 + 2)**2
Let x(k) = -5*k**4 + 15*k**2. Let u(a) = a**5 + 4*a**4 - 16*a**2 - a. Let j(w) = -5*u(w) - 6*x(w). Let j(n) = 0. Calculate n.
-1, 0, 1
Let p(c) be the second derivative of c**8/1176 - c**7/735 - c**6/420 + c**5/210 + 2*c**2 + 4*c. Let x(i) be the first derivative of p(i). Factor x(j).
2*j**2*(j - 1)**2*(j + 1)/7
Let s = 185/564 - -1/188. Factor -u**4 + 0 - s*u**5 - u**3 - 1/3*u**2 + 0*u.
-u**2*(u + 1)**3/3
Factor -2*r + 0 - 169/2*r**3 - 26*r**2.
-r*(13*r + 2)**2/2
Let k(o) = 2*o**2 - 3 - 4*o**3 + 1 + 2*o - 4*o**3 + 7*o**3. Let q be k(2). Let 10/7*s + 6/7*s**4 - 4/7 - 2/7*s**q - 10/7*s**3 = 0. What is s?
-1, 2/3, 1
Let l be 480/(-42) + 2/2. Let w = l - -11. Factor w + 2/7*q**2 - 6/7*q.
2*(q - 2)*(q - 1)/7
Let a(s) be the first derivative of -s**4/44 - s**3/11 - s**2/11 + 19. Let a(f) = 0. What is f?
-2, -1, 0
Let c(k) be the third derivative of -k**6/60 - 7*k**5/120 - k**4/24 + k**3/12 + 11*k**2. Factor c(m).
-(m + 1)**2*(4*m - 1)/2
Suppose 9/2*b - 3/2*b**2 + 3/2 - 9/2*b**3 = 0. What is b?
-1, -1/3, 1
Let m(k) = k**2 + k + 2. Let j be m(-2). Find o, given that 4*o**2 + 4*o**3 - 2*o**2 - 6*o**j + 8*o**4 = 0.
-1, 0
Let v = 8/9 + -2/9. Let 0 - 1/3*q**4 - v*q**3 - 1/3*q**2 + 0*q = 0. What is q?
-1, 0
Determine p, given that 46/9*p**2 - 16/9*p + 50/9*p**5 - 8/9 - 110/9*p**4 + 38/9*p**3 = 0.
-2/5, 1
Factor 134*r + 45*r**3 - 25*r**2 + 145*r**2 + 5*r**4 - 54*r.
5*r*(r + 1)*(r + 4)**2
Let s(a) be the first derivative of 2*a**3/21 + a**2/7 + 3. Factor s(u).
2*u*(u + 1)/7
Find y, given that 1/2*y**2 - 1/2*y**4 + 1/4*y**5 + 0*y**3 - 1/4*y + 0 = 0.
-1, 0, 1
Let j(g) be the third derivative of -g**6/180 - g**5/60 - g**4/72 - 36*g**2. Factor j(t).
-t*(t + 1)*(2*t + 1)/3
Let g = 7555/9 - 839. Let h be 3*2*2/54. Factor -2/9*a - 2/9*a**5 - 2/9*a**4 + g*a**3 + 4/9*a**2 - h.
-2*(a - 1)**2*(a + 1)**3/9
Factor 5*r**2 - 4*r + 8*r**2 + 2 - 11*r**2.
2*(r - 1)**2
Let q(b) be the first derivative of -3/4*b**4 + 0*b + 1/2*b**6 + 0*b**2 - 3/5*b**5 + b**3 - 6. Factor q(y).
3*y**2*(y - 1)**2*(y + 1)
Let x(n) be the first derivative of 3 + 3/20*n**4 + 0*n + 3/25*n**5 - 1/5*n**3 - 3/10*n**2. Let x(k) = 0. Calculate k.
-1, 0, 1
Let x(v) be the first derivative of 2/3*v**3 + v**2 - 1/2*v**4 - 2*v - 4. Solve x(f) = 0 for f.
-1, 1
Let a(s) be the third derivative of s**7/70 + s**6/40 - s**5/20 - s**4/8 - 17*s**2. What is u in a(u) = 0?
-1, 0, 1
Suppose -4*p = -9*p + 10. Let u(m) = 3*m - 4*m**3 + p + 0 - 4. Let j(d) = d**3 + d**2 + 1. Let r(k) = j(k) + u(k). Find b, given that r(b) = 0.
-1, 1/3, 1
Factor -8*b**3 - 8*b**3 + 13*b**3.
-3*b**3
What is j in -4*j**4 + 7*j - 8*j**2 + 10*j**3 + 0*j - 3*j - 2*j = 0?
0, 1/2, 1
Let q(m) be the second derivative of -21*m**5/20 + 5*m**4/4 + m**3 + 18*m. Factor q(r).
