 1)**3*(q + 4)/7
Let z(k) be the third derivative of 1/112*k**8 + 0*k**3 + 0*k**7 + 0*k + 0*k**4 + 0*k**5 + 6*k**2 - 1/40*k**6 + 0. Factor z(c).
3*c**3*(c - 1)*(c + 1)
Let m be 4/14 - (-207)/378. Let f(c) be the second derivative of -c + 0 + 0*c**2 - 3/10*c**5 - m*c**4 - 2/3*c**3. Find h such that f(h) = 0.
-1, -2/3, 0
Let l(g) be the third derivative of 1/180*g**6 - 1/945*g**7 - 1/54*g**4 + 0*g + 2*g**2 + 0*g**3 + 0 + 1/270*g**5 - 1/1512*g**8. Find p such that l(p) = 0.
-2, -1, 0, 1
Factor -4/9*i + 0 + 2/9*i**2.
2*i*(i - 2)/9
Let x be 8/(-96) + 6/8. What is c in 4/3*c**2 + 2/3 + x*c**5 - 2*c**4 - 2*c + 4/3*c**3 = 0?
-1, 1
Let w = -36 + 38. Determine l so that -2/7*l**w - 2/7 - 4/7*l = 0.
-1
Find p, given that 45/2*p**3 + 1/4*p**5 + 135/2*p**2 + 243/4 + 405/4*p + 15/4*p**4 = 0.
-3
Let f(u) = 17*u**2 + 152*u + 568. Let m(x) = 11*x**2 + 101*x + 379. Let a(k) = 5*f(k) - 8*m(k). Factor a(t).
-3*(t + 8)**2
Let f(v) be the third derivative of 0*v - 1/70*v**7 + v**2 + 0*v**5 + 0*v**6 + 1/112*v**8 + 0 + 0*v**3 + 0*v**4. Factor f(y).
3*y**4*(y - 1)
Let t(o) = -o**3 - 3*o**2 - 7*o - 4. Let i be t(-5). Let f be 45/i + (-1)/(-3). Factor 8/9*w + 2/9*w**2 + f.
2*(w + 2)**2/9
Let 0 + 1/7*b**4 + 1/7*b**3 + 0*b + 0*b**2 = 0. What is b?
-1, 0
Let h(k) be the second derivative of k**7/273 - k**6/195 + 9*k. Determine v, given that h(v) = 0.
0, 1
Let s(o) = -1 - 2 + 6*o - 5 + 6. Let p be s(1). Factor 0*x + 3/4*x**p + 0 + x**3 - x**2.
x**2*(x + 2)*(3*x - 2)/4
Let -1/7*b**3 + 3/7 + 5/7*b + 1/7*b**2 = 0. Calculate b.
-1, 3
Let s(q) be the second derivative of q**4/36 - 2*q**3/9 + 2*q**2/3 + 8*q. Solve s(h) = 0 for h.
2
Let z be 8/6*(2/2)/2. Let r(u) be the first derivative of 1/6*u**6 + 1/2*u - u**2 - 2 + 1/4*u**4 - 1/2*u**5 + z*u**3. Factor r(x).
(x - 1)**3*(x + 1)*(2*x - 1)/2
Let d = 48/5 - 187/20. Factor -d*t**2 - 1/2 - 3/4*t.
-(t + 1)*(t + 2)/4
Factor 5*o**3 - 9*o**3 + 4*o**5 + 1 - 1.
4*o**3*(o - 1)*(o + 1)
Let r(p) be the third derivative of -p**6/120 + 3*p**5/40 - p**4/4 + p**3 - 3*p**2. Let a(j) be the first derivative of r(j). Factor a(l).
-3*(l - 2)*(l - 1)
Let b(m) = -10*m**2 + 4*m + 8. Let h(z) = 21*z**2 - 8*z - 16. Let c(u) = -13*b(u) - 6*h(u). Factor c(s).
4*(s - 2)*(s + 1)
Let x(n) be the second derivative of n**5/270 - n**4/108 - 2*n**3/27 - n**2/2 + n. Let k(g) be the first derivative of x(g). Factor k(s).
2*(s - 2)*(s + 1)/9
Let j(d) be the second derivative of d**5/30 - d**4/12 - 2*d**2 + 4*d. Let k(q) be the first derivative of j(q). Factor k(n).
2*n*(n - 1)
Let t = -11 + 22. Let p(d) = d**5 - 10*d**4 + 20*d**3 + 20*d**2 + d - 21. Let g(v) = -2*v**4 + 4*v**3 + 4*v**2 - 4. Let c(n) = t*g(n) - 2*p(n). Factor c(w).
-2*(w - 1)**2*(w + 1)**3
Let l(k) = k + 2. Let j(o) = 2*o + 3. Let y(x) = -2*j(x) + 3*l(x). Let v be y(-4). Factor w + 1 + v*w + 3*w**3 - 7*w**2 - 2.
