3/3 + 3*n**2/2 + 2. Let f(v) be the second derivative of o(v). Find u such that f(u) = 0.
-1
Let c(j) be the second derivative of -j**9/12096 + j**7/1680 - j**5/480 + j**3/3 + 5*j. Let d(r) be the second derivative of c(r). Factor d(a).
-a*(a - 1)**2*(a + 1)**2/4
Let m = -4/65 + 108/65. Factor 34/5*u**2 + m*u**3 + 8/5 + 8*u.
2*(u + 2)**2*(4*u + 1)/5
Let o be 5/15 + (-4)/(-6). Let m be o + -6 + 3 - -2. Factor -2/3*b**2 - 2*b**3 - 2/3*b**5 - 2*b**4 + 0*b + m.
-2*b**2*(b + 1)**3/3
Let w(c) be the first derivative of -c**4/4 + 2*c**3/3 + c**2/2 - 2*c - 40. Factor w(a).
-(a - 2)*(a - 1)*(a + 1)
Let z = 29/8 + -25/8. Factor 2*a**4 + z*a + 9/2*a**3 + 3*a**2 + 0.
a*(a + 1)**2*(4*a + 1)/2
Let k(s) be the second derivative of s**3 + 0 + 1/10*s**5 + s**2 - s + 1/2*s**4. Factor k(t).
2*(t + 1)**3
Let l(d) be the third derivative of 0 + 1/60*d**6 + 0*d - 2*d**2 + 2/9*d**3 - 1/45*d**5 - 1/12*d**4. Suppose l(o) = 0. What is o?
-1, 2/3, 1
Let l(q) = 4*q**3 + 5*q - 6*q**2 + 2 - 6*q - 5*q**3 + 8*q. Let u be l(-7). Let 6*i + 15*i**4 + 2*i - 12 - 3*i**5 - 3*i**u - 21*i**3 + 16*i = 0. Calculate i.
-1, 1, 2
Let b(s) be the first derivative of 26*s**3/7 - s**2 - 4*s/7 + 8. Factor b(q).
2*(3*q - 1)*(13*q + 2)/7
Let d(g) = 7*g**3 - 9*g**2 + 6*g - 4. Let o(z) = -z**3 + z**2. Let x(m) = -2*d(m) - 18*o(m). Let x(q) = 0. What is q?
-2, 1
Let k(q) = -q**3 + 4*q + 2. Let z be k(-2). Factor -z*p**2 + 0*p - 2/3*p**3 + 8/3.
-2*(p - 1)*(p + 2)**2/3
Solve 8/7*k**2 - 2/7*k**4 - 4/7*k**3 + 16/7*k + 0 = 0.
-2, 0, 2
Let f = -29429/135 - -218. Let h(c) be the second derivative of f*c**6 + 0 - 1/54*c**4 - 3*c + 0*c**2 + 0*c**5 + 0*c**3. Factor h(g).
2*g**2*(g - 1)*(g + 1)/9
Let l(h) be the first derivative of -h**5/15 - 7*h**4/12 - 13*h**3/9 + h**2/2 + 6*h - 17. Let l(c) = 0. Calculate c.
-3, -2, 1
Let j(g) be the second derivative of -g**7/210 - g**6/30 - 2*g**5/25 - g**4/15 - 8*g. Suppose j(t) = 0. What is t?
-2, -1, 0
Factor w + 9*w**3 - 33*w + 16*w**2 - w**3 - 4*w**4.
-4*w*(w - 2)**2*(w + 2)
Let r(b) be the first derivative of b**4/14 - 4*b**3/21 - 5*b**2/7 + 12*b/7 + 4. Factor r(d).
2*(d - 3)*(d - 1)*(d + 2)/7
Factor -384*w**2 - 2*w**4 + 15*w**3 - 3*w**4 + 374*w**2.
-5*w**2*(w - 2)*(w - 1)
Let v(m) = m**4 - 3*m**3 - 4*m**2 + 3. Let t(c) = c**2 + c - 1. Let f(q) = -3*t(q) - v(q). Factor f(i).
-i*(i - 3)*(i - 1)*(i + 1)
Let p = 865 + -863. Suppose 4/5 - 2/5*l**p - 2/5*l = 0. Calculate l.
-2, 1
Let i(o) = -9*o**2 + 2*o - 4. Let x(k) = -10*k**2 + 2*k - 5. Let v = -15 + 9. Let n = v - -11. Let p(a) = n*i(a) - 4*x(a). Factor p(d).
-d*(5*d - 2)
Let l(p) be the third derivative of p**7/1260 + p**6/240 + p**5/360 - p**4/48 - p**3/18 + 5*p**2. Determine q, given that l(q) = 0.