-3*r*(r - 1)*(7*r + 2)
Let s(n) be the second derivative of n**6/35 - n**5/14 - n**4/42 + 5*n**3/21 - 2*n**2/7 + 2*n. Find v, given that s(v) = 0.
-1, 2/3, 1
Factor -534*p**2 - 3*p + 3 + 525*p**2 - 2*p**3 + 6*p**4 + 5*p**3.
3*(p - 1)*(p + 1)**2*(2*p - 1)
Find o, given that -8/9 - 4/9*o + 8/9*o**2 + 4/9*o**3 = 0.
-2, -1, 1
Let g(f) be the second derivative of 1/84*f**7 + 0*f**3 + 3/40*f**5 + 1/24*f**4 + 1/20*f**6 + 0*f**2 + 0 + f. What is n in g(n) = 0?
-1, 0
Let n(d) be the second derivative of 1/60*d**6 - 1/10*d**5 - d + 1/21*d**7 - 1/24*d**4 + 0*d**3 + 0 + 0*d**2. Determine q so that n(q) = 0.
-1, -1/4, 0, 1
Let a(i) be the third derivative of i**5/180 + i**4/72 - 22*i**2. Factor a(j).
j*(j + 1)/3
Factor 0 - 4/5*x**3 + 4/5*x**2 + 8/5*x.
-4*x*(x - 2)*(x + 1)/5
Let x(l) be the first derivative of 0*l + 1/16*l**4 - 1/20*l**5 + 1/12*l**3 - 4 - 1/8*l**2. Factor x(z).
-z*(z - 1)**2*(z + 1)/4
Suppose 3*o - 9 = 3*i, -4*o - i + 2*i = -12. Factor 1/4*c**4 + 1/4*c**o + 0*c - 1/2*c**5 + 0 + 0*c**2.
-c**3*(c - 1)*(2*c + 1)/4
Let n = 323997 + -2263918/7. Let a = -567 + n. Find k such that 4/7 - 86/7*k**3 + a*k**2 - 34/7*k + 24/7*k**4 = 0.
1/4, 1/3, 1, 2
Factor 0 + 1/4*m**2 - 2*m**3 + 2*m - 1/4*m**4.
-m*(m - 1)*(m + 1)*(m + 8)/4
Let o(y) be the second derivative of y**5/90 - y**3/27 + 9*y. Factor o(n).
2*n*(n - 1)*(n + 1)/9
Let m(i) be the first derivative of 16*i**6/39 + 16*i**5/13 + 25*i**4/26 - 10*i**3/39 - 5*i**2/13 + 2*i/13 + 8. Let m(r) = 0. Calculate r.
-1, 1/4
Let c(v) be the third derivative of -v**11/110880 + v**9/20160 - v**5/20 + 4*v**2. Let z(x) be the third derivative of c(x). Factor z(s).
-3*s**3*(s - 1)*(s + 1)
Let n(d) = -3*d + 1. Let i be n(1). Let b be i - (-8)/(-20)*-6. Suppose -b - 2/5*j**3 - 6/5*j - 6/5*j**2 = 0. What is j?
-1
Let u be (6/21)/((-9)/(-21)). Suppose -2 - 2 = -o. Factor 1/3*n**o - 1/3 + 0*n**2 + 2/3*n - u*n**3.
(n - 1)**3*(n + 1)/3
Let q = -9 + 14. Factor -2*p**4 - 2*p**5 + 48*p**2 + 2*p**3 - 46*p**2 + 0*p**q.
-2*p**2*(p - 1)*(p + 1)**2
Solve -1/3*o + 1/2 - 1/6*o**2 = 0.
-3, 1
Suppose -42*u = 4*u - 92. Factor -2/13*v**u - 4/13*v - 2/13.
-2*(v + 1)**2/13
Let p(t) be the first derivative of -t**4/4 - t**3/3 - t + 2. Let h(x) = -4*x**3 - 2*x**2 - 3. Let i(r) = -2*h(r) + 6*p(r). Let i(q) = 0. Calculate q.
0, 1
Suppose 42*j**2 + 2*j**4 - 11*j + 3 - 23*j**2 - 11*j**3 - 2*j = 0. Calculate j.
1/2, 1, 3
Let j(n) = -n**4 - 7*n**3 + 8*n**2 + 6. Let z(s) = -s**3 + s**2 + 1. Let v(w) = -j(w) + 6*z(w). Solve v(a) = 0.
-2, 0, 1
Let j(m) be the third derivative of -6*m**2 + 0*m**4 + 0*m + 1/40*m**6 + 0 + 0*m**3 + 1/60*m**5. Factor j(h).
h**2*(3*h + 1)
Let w(d) be the first derivative of d**4/24 + d**3/6 + d**2/4 + 3*d - 3. Let u(h) be the first derivative of w(h). Factor u(z).
