.
-1, 1
Let t(y) be the second derivative of -2/27*y**3 + 0*y**2 + 1/54*y**4 - y + 0. Factor t(h).
2*h*(h - 2)/9
Let a(n) be the third derivative of -n**7/50 - 107*n**6/200 - 111*n**5/20 - 205*n**4/8 - 25*n**3 - 34*n**2. Let a(f) = 0. What is f?
-5, -2/7
Let g(h) be the third derivative of 2*h**7/105 + h**6/6 + 3*h**5/5 + 7*h**4/6 + 4*h**3/3 + 38*h**2. Factor g(u).
4*(u + 1)**3*(u + 2)
Find p, given that 5*p - 9*p**3 + 3*p**4 - 8*p**2 - p + 5*p**2 + 5*p = 0.
-1, 0, 1, 3
Suppose 0 = -j - 5*w - 18, w = -2*w - 12. Suppose u = 3*l - 5 - j, 2*l - 6 = 0. Let 0 - 4/5*x - 2/5*x**u = 0. What is x?
-2, 0
Let c(o) = 45*o**3 + 80*o**2 + 90*o - 55. Let p(a) = -5*a**3 - 9*a**2 - 10*a + 6. Let v(x) = -6*c(x) - 55*p(x). Factor v(b).
5*b*(b + 1)*(b + 2)
Let x be (-14)/(-8) + 24/(-16). Factor 0 + x*k**4 + 1/2*k**3 + 0*k + 0*k**2.
k**3*(k + 2)/4
Let a(f) = f**3 - f + 4. Let b be a(0). What is c in -2*c + c**2 + 5*c**2 - c**2 - b*c**2 + 1 = 0?
1
Suppose 0 = -2*l - 0*l. Let i(s) be the third derivative of 0*s**3 + 1/120*s**5 + l + 0*s + 1/48*s**4 + s**2. Factor i(f).
f*(f + 1)/2
Let f(v) = -v**3 + v**2 + v + 1. Let y be (-3)/30*6*-5. Let c(w) = 3*w**2 - 9. Let k(o) = y*f(o) + c(o). Factor k(z).
-3*(z - 2)*(z - 1)*(z + 1)
Solve 2*g**4 - 6*g**4 - g**5 + 0*g**3 - 2*g**2 - 5*g**3 + 0*g**2 = 0.
-2, -1, 0
Factor 0*i**2 + 0 - 3/5*i**4 + 3/5*i**5 + 0*i - 6/5*i**3.
3*i**3*(i - 2)*(i + 1)/5
Let n be (10/25*3)/((-4)/(-20)). Find a such that -17/2*a + n*a**4 + 1 - 43/2*a**3 + 23*a**2 = 0.
1/4, 1/3, 1, 2
Let l(i) be the first derivative of i**8/672 - i**7/210 + i**5/60 - i**4/48 + i**2/2 - 1. Let k(d) be the second derivative of l(d). Let k(a) = 0. What is a?
-1, 0, 1
Solve -1 + 5 + 0 - 7*m**3 - 6*m + 9*m**3 = 0.
-2, 1
Let c(r) be the second derivative of 1/12*r**3 - 1/40*r**5 - 4*r + 0*r**2 + 0*r**4 + 0. Factor c(y).
-y*(y - 1)*(y + 1)/2
Let d be ((-16)/20)/(9/(-110)). Let l = -26/3 + d. Suppose -l*x**5 + 10/9*x**3 - 4/9*x**4 + 0*x + 4/9*x**2 + 0 = 0. What is x?
-1, -2/5, 0, 1
Let o be (-10)/11 - 11/(22/(-4)). Factor -2/11*q**2 + o*q - 18/11.
-2*(q - 3)**2/11
Let f(z) be the third derivative of -2*z**7/735 + z**6/42 - z**5/35 - 3*z**4/14 - 22*z**2. Factor f(j).
-4*j*(j - 3)**2*(j + 1)/7
Suppose -2*z - 3 = -7. Let k(p) = 2*p**3 - 4*p**2 - 2*p. Let f(s) = s**4 + s**3 + s**2 - s. Let b(q) = z*k(q) + 4*f(q). Factor b(j).
4*j*(j - 1)*(j + 1)*(j + 2)
Let f(p) be the first derivative of -p**4/4 - p**3/3 - 9. Factor f(n).
-n**2*(n + 1)
Find d such that -10*d**4 - 7*d + d + 2*d - 14*d**2 - d**3 - 2*d**5 - 17*d**3 = 0.
-2, -1, 0
Let t = 10 - 7. What is p in -4*p + p - 20*p**2 + 9 - t*p + 21*p**2 = 0?
3
Let n(z) be the second derivative of -z**6/300 + z**4/60 - z**2/20 - 3*z. Factor n(r).