(w - 1)**2*(3*w - 1)
Let b = -88/5 - -18. Let w be (0/(-1))/(10 + -11 - -3). Factor 2/5*f + w + 4/5*f**2 + b*f**3.
2*f*(f + 1)**2/5
Let u(j) be the second derivative of j**6/15 + j**5/2 + 7*j**4/6 + j**3 + 34*j. Suppose u(t) = 0. What is t?
-3, -1, 0
Let a be (1/3)/(5/465). Let i = a - 92/3. What is g in 0*g + i - 1/3*g**2 = 0?
-1, 1
Let h be 5 + 3 + 0/2. Determine f, given that -20 - 6*f**5 + 60*f**4 - 30*f - h*f**5 + 24 - 100*f**3 + 80*f**2 = 0.
2/7, 1
Let x(f) be the third derivative of -f**6/24 - f**5/6 - 5*f**4/24 - 16*f**2. Find p, given that x(p) = 0.
-1, 0
Let o(v) be the third derivative of v**7/175 + 11*v**6/300 + v**5/10 + 3*v**4/20 + 2*v**3/15 + 7*v**2. Suppose o(q) = 0. What is q?
-1, -2/3
Let s(c) = c**3 + 11*c**2 - 29*c - 317. Let z be s(-11). Factor 0*x + 1/2*x**z - 1/2*x**4 + 0*x**3 + 0.
-x**2*(x - 1)*(x + 1)/2
Factor 2/3*u**2 - 2/3*u**3 - 2/3 + 2/3*u.
-2*(u - 1)**2*(u + 1)/3
Let s(j) = -j**2 - 8*j + 3. Let h be s(-8). Suppose h*z = z + 12. Find a, given that 5*a**3 + 3*a - 3*a**3 + 3*a + z*a**2 - 2*a = 0.
-2, -1, 0
Suppose -3*r + 224 = 4*r. Let q = r + -28. Factor 2/9*f**2 + 2/9*f - 2/9*f**q - 2/9*f**3 + 0.
-2*f*(f - 1)*(f + 1)**2/9
Suppose 2*d + 4 = -4. Let s(v) = v + 6. Let o be s(d). Let -2 + 6*t**2 - 4*t**4 + 0*t**3 - 2*t + o*t**3 + 0*t**2 = 0. What is t?
-1, -1/2, 1
Let u(b) be the second derivative of -b**4/30 - 14*b**3/15 - 49*b**2/5 + 27*b. Determine o, given that u(o) = 0.
-7
Suppose 6 = 2*a + 2. Suppose -4*y + a*c + 3*c = 3, -3*c = -9. Factor -5/3*q**y + 2/3*q - q**2 + 0.
-q*(q + 1)*(5*q - 2)/3
Determine g, given that 3/2*g**3 - 3/2*g - 9/2*g**2 + 3/2 + 3*g**4 = 0.
-1, 1/2, 1
Let q be 75/5 + (-2)/(-1). Let l = -151/9 + q. Determine g, given that l*g**2 + 0*g + 0 = 0.
0
Let o(s) = 5*s - 6. Let z be o(3). Let l(k) = -12*k**2 - 21*k - 12. Let h(i) = -i - 1. Let w(b) = z*h(b) - l(b). Factor w(q).
3*(2*q + 1)**2
Let d = 2 - 2. Suppose 4*i + 19 = 5*s + 6*i, d = 2*s + 4*i - 14. Factor -w + s*w**2 - 3*w**2 + w**2.
w*(w - 1)
Let w = -591 - -594. Factor 1/5*f**w + 0*f**2 + 0 - 1/5*f.
f*(f - 1)*(f + 1)/5
Let p = 7/6 + -5/6. Factor 0 - p*r**4 - 2/3*r**2 + 7/6*r**3 - 2/3*r.
-r*(r - 2)**2*(2*r + 1)/6
Let z be (-60)/(-14) - (-16)/(-4). Factor -z*v**4 + 2/7*v + 4/7*v**2 - 4/7*v**3 - 2/7 + 2/7*v**5.
2*(v - 1)**3*(v + 1)**2/7
Let s(a) be the third derivative of a**5/15 - 3*a**4/2 - 44*a**3/3 + 5*a**2 - 3. Factor s(d).
4*(d - 11)*(d + 2)
Let k = 11 + -39. Let q(u) = -2*u**3 - 2*u**2 + 3*u. Let i(a) = -10*a**3 - 10*a**2 + 14*a. Let r(c) = k*q(c) + 6*i(c). Let r(s) = 0. What is s?
-1, 0
Let n be (3/(-57))/((-3)/(-9)). Let g = 31/76 + n. Factor g*x + 0 - 3/4*x**2 + 1/2*x**3.
x*(x - 1)*(2*x - 1)/4
Factor 40*i + 3*i**2 + i**2 - 45 + 145.
