s f?
-1, 0
Let a = 295/582 + -2/291. Factor -3/4*r**3 - a*r + 5/4*r**2 + 0.
-r*(r - 1)*(3*r - 2)/4
Let g(i) be the second derivative of i**7/2100 - i**6/900 - i**3/3 - 2*i. Let v(p) be the second derivative of g(p). Factor v(s).
2*s**2*(s - 1)/5
Let q(w) be the first derivative of -w**6/2 + 3*w**5/5 - 1. Factor q(f).
-3*f**4*(f - 1)
Let x(l) = 66*l**5 + 78*l**4 - 66*l**3 - 78*l**2 + 27*l. Let q(c) = -5*c**5 - 6*c**4 + 5*c**3 + 6*c**2 - 2*c. Let z(u) = -27*q(u) - 2*x(u). Factor z(t).
3*t**2*(t - 1)*(t + 1)*(t + 2)
Let i(c) = -4*c - 24. Let f be i(-6). Let o be (f + -16)/(-6 + 4). Find t such that 10*t**2 + 8/5 - o*t = 0.
2/5
Suppose 5 = -b + 6. Let f be (b - -3)/4 - -3. Suppose 0*n + 2/3*n**f - 2/3*n**2 - 2/3*n**3 + 2/3*n**5 + 0 = 0. What is n?
-1, 0, 1
Let m = -31 - -33. Factor -9/2*d - 3 - 3/2*d**m.
-3*(d + 1)*(d + 2)/2
Let t = 27 + -23. Solve 4/5*g**3 + 0 + 2/5*g**2 + 0*g + 2/5*g**t = 0.
-1, 0
Let s(r) = -r**2 - 9*r - 8. Let f(t) = -2*t**2 - 3*t + 3. Let u be f(-3). Let m be s(u). Let 3 + m*g - 8*g**2 + 0 - 5 = 0. Calculate g.
1/4, 1
Factor -3/5*y**4 + 0*y + 0 + 3/5*y**3 + 0*y**2.
-3*y**3*(y - 1)/5
Suppose 0 = 4*z - 2*p, p - 8 = -p. Factor -2*m**z + 0*m**2 + 6*m**3 + 5*m**5 - 6*m**4 - 3*m**5.
2*m**2*(m - 1)**3
Factor -1/2*b**2 - 1/2*b**4 + b**3 + 0*b + 0.
-b**2*(b - 1)**2/2
Let a(i) be the second derivative of -i**5/60 + i**4/12 + i**3/18 - i**2/2 - 26*i. Let a(u) = 0. What is u?
-1, 1, 3
Let f = -81/7 - -331/28. Factor 3/2*x**2 + 1/4 + x + x**3 + f*x**4.
(x + 1)**4/4
Suppose 16*x + 14 = 23*x. Factor 2/5*r**x - 4/5 + 2/5*r.
2*(r - 1)*(r + 2)/5
Determine t, given that -2/3*t**2 - 32/3*t - 128/3 = 0.
-8
Let a(v) = 5*v**5 - 12*v**4 + 23*v**2 + 6*v - 6. Let c(k) = k**5 - k**4 - k**2 + 1. Let l(y) = -a(y) + 3*c(y). Let l(p) = 0. Calculate p.
-1, 1/2, 3
Let k(y) = -y**5 - 19*y**4 + 34*y**3 - 34*y**2 + 11*y - 7. Let l(z) = 3*z**5 + 39*z**4 - 69*z**3 + 69*z**2 - 21*z + 15. Let n(r) = 9*k(r) + 4*l(r). Factor n(d).
3*(d - 1)**5
Let a = 5 + -11. Let h = -3 - a. Let -3*c**4 + 3*c**2 + c**h - 3*c**2 + 0*c**4 = 0. What is c?
0, 1/3
Let c(y) be the first derivative of -y**3/3 + 3*y**2 + 7*y - 28. Factor c(s).
-(s - 7)*(s + 1)
Let m(a) be the first derivative of 5*a**3/3 + 6*a**2 + 10*a - 4. Let n(f) = -11*f**2 - 24*f - 19. Let j(z) = -5*m(z) - 2*n(z). Suppose j(w) = 0. What is w?
-2
Let p(h) be the third derivative of -h**5/60 - h**4/12 + h**3/3 - 4*h**2. Let m(f) = -6*f**2 - 10*f + 11. Let x(l) = 6*m(l) - 33*p(l). Factor x(i).
-3*i*(i - 2)
Find u, given that -8*u - 2*u**4 - 2*u**4 + 6*u**3 - 6*u**4 + 8*u**4 = 0.
-1, 0, 2
Suppose 56 = 2*d + 176. Let g = -239/4 - d. Suppose g*w + 1/4*w**2 - 5/4*w**3 + 3/4*w**4 + 0 = 0. What is w?
-1/3, 0, 1
Let q(i) be the third derivative of 3*i**6/40 + i**5/4 - i**4/2 - 2*i**3 + 5*i**2. Factor q(x).