(z + 1)**2/2
Suppose -4/7*n**2 - 2/7*n**3 + 0*n + 0 = 0. What is n?
-2, 0
Let p(d) = 10*d + 18. Let j(y) = -y**2 + 9*y + 19. Let l(k) = -2*j(k) + 3*p(k). Let l(i) = 0. What is i?
-4, -2
Let z be (-3)/(1/(-1) + 0). Factor z*g - g + 2*g**3 - 4*g**2 + 0*g**3.
2*g*(g - 1)**2
Let s(q) be the first derivative of 2*q**6/3 + 24*q**5/5 + 13*q**4 + 16*q**3 + 8*q**2 + 13. Solve s(a) = 0.
-2, -1, 0
Let l = 391/780 + -1/780. Factor 1/4*p**2 - 1/4*p - l.
(p - 2)*(p + 1)/4
Let u(d) be the second derivative of 0*d**2 + 1/12*d**4 + 0 + 0*d**3 - 1/20*d**5 - 3*d. What is z in u(z) = 0?
0, 1
Let t(a) be the first derivative of -2*a**3/11 + 2*a**2/11 + 6. Let t(r) = 0. Calculate r.
0, 2/3
Suppose 0*m - 4/5*m**3 + 0 - 8/5*m**2 = 0. What is m?
-2, 0
Let s be 2/(-18) - (-415)/90. Suppose 3*x - s - 1/2*x**2 = 0. Calculate x.
3
Let r(j) be the first derivative of -j**4/5 + 7*j**3/15 + j**2/5 + 6. Suppose r(u) = 0. Calculate u.
-1/4, 0, 2
Suppose 4*t + 37 = -5*o - 8, 2*o = -4*t - 42. Let l be 4/(-10) - 9/t. Factor -1/2*h**2 + 0 - l*h.
-h*(h + 1)/2
Let y(p) be the first derivative of 0*p**2 + 0*p + 1 + 1/12*p**3 - 1/16*p**4. Solve y(z) = 0 for z.
0, 1
Let r = -1586/7 + 228. Factor -2*p**3 + 0 + r*p**2 + 4/7*p.
-2*p*(p - 1)*(7*p + 2)/7
Let v(r) be the first derivative of -r**7/315 - r**6/180 + r**5/90 + r**4/36 + 2*r**2 + 4. Let p(h) be the second derivative of v(h). Let p(o) = 0. Calculate o.
-1, 0, 1
Let t(g) = -5*g**5 - g**4 + 3*g**3 + g**2 + 5*g + 3. Let l(r) = -14*r**5 - 4*r**4 + 8*r**3 + 4*r**2 + 14*r + 8. Let h(z) = 3*l(z) - 8*t(z). Factor h(y).
-2*y*(y - 1)*(y + 1)**3
Let f be -4 + (-12)/(-8) - -3. Let z(y) = -y**3 - y**2 + y + 2. Let u be z(-2). Factor 1/2*b**u + 0*b**2 + 0*b + 0 - f*b**3.
b**3*(b - 1)/2
Let y(o) be the third derivative of o**5/30 - o**4/4 - 4*o**3/3 - 7*o**2. Factor y(f).
2*(f - 4)*(f + 1)
Let b(v) be the third derivative of -1/672*v**8 - 1/48*v**4 + 1/60*v**5 + 1/120*v**6 + 0*v + 0 - 1/12*v**3 + v**2 - 1/420*v**7. Find a such that b(a) = 0.
-1, 1
Let n(h) be the first derivative of 1/2*h**3 - 3/8*h**2 + 3/16*h**4 - 6 - 3/2*h. Factor n(w).
3*(w - 1)*(w + 1)*(w + 2)/4
Suppose -3/5*a + 6/5 - 3/5*a**2 = 0. Calculate a.
-2, 1
Let -1/4 + 0*h**2 - 1/2*h + 1/2*h**3 + 1/4*h**4 = 0. Calculate h.
-1, 1
Suppose 0 + 1/2*p**2 - p = 0. Calculate p.
0, 2
Suppose -g + 23 = -3*c, -14 = -4*c + 3*c - 4*g. Let d = c - -8. Factor 2 - 2*n**d + n**2 - n**2.
-2*(n - 1)*(n + 1)
Let a be (-3)/(-15) - (8/(-20) - 0). Factor -2/5*b**2 - 1/5*b**5 + a*b**4 - 1/5 - 2/5*b**3 + 3/5*b.
-(b - 1)**4*(b + 1)/5
Let t(s) be the second derivative of s**4/96 + s**3/12 + s**2/4 - 24*s. Factor t(z).
(z + 2)**2/8
Suppose c = -0*c - 1. Let a be (c - -2)*1/2. Factor 0 - a*u**2 + 1/2*u.
-u*(u - 1)/2
Suppose z + 5*h = 0, 4*h - 8 = 2*z + 6.