-2, -1, 1
Let m(y) = 2*y**3 - 8*y**2 + 18*y + 4. Let d be 2 + 0 - (-6 + 3). Let x(c) = c**3 - 5*c**2 + 12*c + 3. Let f(i) = d*m(i) - 8*x(i). Factor f(g).
2*(g - 2)*(g + 1)**2
Let r(h) = -h + 2. Let z be r(-7). Suppose z*a = 4*a. Let -2/7*m**2 + 0*m + 2/7*m**3 + a = 0. What is m?
0, 1
Let d(j) = 3*j**2 - 32*j - 123. Let f(o) = o**2 - 16*o - 62. Let l(w) = 4*d(w) - 10*f(w). Find z, given that l(z) = 0.
-8
Factor -8 - 4*j**4 + 2*j**2 + 3*j**2 - 4*j + 4*j**3 + 2*j**2 + 5*j**2.
-4*(j - 2)*(j - 1)*(j + 1)**2
Let p = 97/10530 + 2/1053. Let m(h) be the third derivative of 0*h**3 - p*h**5 + 0*h + 2*h**2 - 1/180*h**6 + 1/315*h**7 + 0 + 1/36*h**4. Factor m(r).
2*r*(r - 1)**2*(r + 1)/3
Let h = -23 + 47/2. Factor 2*o**2 - 3*o**3 - 1/2*o**5 + 2*o**4 + 0 - h*o.
-o*(o - 1)**4/2
Let d(n) be the second derivative of -n**6/240 + n**5/40 - n**4/16 + n**3/12 - n**2/16 - 5*n. Suppose d(g) = 0. What is g?
1
Let b(c) be the first derivative of 8*c**7/21 + 4*c**6/45 - c**5/12 - c**4/36 + 5*c + 4. Let i(m) be the first derivative of b(m). Let i(k) = 0. Calculate k.
-1/4, 0, 1/3
Let i(o) be the first derivative of -o**8/840 - o**7/420 + o**6/180 + o**5/60 + 4*o**3/3 + 4. Let l(f) be the third derivative of i(f). Factor l(v).
-2*v*(v - 1)*(v + 1)**2
Determine m so that -1/5*m**5 + 0 + 1/5*m**2 - 2/5*m - 1/5*m**4 + 3/5*m**3 = 0.
-2, -1, 0, 1
Let k(z) be the third derivative of -z**8/112 - 17*z**7/210 - z**6/4 - 3*z**5/10 + z**4/24 + z**3/2 + 13*z**2. Factor k(b).
-(b + 1)**3*(b + 3)*(3*b - 1)
Factor -1/6*a**3 + 1/3*a**2 - 1 + 5/6*a.
-(a - 3)*(a - 1)*(a + 2)/6
Let p(l) be the second derivative of l**10/40320 - l**9/20160 - l**8/8960 + l**7/3360 + l**4/3 - 6*l. Let r(w) be the third derivative of p(w). Factor r(i).
3*i**2*(i - 1)**2*(i + 1)/4
Let o(l) = 5*l**2 - 37*l - 49. Let j(y) = y**2 - 9*y - 12. Let f(h) = -18*j(h) + 4*o(h). Factor f(m).
2*(m + 2)*(m + 5)
Factor -8*g**3 - 10*g + 5*g**5 + 3*g**2 + 14*g**2 + 8*g**2 - 5*g**4 - 7*g**3.
5*g*(g - 1)**3*(g + 2)
Let o = 4 + 2. Factor -o + w**2 + 3 + 3 + w.
w*(w + 1)
Let m(u) = u. Let x(o) be the first derivative of o**3 - 2*o**2 - 1. Let p(n) = -2*m(n) + x(n). Find t, given that p(t) = 0.
0, 2
Let i(x) be the first derivative of -x**3/24 - 5*x**2/8 - 50. Factor i(j).
-j*(j + 10)/8
Suppose -3*g + 4 = -5*g. Let s(p) = 2*p**4 - p**3 - p**2 - 1. Let d(t) = t**4 - t - 1. Let h(y) = g*s(y) + 2*d(y). Solve h(q) = 0.
-1, 0, 1
Let p(k) be the first derivative of -10/7*k**3 - 5 + k**2 - 2/7*k + 9/14*k**4. Factor p(w).
2*(w - 1)*(3*w - 1)**2/7
Let c(r) be the second derivative of r**6/270 - r**5/72 + r**4/72 + r**3/3 - 8*r. Let z(p) be the second derivative of c(p). Factor z(v).
(v - 1)*(4*v - 1)/3
Let q(f) be the second derivative of -8/15*f**3 - 3*f - 1/50*f**5 + 0 - 4/5*f**2 - 1/6*f**4. Solve q(x) = 0.
