 of s**7/4200 + s**6/400 + s**5/100 - s**4/6 + 3*s**2. Let l(y) be the second derivative of g(y). Factor l(j).
3*(j + 1)*(j + 2)/5
Let z = -1 + -2. Let n = 2 - z. Determine u, given that 3 - 5*u + 3*u**2 - n + 4*u**2 = 0.
-2/7, 1
Let r(s) = 7*s**2 + s + 4. Let g(i) = 0 + 2*i + 7 + 8*i**2 - 2. Let j(n) = 4*g(n) - 5*r(n). Suppose j(x) = 0. What is x?
0, 1
Let w(f) be the first derivative of 15/4*f**4 - 15/2*f**2 - 2*f**3 + 6*f + 3. Determine d, given that w(d) = 0.
-1, 2/5, 1
Let j(l) be the first derivative of 1/18*l**4 + 0*l**3 + 1/6*l**5 + 4 - l + 0*l**2. Let r(w) be the first derivative of j(w). Let r(h) = 0. Calculate h.
-1/5, 0
Let d(f) be the first derivative of -f**5/30 - f**4/6 - 2*f**3/9 + 4*f - 2. Let u(h) be the first derivative of d(h). Factor u(x).
-2*x*(x + 1)*(x + 2)/3
Let t(n) be the third derivative of n**7/630 - n**6/60 + n**5/180 + n**4/3 + 8*n**3/9 - 26*n**2. Suppose t(a) = 0. What is a?
-1, 4
Let t be 3 - (2 + -2 + 0). Let p be ((-1)/(-3))/(t/18). Suppose 4*c + 0 - 2*c**p - 3 + 1 = 0. What is c?
1
Let a(c) = 6*c**4 - 6*c**3 - 2*c**2 - 2*c + 4. Let j(o) = 5*o**4 - 5*o**3 - 2*o**2 - o + 3. Let z(m) = 3*a(m) - 4*j(m). Factor z(r).
-2*r*(r - 1)**2*(r + 1)
Let v(a) = a**2 + 13*a + 14. Let q be v(-12). Factor -3*b**4 + 2*b**4 + 162*b + 30*b**3 - 5*b**4 - 108*b**q + 3*b**4 - 81.
-3*(b - 3)**3*(b - 1)
Let c(y) = -8*y**3 - 4*y**2 + 5*y. Let f(b) = -9*b**3 - 5*b**2 + 6*b. Let k(i) = -5*c(i) + 4*f(i). Let w be k(1). Factor 0*q - q + 3*q**w - 2*q**3.
q*(q - 1)*(q + 1)
Factor 1/3 - 1/2*v**2 + 5/6*v.
-(v - 2)*(3*v + 1)/6
Factor -52*s**2 + 24*s**2 + 30*s**2 - 4*s.
2*s*(s - 2)
Find g, given that 0 - 4*g**4 + 4/3*g - 4/3*g**2 - 20/3*g**3 = 0.
-1, 0, 1/3
Let l(f) be the first derivative of f**4/38 - 8*f**3/57 + 5*f**2/19 - 4*f/19 - 12. Let l(r) = 0. Calculate r.
1, 2
Let w(l) = 16*l**5 + 24*l**4 - 72*l**3 + 48*l**2 - 16*l + 20. Let f(i) = -i**5 + i**3 - 1. Let h(s) = -20*f(s) - w(s). Factor h(c).
4*c*(c - 2)**2*(c - 1)**2
Let z = 55941/8740 - 1/1748. Solve -16/5*i + 2/5*i**2 + z = 0 for i.
4
Let s(u) = -u**4 - u**3 + u**2 + u - 1. Let c(a) = -4 + a**5 + 5*a - 6*a**3 - 5*a**4 + a**5 - a**3 - 1 + 5*a**2. Let r(p) = -c(p) + 5*s(p). Factor r(y).
-2*y**3*(y - 1)*(y + 1)
Let h(x) be the first derivative of 3*x**4/20 - 2*x**3/5 + 3*x**2/10 + 1. Factor h(m).
3*m*(m - 1)**2/5
Let k(n) be the first derivative of -1/9*n**3 - 1/6*n**2 + 2/3*n - 2. Factor k(b).
-(b - 1)*(b + 2)/3
Suppose 0 = 5*h + 15, -7*h - 12 = -b - 3*h. Suppose b = -4*n - 16, -3*n + 2*n = -z + 7. Solve -19/3*s**z + 4*s**4 - 2/3 + 0*s**2 + 3*s = 0.
-2/3, 1/4, 1
Let m(l) = l + 4. Let n be m(-4). Factor 3*j + 3*j**2 + 0*j**2 - 6 + n*j + 0.
3*(j - 1)*(j + 2)
Let h = 353 - 3869/11. Factor h*a**2 + 10/11*a + 2/11 + 6/11*a**3.