-(r - 1)**2*(r + 1)**2/10
Let c(o) be the second derivative of -o**8/6720 - o**7/3780 + o**6/720 + o**5/180 - o**4/6 - 3*o. Let t(y) be the third derivative of c(y). Factor t(h).
-(h - 1)*(h + 1)*(3*h + 2)/3
Let p(r) be the first derivative of -4/9*r + 1/3*r**2 - 1 - 2/27*r**3. Determine z so that p(z) = 0.
1, 2
Factor -2/7*v**5 + 0 + 0*v**2 + 0*v - 4/7*v**3 + 6/7*v**4.
-2*v**3*(v - 2)*(v - 1)/7
Let y(p) be the first derivative of 1/18*p**4 - 1 + 1/2*p**2 + 1/9*p**3 + 1/90*p**5 + 0*p. Let n(c) be the second derivative of y(c). Find b such that n(b) = 0.
-1
Let g(f) be the third derivative of f**5/12 - 55*f**4/24 - 3*f**2 + 13. Let g(w) = 0. What is w?
0, 11
Let r(i) be the second derivative of 20*i**7/21 - 10*i**6/3 + 33*i**5/8 - 25*i**4/12 + 5*i**3/12 - 17*i. Factor r(f).
5*f*(f - 1)**2*(4*f - 1)**2/2
Let x(q) be the second derivative of q**7/420 + q**6/60 + q**5/30 + q**3/2 + 5*q. Let z(h) be the second derivative of x(h). Factor z(j).
2*j*(j + 1)*(j + 2)
Suppose 7*r**5 - 6*r**3 + 21 - 42*r**2 - 5*r**5 + 3*r + 31*r**4 + r**5 - 10*r**4 = 0. What is r?
-7, -1, 1
Let a(f) be the first derivative of 3/10*f**4 + 0*f**2 - 2/15*f**3 + 0*f + 1/15*f**6 - 6/25*f**5 + 2. Solve a(t) = 0 for t.
0, 1
Let l(s) be the second derivative of -s**8/3360 + s**7/315 - s**6/90 + s**4/4 - 3*s. Let n(v) be the third derivative of l(v). Suppose n(i) = 0. Calculate i.
0, 2
Let s(t) be the first derivative of -4 + 1/14*t**4 - 2/7*t**3 - 2/7*t + 3/7*t**2. Suppose s(l) = 0. What is l?
1
Let l = -192 + 196. Let i(m) be the third derivative of 1/9*m**3 + 1/24*m**4 + l*m**2 + 1/180*m**5 + 0 + 0*m. Suppose i(c) = 0. What is c?
-2, -1
Let r(h) be the third derivative of h**9/3024 - h**8/840 + h**6/180 - h**5/120 - h**3/6 - 3*h**2. Let j(k) be the first derivative of r(k). Factor j(n).
n*(n - 1)**3*(n + 1)
Let i(z) be the third derivative of 0*z**3 + 0*z - 2*z**2 + 0 + 0*z**5 - 1/480*z**6 + 1/96*z**4. Factor i(a).
-a*(a - 1)*(a + 1)/4
Let f(c) = c**3 - 4*c**2 - c - 18. Let k be f(5). Factor -1/4*t**k - 1/4*t**4 + 0*t + 0 - 1/2*t**3.
-t**2*(t + 1)**2/4
Let v = 666 - 1994/3. Factor 4/3 - v*q - 4/3*q**2 + 4/3*q**3.
4*(q - 1)**2*(q + 1)/3
Let n be 2 - 0 - (2 - 0). Let x(v) be the first derivative of -1 + v**3 + 4*v**2 + n*v**2 - 10*v**2 + 12*v. Suppose x(k) = 0. What is k?
2
Suppose -s - 2 = -f, 8*s - 3*s = -3*f + 30. Let m be ((-6)/s)/2 + 3. Factor 8*j**2 - 8*j**2 + 2*j**3 + m*j**4.
2*j**3*(j + 1)
Let s(w) be the third derivative of 1/33*w**3 + 4*w**2 + 0*w + 0*w**4 + 0 - 1/330*w**5. Factor s(m).
-2*(m - 1)*(m + 1)/11
Let t(c) be the first derivative of c**5/5 + c**4/2 - 36. Factor t(g).
g**3*(g + 2)
Determine d so that -3/2 + 2*d - 1/2*d**2 = 0.
1, 3
Let -20 - 5*a**2 - 10*a + a**2 - 14*a - 16 = 0. What is a?
-3
Factor -9*k**2 - 2*k + 2*k**2 + 5*k**2 + 12.
-2*(k - 2)*(k + 3)
Let g = 2 - 3. Let s = 3 + g. Factor -n**2 + 0*n**2 + 6*n + 4 + 3*n**s.
