**2 - 8. Let r(d) be the second derivative of c(d). Solve r(u) = 0 for u.
0, 3
Let f(c) be the third derivative of c**5/360 - 19*c**4/144 - 5*c**3/9 + 99*c**2 + 2. Factor f(w).
(w - 20)*(w + 1)/6
Suppose 3*j = 2*v + 7*j + 2, -2*j + 8 = 4*v. Factor 2*z**2 + 0*z**2 + 7*z**v - 3*z**4 - z**4.
-z**2*(z - 2)*(4*z + 1)
Let n(u) be the third derivative of u**5/140 - 5*u**4/7 - 6*u**3 - 499*u**2 + 2*u. Let n(z) = 0. Calculate z.
-2, 42
Suppose 10*w = 26*w. Let s(q) be the third derivative of 1/210*q**6 + 1/735*q**7 + 0 + 0*q - 1/210*q**5 + 4*q**2 - 1/42*q**4 + w*q**3. Factor s(m).
2*m*(m - 1)*(m + 1)*(m + 2)/7
Let l = 5911/4172 + 7/596. Find r such that 4/7*r**3 - 10/7*r**2 + l*r**4 + 0 - 4/7*r = 0.
-1, -2/5, 0, 1
Factor -2/7*c**2 + 20/7*c - 18/7.
-2*(c - 9)*(c - 1)/7
Let m = -10789/3 + 3598. Suppose 0 + 10/3*a + 20/3*a**3 - m*a**4 - 25/3*a**2 = 0. What is a?
0, 1, 2
Factor -5/4*w**2 - 9 - 23*w.
-(w + 18)*(5*w + 2)/4
Let b(u) = u**4 - u**3 + 6*u + 1. Let j(n) = 3*n**4 - 170*n**3 + 385*n**2 - 44*n + 7. Let w(z) = 14*b(z) - 2*j(z). Find h such that w(h) = 0.
-43, 0, 1/4, 2
Let g(l) = -l**3 + 7*l**2 - 4*l - 12. Let t be -6*(1/2 - 12/8). Let u be g(t). Factor u + 2*s**2 + 4/5*s + 2/5*s**4 + 8/5*s**3.
2*s*(s + 1)**2*(s + 2)/5
Let c = 2 + 12. Let n = -12 + c. What is i in -15*i + 5*i**n - 6*i + i**2 - 2 - 4 + 21*i**3 = 0?
-1, -2/7, 1
Let a(j) be the first derivative of j**9/4536 + j**8/2520 - j**7/252 + j**6/180 - j**3/3 - 3. Let m(l) be the third derivative of a(l). Factor m(x).
2*x**2*(x - 1)**2*(x + 3)/3
Let v(w) be the second derivative of 3*w**5/20 - 27*w**3/2 - 81*w**2 + 203*w - 2. Factor v(z).
3*(z - 6)*(z + 3)**2
Let t(m) = m + 1. Let w(b) = -b**2 + 7*b - 9. Let x be w(4). Let d be t(x). Factor 1/4*o**2 + 0 + 1/4*o**d + 0*o - 1/2*o**3.
o**2*(o - 1)**2/4
Suppose -7/2 - 4*u - 1/2*u**2 = 0. Calculate u.
-7, -1
Suppose -4*i - 2*s - 2*s + 8 = 0, 4 = i + 2*s. Let z(a) be the first derivative of i*a**2 + 0*a**4 + 2/5*a**5 - 2/3*a**3 - 2 + 0*a. Factor z(l).
2*l**2*(l - 1)*(l + 1)
Suppose -1 + 2 = -z, 34 = -2*q + 4*z. Let n = q + 22. Factor -3/2*a**n + 6*a + 12 - 3*a**2.
-3*(a - 2)*(a + 2)**2/2
Let p(o) be the second derivative of 0 + 0*o**2 + 17*o - 1/36*o**4 - 1/9*o**3. Find c, given that p(c) = 0.
-2, 0
Let k(p) = 2*p**3 - 6*p**2 - 6*p + 2. Let h(g) = g**4 - 3*g**3 + 14*g**2 + 13*g - 5. Let u(o) = 2*h(o) + 5*k(o). Determine r, given that u(r) = 0.
-2, -1, 0, 1
Suppose 3*t - 1 - 15 = -2*p, 0 = -5*t - 2*p + 24. Suppose -t*w + 5*j = -6, 2*w + 3*j - 12 - 2 = 0. Factor s**w + 36*s**2 + 8*s**3 - 50 + s**4 + 8*s**3 - 4.
2*(s - 1)*(s + 3)**3
Suppose -9*k = -6*k - 45. Suppose 5*c = -5*v - k, 4*c + 0*c + 12 = 0. Find l, given that -5/3*l**3 + 0*l**2 + v + 5/3*l = 0.
-1, 0, 1
Let b be (-13)/104 + (-25)/(-8). Find l, given that 86*l**2 + 2*l + 0*l + 2*l**5 - 4*l**b - 86*l**2 = 0.
-1, 0, 1
Factor 675*f**3 + 375/2*f**4 + 69*f + 9/2 + 360*f**2.
3*(f + 3)*(5*f + 1)**3/2
Factor 5*v**5 - 52*v**3 - 45*v + 12*v**3 + 90*v**2 - 4049*v**4 + 4039*v**4.