2*(a + 1)**2*(3*a + 1)/11
Let c(n) be the first derivative of -2/5*n**5 - 3*n**2 + 3/2*n**4 + 4*n - 2/3*n**3 + 1. Factor c(s).
-2*(s - 2)*(s - 1)**2*(s + 1)
Let i be (-9 + 0)/((-6)/4). Determine g so that -3*g - 2*g**2 + 4*g**2 + 8 + g - i*g = 0.
2
Let c be 12/16 + 62/(-8). Let s(v) = -v**2 - 8*v - 7. Let t be s(c). Solve t + 1/3*y**3 + 1/3*y**2 + 0*y = 0 for y.
-1, 0
Let x(g) = 7*g**3 + 9*g**2 + 7*g - 5. Let z(o) = 6*o**3 - 10*o**3 + 6*o + 10*o**3 + 8*o**2 - 4. Let k(w) = -4*x(w) + 5*z(w). Determine m, given that k(m) = 0.
-1, 0
Factor -1/2 + 11/4*q**3 - 7/4*q**2 + 9/4*q**4 - 11/4*q.
(q - 1)*(q + 1)**2*(9*q + 2)/4
Suppose 5*v = 16 - 6. Suppose -5 = -3*s + 4*c, 2*s - v*c - 9 = -5*c. Factor 0*h**2 - 2/5*h**4 + 0*h**s - 2/5*h**5 + 0*h + 0.
-2*h**4*(h + 1)/5
Let b(p) = -3*p**3 - 15*p**2 + 16*p - 13. Let j(n) = -4*n**3 - 16*n**2 + 16*n - 14. Let w(k) = 6*b(k) - 5*j(k). Suppose w(y) = 0. What is y?
1, 2
Let t(f) be the second derivative of -f**7/168 + f**6/120 + f**5/40 - f**4/24 - f**3/24 + f**2/8 + 6*f. Solve t(i) = 0 for i.
-1, 1
Let c(d) be the second derivative of 1/30*d**6 + 5*d - 1/4*d**5 + 0 - 7/6*d**3 + 3/4*d**4 + d**2. Factor c(i).
(i - 2)*(i - 1)**3
Suppose 5*r + 1 = 4*r. Let n = r + 4. Factor 5*z**5 + 1 + z**4 + 3*z**2 + z - 4*z**5 - 5*z**2 - 2*z**n.
(z - 1)**2*(z + 1)**3
Let j(o) be the third derivative of -o**8/504 - 11*o**7/315 - o**6/18 + 53*o**5/45 - 133*o**4/36 + 49*o**3/9 + 9*o**2 - 3*o. Let j(l) = 0. Calculate l.
-7, 1
Let c(w) be the first derivative of -w**4/12 + w**3/9 + w**2/3 + 38. Factor c(u).
-u*(u - 2)*(u + 1)/3
Let d(n) be the third derivative of 0*n - n**2 + 1/180*n**6 + 1/108*n**4 + 0*n**3 + 1/90*n**5 + 1/945*n**7 + 0. Factor d(v).
2*v*(v + 1)**3/9
Let h(q) be the first derivative of -3*q**6/8 - 3*q**5/20 + 15*q**4/16 + q**3/4 - 3*q**2/4 + 6. Solve h(n) = 0.
-1, 0, 2/3, 1
Let x(b) be the second derivative of -3*b + 0 + 1/2*b**2 + 1/5*b**5 + 2/3*b**3 + 1/30*b**6 + 1/2*b**4. Determine p, given that x(p) = 0.
-1
Let b = 3/35 + 17/210. Factor 0 - 1/3*y + b*y**2.
y*(y - 2)/6
Let m(k) be the first derivative of -2/3*k**3 + 0*k + 8 - k**2. Factor m(s).
-2*s*(s + 1)
Suppose -2*o + 28 = 2*o. Suppose 10 = o*l - 2*l. Determine t so that 0 - 1/4*t - 1/4*t**l = 0.
-1, 0
Let t(j) be the third derivative of -j**5/30 - j**4/12 - 16*j**3/3 + j**2. Let v(c) = c**2 + c + 13. Let g(d) = -5*t(d) - 12*v(d). Factor g(i).
-2*(i - 1)*(i + 2)
Let n(f) be the second derivative of 0*f**2 + 0*f**3 - 1/4*f**4 - 7*f + 0 - 1/14*f**7 + 3/20*f**5 + 1/10*f**6. Determine z, given that n(z) = 0.
-1, 0, 1
Let z(l) = -2*l**5 - l**4 + 8*l**3 - 2*l**2 + 3*l. Let m(w) = w**5 - w**4 - w**3 - w. Let s(b) = 3*m(b) + z(b). Factor s(r).
r**2*(r - 2)*(r - 1)**2
Let d(l) = -l**3 - l**2 - l + 1. Let h(j) = 7*j**3 - 5*j**2 + 13*j - 7. Let n(g) = 4*d(g) + h(g). Factor n(p).