2*(n + 1)*(n + 2)
Let k(g) = -9*g**2 + 11*g - 16. Let b(z) = 12*z - 24*z**2 + 4*z**2 + 16*z - 40 - 2*z**2. Let o(j) = -5*b(j) + 12*k(j). Factor o(l).
2*(l - 2)**2
Let s(c) = 2*c**5 + 3*c**4 + 4*c**3 + 2*c**2 - 3*c - 5. Let z(m) = 5*m**5 + 7*m**4 + 8*m**3 + 4*m**2 - 6*m - 11. Let j(i) = 14*s(i) - 6*z(i). Factor j(t).
-2*(t - 2)*(t - 1)*(t + 1)**3
Factor 1/2 - 1/4*z - 1/4*z**2.
-(z - 1)*(z + 2)/4
Let j(s) = s - 1. Let b be j(-5). Let l(r) = -r**3 - r**2 + r + 1. Let x(k) = -8*k**3 - 2*k**2 + 6*k + 6. Let n(a) = b*l(a) + x(a). Factor n(c).
-2*c**2*(c - 2)
Let s(d) be the second derivative of 2*d - 8/27*d**3 + 8/27*d**4 + 1/9*d**2 + 0. Solve s(m) = 0 for m.
1/4
Let u(b) = -b**5 - 4*b**3 + 6*b**2 - b - 6. Let x(g) = 2*g**5 + 7*g**3 - 11*g**2 + 2*g + 11. Let p(n) = 11*u(n) + 6*x(n). Find z such that p(z) = 0.
-1, 0, 1
Let n = -542 - -542. Factor -1/5*y**5 + 0 - 3/5*y**4 - 1/5*y**2 + n*y - 3/5*y**3.
-y**2*(y + 1)**3/5
Suppose -l - 3*l = 7*l. Factor -1/2*q + l - 1/2*q**3 - q**2.
-q*(q + 1)**2/2
Let i(q) be the third derivative of 1/175*q**7 + 1/840*q**8 + 0*q**4 + 1/100*q**6 + 0*q - q**2 + 1/150*q**5 + 0 + 0*q**3. Factor i(d).
2*d**2*(d + 1)**3/5
Let l be (2/(-6))/(3/(-45)). Suppose -4*x = 3*z + 3 - 2, -z - l = -x. Solve 22/5*c - 4/5 - 14/5*c**5 + 32/5*c**4 - 28/5*c**x - 8/5*c**3 = 0 for c.
-1, 2/7, 1
Let d(w) = -w**2 - 9*w + 10. Let v be d(-10). Suppose 0*m - 2*x = -5*m - 10, v = 2*m + 3*x - 15. Factor m*s**4 + 1/4*s + 0*s**2 + 1/4*s**5 - 1/2*s**3 + 0.
s*(s - 1)**2*(s + 1)**2/4
Let r(p) be the second derivative of -1/2*p**2 + 0 + p + 0*p**4 + 1/30*p**6 - 1/10*p**5 + 1/3*p**3. Factor r(b).
(b - 1)**3*(b + 1)
Suppose 3*z - 25 = -2*z. Let c(n) be the first derivative of 0*n - 1/3*n**2 - 1/9*n**6 + 1/3*n**4 + 0*n**z + 0*n**3 + 1. What is s in c(s) = 0?
-1, 0, 1
Let f(a) = a**3 + 2*a**2 - 2*a - 1. Suppose 0*u - 2*u - 4 = 0. Let s be f(u). Determine b, given that 6*b - b**s - 6*b - b**2 = 0.
-1, 0
Let j(q) = -5*q**5 - 6*q**4 - 8*q**3 - 6*q**2 + q - 6. Let x(h) = -4*h**5 - 5*h**4 - 7*h**3 - 5*h**2 + h - 5. Let n(g) = 5*j(g) - 6*x(g). Factor n(t).
-t*(t - 1)**2*(t + 1)**2
Let o be (-3)/2*12/(-9). Determine x, given that -2*x**3 + 3*x - x**3 - o*x + 2*x**3 - x**2 + x**4 = 0.
-1, 0, 1
Solve 2*g**3 - 3*g**3 + 2*g**3 - 6*g**2 + 4*g + g**3 = 0 for g.
0, 1, 2
Let b = -37 - -113/3. Let b*s**3 + 0 - 7/3*s**4 + 7/3*s**2 - 2/3*s = 0. Calculate s.
-1, 0, 2/7, 1
Factor -5 + 0 + 4*f + 5*f**2 - f**3 - 4*f**2 + 1.
-(f - 2)*(f - 1)*(f + 2)
Let a(j) be the first derivative of j**5/120 - j**4/96 + 4*j**2 - 1. Let d(g) be the second derivative of a(g). Let d(y) = 0. What is y?
0, 1/2
Let a(q) = -q**3 + 3*q**2 + 5*q - 6. Let k