-2, -1
Let s be (56/(-16) - -1)/(5/(-3)). Solve -5/2*l + 1/2*l**3 - 1/2*l**4 + s*l**2 + 1 = 0.
-2, 1
Let b be 16/(-28)*63/(-18). What is d in -3/2*d**3 + 1 - b*d**2 + 1/2*d = 0?
-1, 2/3
Solve -8/3 - 4/3*l**3 - 16/3*l**2 - 20/3*l = 0 for l.
-2, -1
Let a(n) be the third derivative of n**6/900 - n**5/150 + n**4/60 - n**3/3 + 2*n**2. Let c(h) be the first derivative of a(h). Factor c(g).
2*(g - 1)**2/5
Let d(w) be the first derivative of -w**4/4 + 3*w**3 - 7*w**2/2 - 6*w + 1. Let g be d(8). Factor 0 + 0*y**4 + 1/2*y - y**3 + 1/2*y**5 + 0*y**g.
y*(y - 1)**2*(y + 1)**2/2
Let i(j) be the third derivative of -j**7/175 + j**6/50 + j**5/50 - j**4/10 - 5*j**2. Factor i(w).
-6*w*(w - 2)*(w - 1)*(w + 1)/5
Factor 8/11 + 8/11*z - 6/11*z**2.
-2*(z - 2)*(3*z + 2)/11
Let r(q) be the first derivative of 3*q**5/20 - q**3/2 - 6*q + 4. Let g(t) be the first derivative of r(t). Suppose g(f) = 0. What is f?
-1, 0, 1
Let g(j) be the first derivative of 2 + 0*j + 1/540*j**6 + 0*j**3 + 1/2*j**2 + 1/270*j**5 + 0*j**4. Let q(h) be the second derivative of g(h). Factor q(n).
2*n**2*(n + 1)/9
Let d(s) be the third derivative of -s**6/1080 - 7*s**5/540 - 5*s**4/72 - s**3/6 - 2*s**2 - 7*s. Factor d(b).
-(b + 1)*(b + 3)**2/9
Suppose 0*x + 0 + 2/5*x**2 - 1/5*x**3 = 0. What is x?
0, 2
Let r(k) be the second derivative of -2*k**4/3 - k**3 + k**2 + 7*k. Factor r(p).
-2*(p + 1)*(4*p - 1)
Let o = 444 - 441. Factor -64/5*p - 16/5*p**o + 2/5*p**4 + 48/5*p**2 + 32/5.
2*(p - 2)**4/5
Let v be 2/1 + (3 - (4 - 1)). Let g(s) be the third derivative of 0 + 1/120*s**6 - 1/6*s**3 + 1/24*s**5 + 3*s**v + 0*s + 1/48*s**4. Factor g(t).
(t + 1)*(t + 2)*(2*t - 1)/2
Let u = 10 - 5. Let d(b) be the second derivative of 0*b**3 - 1/90*b**6 + 0*b**u + 0 - b + 0*b**4 + 0*b**2. Let d(m) = 0. What is m?
0
Factor -1 - 1 - 2 + 4*j**4 - 8*j + 30*j**3 - 22*j**3.
4*(j - 1)*(j + 1)**3
Factor 9*n**3 - 2*n**2 - 7*n**4 - 484*n + 484*n.
-n**2*(n - 1)*(7*n - 2)
Let l(x) be the first derivative of x**3 + 1/10*x**5 - 1/2*x**2 + 2 - 9/16*x**4 + 0*x. Let l(z) = 0. What is z?
0, 1/2, 2
Let r(k) = k**3 - k - 1. Let z(h) = -2*h**4 - 7*h**3 + 7*h + 5. Let l(g) = -6*r(g) - 2*z(g). Factor l(o).
4*(o - 1)*(o + 1)**3
Let x(t) be the third derivative of -t**8/1848 - 2*t**7/1155 + t**6/220 + 2*t**5/165 - t**4/33 - 21*t**2. Determine n so that x(n) = 0.
-2, 0, 1
Factor -2*d**2 - 8/9*d**3 - 4/9*d + 0.
-2*d*(d + 2)*(4*d + 1)/9
Suppose 2*h = 10, 3*d - h + 4 + 7 = 0. Let k(b) = b**2 - b - 1. Let f(c) = -4*c**3 + 18*c**2 - 11*c - 9. Let q(a) = d*f(a) + 18*k(a). Solve q(x) = 0 for x.
0, 1/4, 2
Let g be 5/(-20)*(-36)/3. Factor -14/5*p - 2*p**g - 18/5*p**2 - 2/5*p**4 - 4/5.
-2*(p + 1)**3*(p + 2)/5
Suppose 6*p**2 - 2*p**2 + 5*p**3 - 5*p**2 - 9*p**2 = 0. Calculate p.
0, 2
Let t = -41 - -44. Factor 0 - 2*