3*(p - 1)**3
Let t(b) be the second derivative of b**5/40 + b**4/12 - 3*b. Factor t(i).
i**2*(i + 2)/2
Let i(a) be the first derivative of -a**8/6720 + a**7/1680 + a**6/480 - a**5/120 - a**4/24 - a**3 + 2. Let v(y) be the third derivative of i(y). Factor v(k).
-(k - 2)**2*(k + 1)**2/4
Let u(w) be the third derivative of 1/210*w**5 + 4*w**2 + 0*w - 1/42*w**4 - 1/21*w**3 + 1/210*w**6 + 0. Factor u(v).
2*(v - 1)*(v + 1)*(2*v + 1)/7
Let d(g) = g**3 + 8*g**2 + g + 10. Let s be d(-8). Factor 32*z - 8*z - 3 - 33*z**s - 20*z**2 + 5*z**2.
-3*(4*z - 1)**2
Let n(o) = -o**3 - 12*o**2 + 11*o - 2. Let w(i) = 3*i**3 + 48*i**2 - 45*i + 9. Let b(p) = 15*n(p) + 4*w(p). Find j such that b(j) = 0.
1, 2
Let u(g) = -g**2 + 4*g + 4. Let a be u(4). Factor -17*t**2 - t**3 - 11*t**3 + t**4 - a*t**4 - 6*t + 2*t**2.
-3*t*(t + 1)**2*(t + 2)
Let a(k) be the third derivative of k**8/16800 - k**6/1800 + 5*k**4/24 + 5*k**2. Let s(p) be the second derivative of a(p). What is c in s(c) = 0?
-1, 0, 1
Let y(o) be the second derivative of 2*o - 1/48*o**4 + 0*o**2 - 1/80*o**5 + 0 + 1/12*o**3. Factor y(x).
-x*(x - 1)*(x + 2)/4
Let m(z) be the first derivative of -z**6/10 - 12*z**5/25 - 3*z**4/5 + 2*z**3/5 + 3*z**2/2 + 6*z/5 + 11. Determine d, given that m(d) = 0.
-2, -1, 1
Suppose 4*c**3 + 64*c - 21*c**2 - 23*c**2 + c**2 + 11*c**2 = 0. Calculate c.
0, 4
Let f be 7 + (-1 - -1) + -2. Suppose f*x = -2 + 17. Determine c so that -2/5*c + 0 + 9/5*c**x + 1/5*c**2 + c**5 - 13/5*c**4 = 0.
-2/5, 0, 1
Suppose 4*n + 7 = 2*i - 15, -3*n + 4*i = 14. Let y be n + 7 - 2/(-10). Determine c, given that y*c**2 + 6/5*c + 2/5*c**3 + 2/5 = 0.
-1
Let y(c) = 71*c**3 + 141*c**2 + 91*c + 10. Let g(m) = -14*m**3 - 28*m**2 - 18*m - 2. Let b(l) = 11*g(l) + 2*y(l). What is u in b(u) = 0?
-1, -1/6
Let a(j) = 2*j**2 + 2*j + 2. Let f be a(-1). Factor 6*v + 4*v**3 - f*v**2 - 9*v**3 - 16*v**3 + 17*v**2.
-3*v*(v - 1)*(7*v + 2)
Let y(l) be the second derivative of -l**7/42 + l**6/30 + l. Find q such that y(q) = 0.
0, 1
Let z(o) = -114*o + 1. Let i be z(4). Let q = i - -4099/9. Factor 2/9*s**3 + 0*s - q*s**2 + 0.
2*s**2*(s - 2)/9
Let x(r) be the third derivative of 6*r**7/35 - 7*r**6/10 + r**5/15 + 3*r**4/2 + 4*r**3/3 + 6*r**2. Factor x(o).
4*(o - 2)*(o - 1)*(3*o + 1)**2
Solve 39*h - 54*h**2 + 27*h**2 + 30*h**2 = 0 for h.
-13, 0
Let q(p) be the first derivative of p**5/60 - p**4/24 - p**3/9 + p**2/12 + p/4 + 6. Factor q(x).
(x - 3)*(x - 1)*(x + 1)**2/12
Let c = -11 - -14. Factor 0*d**4 + 3*d + 8*d**2 - c*d**5 - 4*d**4 - 2*d**2 - 2*d**4.
-3*d*(d - 1)*(d + 1)**3
Suppose 3*d - 2*d = 5, -x + 2*d = 10. Let p(w) be the second derivative of -2/7*w**2 + 1/14*w**4 - 1/21*w**3 + x + 3*w. Solve p(t) = 0.
-2/