3 + 12*n**h.
-2*n*(n - 1)**2
Let k(f) be the second derivative of -f**6/720 - f**5/120 + f**4/16 - 2*f**3/3 + 3*f. Let i(h) be the second derivative of k(h). Let i(j) = 0. Calculate j.
-3, 1
Let l(o) be the second derivative of o**10/45360 + o**9/11340 - o**7/1890 - o**6/1080 + o**4/4 - 2*o. Let r(v) be the third derivative of l(v). Factor r(c).
2*c*(c - 1)*(c + 1)**3/3
Let g(y) = y**2 - 3*y + 4. Let a be g(2). Suppose 2*m - a = -x, 2*m - 4*m = -3*x - 18. Factor -16/3*k**2 + 0*k + 0 - 36*k**4 + 24*k**m + 18*k**5.
2*k**2*(3*k - 2)**3/3
Let f(t) be the second derivative of 1/5*t**2 + 1/75*t**6 - 8*t + 2/25*t**5 + 0 + 4/15*t**3 + 1/5*t**4. Factor f(p).
2*(p + 1)**4/5
Let m(j) be the second derivative of -11*j**4/12 + 3*j**3/2 + j**2 + 4*j. Factor m(n).
-(n - 1)*(11*n + 2)
Let o(j) be the second derivative of -j**7/1680 - j**6/180 - j**5/48 - j**4/24 - j**3/2 + j. Let b(p) be the second derivative of o(p). Factor b(d).
-(d + 1)**2*(d + 2)/2
Let b(m) be the second derivative of 5*m**4/72 - m**3/2 - 2*m**2/3 + 18*m. Factor b(a).
(a - 4)*(5*a + 2)/6
Let d(s) = -11*s**3 - 13*s**2 - 12*s. Let p(w) = -17*w**3 - 19*w**2 - 18*w. Let v(x) = -8*d(x) + 5*p(x). Determine q, given that v(q) = 0.
-2, -1, 0
Let v(q) be the second derivative of -q**6/12 - 13*q**5/40 - 3*q**4/8 + q**3/12 + q**2/2 + 7*q. Determine u, given that v(u) = 0.
-1, 2/5
Factor 8/3*j + 2/3*j**2 + 8/3.
2*(j + 2)**2/3
Let k = 395/778 - 3/389. Factor 1/2*q + 1 - k*q**2.
-(q - 2)*(q + 1)/2
Let q(m) = 8*m - 1. Let z be q(3). Suppose -2*i - c + z = 0, -i - 10 - 1 = -4*c. Factor -4*o - i*o**2 - 3*o**4 + 16*o**3 + 3*o**2 - 3*o**4.
-2*o*(o - 2)*(o - 1)*(3*o + 1)
Let m = -62 + 88. Suppose m*j - 30*j = 0. Determine q, given that 0*q + j + 2/11*q**2 = 0.
0
Let l(k) = -4*k**4 + 2*k**3 + 8*k**2 - 2. Let h(q) = 4*q**4 - 2*q**3 - 9*q**2 - q + 2. Let z(t) = -4*h(t) - 6*l(t). Factor z(g).
4*(g - 1)**2*(g + 1)*(2*g + 1)
Let k(m) = -m**3 + 4*m**2 - 2*m - 1. Let o be k(3). Let g(d) be the third derivative of 0 + 0*d + d**o - 1/96*d**4 - 1/60*d**5 + 0*d**3. What is l in g(l) = 0?
-1/4, 0
Let k(r) be the second derivative of -r**8/11760 + r**6/1260 - r**4/168 + 5*r**3/3 + 8*r. Let s(q) be the second derivative of k(q). Factor s(l).
-(l - 1)**2*(l + 1)**2/7
Let p(g) be the second derivative of -g**6/10 - 6*g**5/5 - 6*g**4 - 16*g**3 - 24*g**2 + 22*g. Factor p(s).
-3*(s + 2)**4
Let b(s) = 12*s - 118. Let h be b(10). Factor -54/7 + 2/7*y**3 - 18/7*y**h + 54/7*y.
2*(y - 3)**3/7
Suppose 4*y + 5*u = 37, 8 = -5*y - 5*u + 48. Factor -7/6*z**2 + 1/3*z + 5/6*z**y + 0.
z*(z - 1)*(5*z - 2)/6
Let v(a) = 3 + a + a + 2*a - 3*a. Let o be v(0). Factor 2/3*g**2 + 2/3*g**o - 2/3*g - 2/3.
2*(g - 1)*(g + 1)**2/3
Solve 4/5*h**2 - 16/5 - 12/5*h = 0.
-1, 4
Let d(o) = o**3 + 4*o**2 + 5*o + 4. Let b be d(-3). Let r = 0 - b. Factor 2*w - 1 + 0*w**r - 2*w**3 + 4*w**2 - 3*w**2.