5*v*(v - 3)*(v - 1)**2*(v + 3)
Let m = -3019 + 15111/5. Factor -16/5*l**4 - m*l**2 + 24/5*l**3 + 4/5*l**5 + 0 + 4/5*l.
4*l*(l - 1)**4/5
Let l(d) = 4*d**2 + 31. Let g be l(-5). Find p such that 5*p**3 - 20 - 136*p**2 - 25*p + 5 + g*p**2 = 0.
-1, 3
Let o(z) be the third derivative of z**7/2520 - z**6/180 + z**5/40 + z**4 - 9*z**2. Let l(a) be the second derivative of o(a). Suppose l(w) = 0. What is w?
1, 3
Let v(k) be the second derivative of -7/5*k**5 - 11/3*k**4 - 20*k + 0 - 2/15*k**6 + 0*k**2 - 10/3*k**3. Factor v(q).
-4*q*(q + 1)**2*(q + 5)
Factor 64/3*d - 68/3 + 4/3*d**2.
4*(d - 1)*(d + 17)/3
Suppose 8 = 2*p + o + 3*o, 3*p = -2*o + 16. Factor 2*g**3 - 3*g**3 - 4*g - 2*g**3 + p + 13*g.
-3*(g - 2)*(g + 1)**2
Suppose -5*g - 25 = 3*o, -3*g + 2*o - 25 - 9 = 0. Let h(x) = -x - 5. Let m be h(g). Factor -11*q - 4*q - 2*q**m + 17*q.
-2*q*(q - 1)*(q + 1)
Let t(h) be the first derivative of -3*h**4/4 - 21*h**3 + 135*h**2/2 - 69*h + 79. Solve t(b) = 0.
-23, 1
Let f = 561 - 15146/27. Let z(w) be the second derivative of -f*w**4 - 10*w + 0*w**3 + 1/27*w**6 - 1/30*w**5 + 0 + 0*w**2. Factor z(j).
2*j**2*(j - 1)*(5*j + 2)/9
Factor 8/5*i**2 - 2*i - 2/5*i**3 + 4/5.
-2*(i - 2)*(i - 1)**2/5
Let 105/8*q**2 - 3/8*q**3 - 243/2 - 108*q = 0. What is q?
-1, 18
Let m be (-154)/30 - -5 - 16/(-45). Let z(w) be the first derivative of -5 - 1/6*w**2 + 0*w - 1/12*w**4 + m*w**3. Factor z(b).
-b*(b - 1)**2/3
Find f such that -2/5*f**2 + 0 - 26/5*f = 0.
-13, 0
Let s(d) = -4*d**4 - 2*d**3 - 22*d**2 + 6*d. Let w be (1 + 3)/4*10. Let r(p) = p**3 - p**2 + p. Let l(i) = w*r(i) - s(i). Factor l(g).
4*g*(g + 1)**3
Let r(l) be the second derivative of -241/120*l**5 - 1/252*l**7 - 250/3*l**2 - 7/45*l**6 - 215/36*l**4 + 16*l + 0 + 425/9*l**3. Solve r(t) = 0 for t.
-10, 1
Let g be -3 + (20 + -19 - -2). Factor g*f**3 + 2/3 - 4/3*f**2 + 0*f + 2/3*f**4.
2*(f - 1)**2*(f + 1)**2/3
Let z(i) be the second derivative of -22*i + 0*i**2 + 25/6*i**4 - 1/6*i**6 + 0 + 0*i**3 - 3/4*i**5. Factor z(a).
-5*a**2*(a - 2)*(a + 5)
Let b(x) = 6*x**2 - 4*x + 4. Let w be b(1). Let d(l) = -l**2 + 27*l - 126. Let a be d(w). Factor 0*y - 2/5*y**3 + 0*y**2 - 2/5*y**4 + a.
-2*y**3*(y + 1)/5
Let a = 2/25 + 21/50. Let t(o) be the second derivative of 0 + 9/4*o**2 - a*o**3 + 1/24*o**4 - o. Solve t(z) = 0.
3
Let k be 88/(-33)*(0 + -2). Let v(g) be the third derivative of 13*g**2 - 10/3*g**4 + 0 + 0*g - 23/30*g**5 - 1/20*g**6 + k*g**3. Factor v(n).
-2*(n + 4)**2*(3*n - 1)
Solve -345*g**2 + 32 - 32*g**3 - 7*g**4 + g**4 + 297*g**2 = 0.
-2, 2/3
Let 1/3*y**3 + 2*y + 0 - 5/3*y**2 = 0. What is y?
0, 2, 3
Let d = -18 + 45. Let k be d/3*3/9. Find u such that 10*u**4 - 40*u - 15*u**2 + 0*u**4 + 0 + 20 + 25*u**k = 0.
-2, 1/2, 1
Let y(p) be the third derivative of p**8/42 - 2*p**7/35 - 4*p**6/15 - p**5/5 + 34*p**2 - 2*p. Suppose y(o) = 0. What is o?
-1, -1/2, 0, 3
Let r(o) be the first derivative of 2*o**3/45 - 4*o**2/5 + 8*o/3 + 81. Factor r(w).
2*(w - 10)*(w - 2)/15
Let c(i) be the second derivative of i**6/90 + 3*i**5/20 + 3*i**4/4 + 3*i**3/2 + 10*i - 1. Factor c(k).
k*(k + 3)**3/3
Let s(z) be the first derivative of z**6/270 - 2*z**5/135 + z**4/54 + 3*z**2/2 + 3. Let