3*(x - 1)*(x + 2)*(3*x + 2)
Suppose -27 = -23*r + 19. Factor -1/6*t**r + 1/3 + 1/6*t.
-(t - 2)*(t + 1)/6
Let o = 18/35 - 4/35. Factor 0 + 2*x**2 - o*x**4 - 2/5*x**5 + 4/5*x + 6/5*x**3.
-2*x*(x - 2)*(x + 1)**3/5
Suppose 0 = 4*s + 1 - 9. Suppose 8 = 3*a + s. Factor 4*o**3 + 1 - a*o**5 - 2*o + 0*o**4 - 3 + 4*o**2 - 2*o**4.
-2*(o - 1)**2*(o + 1)**3
Let x = -37 + 40. Let y be x*2*(-4)/(-6). Determine j so that 5/2*j**5 + 0 - 7/2*j**3 + 3/2*j**y - 3/2*j**2 + j = 0.
-1, 0, 2/5, 1
Factor 0 - 2/3*h**4 + 2/3*h**3 + 0*h + 2/9*h**5 - 2/9*h**2.
2*h**2*(h - 1)**3/9
Factor -1 - x + 3*x - 5*x - 3*x**2 - x**3.
-(x + 1)**3
Let p be (-46)/(-110) + (-92)/(-506). Find n, given that 1/5*n**2 - p*n + 2/5 = 0.
1, 2
Suppose -2*x = -c, 2*c = -2*x - 0*c. Let 4/7*o**3 + x*o**2 + 0*o**4 - 2/7*o - 2/7*o**5 + 0 = 0. What is o?
-1, 0, 1
Let y = -893 + 893. Factor 2/13*a + 4/13*a**2 + 2/13*a**3 + y.
2*a*(a + 1)**2/13
Suppose -5*j + 5*u - 9 - 6 = 0, 4*j + 2*u = 12. Factor -j + 1/2*l + 1/2*l**2.
(l - 1)*(l + 2)/2
Let w = 84 - 82. Let d(z) be the third derivative of 0*z**3 + 4*z**w + 1/15*z**5 + 0*z - 1/24*z**4 + 0. Factor d(n).
n*(4*n - 1)
Let x be 26/24 + ((-5)/(-5))/4. What is c in -10/3*c**2 + 4/3*c**3 - x*c + 10/3*c**4 + 0 = 0?
-1, -2/5, 0, 1
Factor 0 - 2/13*m**2 - 2/13*m.
-2*m*(m + 1)/13
Factor 4/23*b + 2/23 - 6/23*b**2.
-2*(b - 1)*(3*b + 1)/23
Let t be -29 + 0 + -1 + -2. Let y be 4/6 + t/(-24). What is s in y*s + s - 3*s**3 + 0*s**3 = 0?
-1, 0, 1
Let c(s) be the third derivative of 1/315*s**7 + 0 + 0*s + 0*s**3 + 1/336*s**8 + 0*s**5 - 1/360*s**6 + 0*s**4 - 5*s**2. Factor c(z).
z**3*(z + 1)*(3*z - 1)/3
Let a(d) = -d**4 - 4*d**2. Let v(x) = x**3. Let s(n) = 5*a(n) + 20*v(n). Solve s(r) = 0 for r.
0, 2
Let q(o) be the first derivative of o**4/8 + o**3/4 - 8*o + 2. Let r(y) be the first derivative of q(y). Factor r(i).
3*i*(i + 1)/2
Let -3/4*m - 5/4*m**3 + 1/4*m**4 + 0 + 7/4*m**2 = 0. Calculate m.
0, 1, 3
Let w(h) = 4*h**2 - h - 9. Let v = 3 + -13. Let a be 2 + (-2 - v) - 1. Let r(o) = -o**2 + 2. Let g(n) = a*r(n) + 2*w(n). Factor g(p).
-p*(p + 2)
Let f be (-36)/(-342) - (-30)/76. Factor -f*z**2 + 1/2*z + 1.
-(z - 2)*(z + 1)/2
Suppose -r + 3*h + 39 = h, 5 = -5*h. Suppose 0*b = -2*b - 5*t - 10, 0 = 5*b - 3*t - r. Let -5*q + 6*q**2 - 3*q**3 + b*q + 0*q**3 = 0. What is q?
0, 2
Let q(i) be the second derivative of 0*i**2 - 1/12*i**4 + 1/12*i**3 + 8*i + 1/40*i**5 + 0. Factor q(v).
v*(v - 1)**2/2
Let a be -2 - -4 - (-1 - 1). Let r(d) = -d**3 - 5*d**2 - 4*d + 3. Let f be r(-4). Suppose t**a + 3*t**2 + t + f*t**3 + 0*t**3 + 0*t**2 = 0. Calculate t.