4*(i + 5)**2
Let m(k) be the second derivative of k**5/90 + k**4/9 + 4*k**3/9 + 7*k**2/2 - 4*k. Let c(p) be the first derivative of m(p). Let c(x) = 0. Calculate x.
-2
Let r(l) be the second derivative of -3*l**5/140 - l**4/7 - 5*l**3/14 - 3*l**2/7 - 9*l. Suppose r(i) = 0. What is i?
-2, -1
Let x be (-1)/6 - (-522)/540. Determine t so that -x - 1/5*t**2 - 4/5*t = 0.
-2
Let g(o) be the second derivative of 1/8*o**3 + 0*o**2 + 0*o**6 + 2*o + 0*o**4 + 1/56*o**7 + 0 - 3/40*o**5. Factor g(u).
3*u*(u - 1)**2*(u + 1)**2/4
Let o be 361/180 - (-26)/(-13). Let f(a) be the third derivative of 1/630*a**7 + 0 + 0*a**4 + 0*a**3 + 1/180*a**5 + 2*a**2 + 0*a - o*a**6. Factor f(b).
b**2*(b - 1)**2/3
Let z(b) be the first derivative of 3 + 5/4*b**2 + b + 1/8*b**4 + 2/3*b**3. Factor z(a).
(a + 1)**2*(a + 2)/2
Let y = 11 + -9. Let l(h) be the first derivative of 4*h - 6*h**y - 7/3*h**3 + 2. Solve l(s) = 0.
-2, 2/7
Factor -4 + 6*j**2 + 2*j**2 - 3*j**4 - j**4.
-4*(j - 1)**2*(j + 1)**2
Let f(z) = -z**5 - z**4 - z**2 - 1. Let o(a) = -2*a**5 - 5*a**4 - 9*a**3 + a**2 - 5. Let b(g) = 5*f(g) - o(g). Solve b(h) = 0 for h.
-2, 0, 1
Let a be 36/10 + 18/(-30). Suppose -a*y + y = 0. Solve y*m + 0 + 2/3*m**2 - 3*m**3 = 0 for m.
0, 2/9
Let c(n) be the third derivative of -n**5/240 - n**4/48 + 4*n**2. Solve c(p) = 0.
-2, 0
Let x(c) be the first derivative of 3 - 1/6*c**3 + 1/2*c + 3/4*c**2 - 3/8*c**4. Factor x(d).
-(d - 1)*(d + 1)*(3*d + 1)/2
What is f in -75/2*f - 45/2*f**2 + 125/2 - 5/2*f**3 = 0?
-5, 1
Solve 19/5*g**2 + 17/5*g - 2/5 = 0 for g.
-1, 2/19
Let g(b) be the first derivative of b**4/4 - 13*b**3/12 + 11*b**2/8 - b/2 + 4. Factor g(u).
(u - 2)*(u - 1)*(4*u - 1)/4
Let o be 16/(-56) - (-2)/((-210)/(-37)). Let z(h) be the second derivative of -1/36*h**4 + 0 + o*h**5 + 1/6*h**2 - 2/9*h**3 - 2*h. Factor z(s).
(s - 1)*(s + 1)*(4*s - 1)/3
Find k, given that -6/13*k + 4/13 + 2/13*k**2 = 0.
1, 2
Let t(b) be the first derivative of b**3/3 - 2*b**2 - 5. Let g be t(5). Find y, given that -y**g + 0*y - 1/4*y**2 + 3/4*y**3 + 0 + 0*y**4 = 0.
-1, 0, 1/2
Find i such that -42/5*i**3 + 0 - 2*i**5 - 34/5*i**4 - 4/5*i - 22/5*i**2 = 0.
-1, -2/5, 0
What is k in 0*k**2 + 1/3*k**4 + 0*k**3 + 0*k + 0 = 0?
0
Let a = 6042 - 90697/15. Let v = 14/3 + a. Suppose -j**4 - 1/5*j**5 - 7/5*j**3 + v*j**2 + 4/5 + 8/5*j = 0. Calculate j.
-2, -1, 1
Let s(w) be the first derivative of 2/27*w**3 + 0*w + 1/9*w**2 - 2/45*w**5 - 1/18*w**4 + 4. Factor s(x).
-2*x*(x - 1)*(x + 1)**2/9
What is r in 20*r - 81 + 34 - 4*r**2 + 23 = 0?
2, 3
Let p be 2/4 - (-20)/(-70). Let h = 23/42 - p. Factor h*t + 0 - 1/3*t**2.
-t*(t - 1)/3
Let h = -4 + 4. Let -3*r + h*r**2 + 2*r**2 + 8 + r - 6*r = 0. Calculate r.
2
Let t be (18/(-6) - -11)/(0 +