-(w - 1)*(w + 1)*(2*w - 1)
Let n(f) = f**3 + 6*f**2 + 4*f - 3. Let w be n(-5). Suppose -10 = -4*z + w*z. Determine k so that -5*k**5 + 7*k**z + k**4 - 5*k**4 - 2*k + 4*k**2 = 0.
-1, 0, 1
Let a(d) be the first derivative of -d**6/12 + 3*d**5/5 - 13*d**4/8 + 2*d**3 - d**2 - 30. Determine v, given that a(v) = 0.
0, 1, 2
Let n(k) be the first derivative of -k**7/1680 + k**6/240 - k**5/120 + 2*k**3 - 8. Let p(j) be the third derivative of n(j). Let p(c) = 0. What is c?
0, 1, 2
Suppose 0 - 1/3*t - t**2 + 4/3*t**3 = 0. Calculate t.
-1/4, 0, 1
Factor 4*k**3 + 37*k**3 - 49*k**2 + 3*k**3 - 47*k**2 - 144*k - 4*k**4.
-4*k*(k - 6)**2*(k + 1)
Let i be -1 - (-30)/4 - 3. Let b = i - 3. Factor 0 + b*q - 1/2*q**2.
-q*(q - 1)/2
Let h(z) be the first derivative of -z**5/15 - 5*z**4/36 - z**3/18 + 2*z + 3. Let j(i) be the first derivative of h(i). Let j(p) = 0. Calculate p.
-1, -1/4, 0
Let r be ((-3)/(-2) + (-20)/40)/6. Factor 0 - 1/6*l**2 + r*l.
-l*(l - 1)/6
Factor 0*h**4 + h**3 - 1/4*h**5 - 3/4*h + 1/2*h**2 - 1/2.
-(h - 2)*(h - 1)*(h + 1)**3/4
Let l be (28/12*3)/(-1). Let b be -4 - (-2 - (-18)/l). Find c, given that 2/7 + 0*c - b*c**2 + 2/7*c**4 + 0*c**3 = 0.
-1, 1
Let t(k) = -7*k**2 + 5*k - 3. Let s be (-30)/4*2/(-3). Let c(p) = -6*p**2 + 4*p - 2. Let f(l) = s*c(l) - 4*t(l). Factor f(v).
-2*(v - 1)*(v + 1)
Let h(m) be the first derivative of m**4/30 - 26*m**3/45 + 11*m**2/3 - 10*m + 33. Factor h(g).
2*(g - 5)**2*(g - 3)/15
Factor 18/11*q**2 - 20/11*q + 2/11.
2*(q - 1)*(9*q - 1)/11
Let k be (2 + -6)/(8/(-12)). Suppose 18 = 3*q + k. Find p such that 11*p**3 + 7*p**3 + 2*p + 3*p**q + 12*p**2 + 5*p**4 = 0.
-1, -1/4, 0
Factor 1/6*s - 1/3 + 1/6*s**2.
(s - 1)*(s + 2)/6
Let r(y) be the first derivative of 75*y**6/2 - 60*y**5 - 24*y**4 + 58*y**3 + 15*y**2/2 - 18*y - 8. Let r(q) = 0. What is q?
-3/5, -2/5, 1/3, 1
Factor -8*y**3 - 15*y**2 + 2*y + 4*y**4 + 12 - y**2 + 6*y.
4*(y - 3)*(y - 1)*(y + 1)**2
Let u(f) be the first derivative of 2 - 1/4*f**2 + 1/10*f**5 - 1/3*f**3 - 1/12*f**6 + 1/4*f**4 + 1/2*f. Solve u(h) = 0.
-1, 1
Let f(w) be the second derivative of -w**6/24 - w**5/20 + w**4/48 - 11*w. Factor f(h).
-h**2*(h + 1)*(5*h - 1)/4
Let g be 9 - (2 + -1 + 0). Suppose 0 = 3*i - 40 - g. Factor 64/3*q**5 + 0*q + i*q**4 + 0 + 1/3*q**2 + 4*q**3.
q**2*(4*q + 1)**3/3
Let t(c) = -c**2 - c. Let l be t(0). Suppose -5*i + i + 8 = l. Factor -1 + i - 1 - 3*f**2.
-3*f**2
Suppose -g - 20 = -6*g. Let h(i) be the first derivative of g + 2/5*i**5 + 0*i + i**4 + 0*i**2 + 2/3*i**3. Solve h(o) = 0 for o.
-1, 0
Let m(l) be the first derivative of -2*l**3/3 - 7*l**2 - 11. Factor m(d).
-2*d*(d + 7)
Factor 0*w**2 + 1/3*w**4 - 1/3 + 2/3*w - 2/3*w**3.