-1, 0
Let a(z) be the first derivative of -3*z**5/20 - 3*z**4/16 + 10. Suppose a(k) = 0. Calculate k.
-1, 0
Let n(g) = -52*g**2 + 31*g - 4. Let o(q) = q**2 - q. Let m(v) = -n(v) - 3*o(v). Determine c, given that m(c) = 0.
2/7
Let l(y) be the first derivative of -y**6/15 + 6*y**5/25 - 3*y**4/10 + 2*y**3/15 - 3. Find m, given that l(m) = 0.
0, 1
Let b = -1/53 - -164/265. Factor 0*n**3 - b + 0*n + 6/5*n**2 - 3/5*n**4.
-3*(n - 1)**2*(n + 1)**2/5
Let b(r) = 2*r - r**3 - 2*r. Let h(x) = -6 - 8*x**3 - 1 - x + 8 - 5*x**2. Let y(o) = -5*b(o) + h(o). Factor y(n).
-(n + 1)**2*(3*n - 1)
Let z(k) = 6*k**4 - 7*k**3 + 4*k**2 + 3*k + 3. Let c(b) = -12*b**4 + 15*b**3 - 8*b**2 - 5*b - 5. Let f(q) = 3*c(q) + 5*z(q). Factor f(s).
-2*s**2*(s - 1)*(3*s - 2)
Let y(m) be the second derivative of -m**4/3 + 3*m**3/5 - 2*m**2/5 - 10*m. Factor y(t).
-2*(2*t - 1)*(5*t - 2)/5
Let n be (4/(-5))/(4/(-30)). Suppose -n*a = -a - 10. Find j such that 20*j**2 + 14*j + a + 4*j**2 - 2*j**3 - 2*j + 18*j**3 = 0.
-1/2
Let x(p) be the third derivative of -p**10/60480 - p**9/10080 - p**8/4480 - p**7/5040 + p**4/6 - 3*p**2. Let d(f) be the second derivative of x(f). Factor d(j).
-j**2*(j + 1)**3/2
Find b such that -10*b**2 - 30 + 22 + b**3 - 4*b + 21*b = 0.
1, 8
Factor -8*z - 8*z**2 - 2*z**2 - 51 + 53.
-2*(z + 1)*(5*z - 1)
Let q(i) = -3*i**2 + 27*i. Let y be q(9). Let g(r) be the second derivative of -1/66*r**4 - 2*r + y - 4/33*r**3 - 4/11*r**2. Suppose g(u) = 0. What is u?
-2
Let c be (-2)/3 + (-18)/9. Let d = c - -19/6. Factor 1/2*j**4 - d*j**2 - 1/2*j**3 + 1/2*j + 0.
j*(j - 1)**2*(j + 1)/2
Find q such that -2/9*q**4 + 40/9*q - 16/9 - 4*q**2 + 14/9*q**3 = 0.
1, 2
Let w(f) = f**3 + 7*f**2 - 9*f + 3. Let y(n) = -6*n**3 - 36*n**2 + 46*n - 15. Let c(a) = -11*w(a) - 2*y(a). Factor c(o).
(o - 3)*(o - 1)**2
Let d(a) be the second derivative of 5*a**7/147 - 8*a**6/105 + a**5/70 + a**4/21 + a. Factor d(g).
2*g**2*(g - 1)**2*(5*g + 2)/7
Suppose 13*h - h = 2*h. Suppose 28 = 3*s - 4*f, 7 = -s - 3*f - 1. Factor -2/3*n**s + h*n**3 + 4/3*n**2 - 2/3 + 0*n.
-2*(n - 1)**2*(n + 1)**2/3
Let v(b) be the first derivative of b**3/7 - 3*b/7 + 16. Determine x so that v(x) = 0.
-1, 1
Let s(u) be the second derivative of -3/20*u**5 - 1/6*u**3 + 2*u + 0*u**2 + 1/4*u**4 + 1/30*u**6 + 0. Find c, given that s(c) = 0.
0, 1
Let r = -12 - -47/4. Let y = r + 1/2. Suppose 0*a + 1/4 - y*a**2 = 0. Calculate a.
-1, 1
Let t = 69/8 + -199/24. Suppose -n**2 + t*n**3 + 2/3 + 1/3*n**4 - 1/3*n = 0. Calculate n.
-2, -1, 1
Let w(h) be the first derivative of -h**7/21 + h**6/15 + h**5/10 - h**4/6 + 5*h - 4. Let c(o) be the first derivative of w(o). Factor c(q).
-2*q**2*(q - 1)**2*(q + 1)
Let g be (0 + 4/(-6))*-3. Factor s**2 + g*s - s + s.
s*(s + 2)
Factor -2 - 2/9*t**2 - 20/9*t.
-2*(t + 1)*(t + 9)/9
What is x in 5*x**3 + 30*x**2 + 9*x + 40 + 31*x + 20*x = 0?
-2
Suppose d + 2*y = 3*d - 206, 2*d = 4*y + 212.