(w - 1)**3*(w + 1)/3
Let i be 10/4*(38/10 - 3). Let q(k) be the first derivative of 4/39*k**3 - 5/13*k**i - 5 + 6/13*k. Let q(y) = 0. Calculate y.
1, 3/2
Let u = -5353/3 - -1834. Let f = u - 49. Factor 2/9 - 2/3*q + 2/9*q**5 + 4/9*q**3 + 4/9*q**2 - f*q**4.
2*(q - 1)**4*(q + 1)/9
Let t be (-150)/(-87) - (4 + -2). Let k = 98/145 + t. Suppose 2/5 + 4/5*h + k*h**2 = 0. Calculate h.
-1
Factor -12*x - 72 - x**2 + 24 - 2*x**2 - 12*x.
-3*(x + 4)**2
Factor 1/2*s**3 + 0*s + 1/2*s**2 + 0.
s**2*(s + 1)/2
Let k(m) = 12*m**2 - 6*m + 3. Let q(h) = -h**2. Let u(b) = k(b) + 9*q(b). Find n, given that u(n) = 0.
1
Let s(w) = -3*w**2 - 9*w - 5. Let g(o) = 2*o**2 + 5*o + 3. Suppose 2*n + 3*x - 23 = -2*n, -4 = -n + x. Let a(d) = n*g(d) + 3*s(d). Let a(h) = 0. Calculate h.
0, 2
Let s = 7 + -5. Let d be (12/8)/(1/s). Find h, given that -d + 6*h**3 + 3 + 0*h**5 + 4*h**4 + h + 4*h**2 + h**5 = 0.
-1, 0
Let v(j) = 6*j**2 + 5*j + 7. Let t(a) = 5*a**2 + 5*a + 6. Let u(x) = -5*t(x) + 4*v(x). Let f be u(-3). Factor -2*q**3 + 3*q**f - 4*q**4 - 2*q**2 + 3*q**4 + 2*q.
2*q*(q - 1)**2*(q + 1)
Let r(o) be the first derivative of -2/3*o**3 + 0*o + 2/5*o**5 - 1/2*o**4 - 3 + o**2. Factor r(h).
2*h*(h - 1)**2*(h + 1)
Solve 49*k**2 + 0*k**3 - k**2 - 4*k**3 + 256 - 192*k = 0 for k.
4
Suppose -2 = d + 10. Let o be ((-2)/(-6))/((-2)/d). Determine q, given that 2*q + o*q**2 + 0*q**2 + 0*q = 0.
-1, 0
Let q(f) be the third derivative of 0*f**4 - 4*f**2 + 0 + 1/100*f**5 + 1/100*f**6 + 0*f + 0*f**3 + 1/350*f**7. Suppose q(r) = 0. Calculate r.
-1, 0
Let x(c) be the second derivative of -c**8/6720 - c**7/3360 + c**3/2 - 2*c. Let m(z) be the second derivative of x(z). Suppose m(b) = 0. Calculate b.
-1, 0
Let u(g) = g - 1. Let d(h) = 2*h**2 + 2*h - 4. Let t(s) = d(s) - 8*u(s). Solve t(j) = 0 for j.
1, 2
Suppose 4 - 27*u**3 - 118*u**3 - 40*u**5 - 38*u - 57*u**3 - 8*u**2 + 138*u**2 + 146*u**4 = 0. What is u?
1/4, 2/5, 1
Factor -7*f - 21*f**3 + f + f + 5*f**4 - 5*f**2 + 26*f**3.
5*f*(f - 1)*(f + 1)**2
Let f(i) be the second derivative of -i - 1/6*i**2 + 5/36*i**4 - 1/20*i**5 + 0 - 1/18*i**3. Factor f(m).
-(m - 1)**2*(3*m + 1)/3
Let g(d) = 2*d - 12. Let i be g(7). Suppose -2*b = n + 3, 3*n = -5*b + 8*n + 15. Factor 0*x**i - 1/3*x**3 + b + 0*x.
-x**3/3
Let q(m) be the second derivative of -m**4/6 + 2*m**3/3 - m**2 + 3*m. Suppose q(w) = 0. What is w?
1
Let w(y) be the third derivative of y**7/1050 - y**6/200 + y**5/100 - y**4/120 + 15*y**2. Factor w(h).
h*(h - 1)**3/5
Let z(f) be the first derivative of 1/6*f**3 - 1/20*f**5 - 1/4*f - 1/24*f**6 - 1/8*f**2 + 1/8*f**4 - 4. Determine n, given that z(n) = 0.
-1, 1
Let r(l) = 2*l**3 + l. Let v be r(1). Factor 7*z**5 - 2*z**2 + z**3 + 2*z**4 - 11*z**3 + v*z**3.
z**2*(z - 1)*(z + 1)*(7*z