*j + 20 = 5*j + 5*l, -2*j - 4*l + 16 = 0. What is k in -2/9*k**5 - 2/9*k + 8/9*k**4 - 4/3*k**3 + 8/9*k**2 + j = 0?
0, 1
Let u = -554 - -558. Factor 8/3*j + 0 - 4*j**2 - 6*j**3 + 9*j**u.
j*(3*j - 2)**2*(3*j + 2)/3
Let z be 0*(-4)/(1 - -3). Let t(o) be the second derivative of 0*o**3 - 2*o + 0*o**2 + 3/20*o**5 - 1/12*o**4 + 2/15*o**6 + z. Factor t(x).
x**2*(x + 1)*(4*x - 1)
Let t(i) be the third derivative of 1/40*i**5 - 1/8*i**4 + 0 - 1/480*i**6 + 4*i**2 + 1/3*i**3 + 0*i. Factor t(c).
-(c - 2)**3/4
Let g(m) be the first derivative of 1/3*m**3 + 1/2*m**2 - 3 - 2*m. Factor g(r).
(r - 1)*(r + 2)
Let q = 10 + -8. Let p = -5 - -8. Find b, given that -3*b**5 + b**3 + 2*b**5 + 0*b**q - 2*b**2 + p*b**2 - b**4 = 0.
-1, 0, 1
What is s in -70*s**4 - 11*s**2 - 4 + s**3 + s**5 + 73*s**4 - 12*s - 2*s**3 = 0?
-2, -1, 2
Let p = 8 - 7. Let s(u) = -u - 1. Let c(k) = -3*k**2 - 5*k + 1. Let m(i) = p*s(i) + c(i). Factor m(o).
-3*o*(o + 2)
Let n(y) = -2*y**5 - 4*y**4 + 8*y**3 + 4*y**2 - 2*y + 4. Let a(d) = -d**3 + 2*d**2 + d**4 + 0 - 1 - 3*d**2. Let l(t) = 4*a(t) + n(t). Factor l(w).
-2*w*(w - 1)**2*(w + 1)**2
Let j(o) be the first derivative of -14*o + 3*o**2 - 1 + 4/3*o**3. Let f(q) = -q**2 - 2*q + 5. Let s(p) = 8*f(p) + 3*j(p). Factor s(x).
2*(x + 1)*(2*x - 1)
Let k(o) be the first derivative of -o**5/10 + 3*o**4/8 + o**3/6 - 3*o**2/4 - 51. Factor k(p).
-p*(p - 3)*(p - 1)*(p + 1)/2
Let m(c) be the first derivative of 12/7*c**2 - 16/7*c - 11/14*c**4 + 12/35*c**5 - 1 - 1/21*c**6 + 4/21*c**3. Suppose m(z) = 0. Calculate z.
-1, 1, 2
Let u(f) be the third derivative of 0*f**4 + 1/210*f**5 - 1/735*f**7 + 0*f**3 + 4*f**2 + 0*f**6 + 0 + 0*f. Factor u(h).
-2*h**2*(h - 1)*(h + 1)/7
Suppose i - 48 = -23*i. Factor -1/2 + 1/4*y**i + 1/4*y.
(y - 1)*(y + 2)/4
What is o in 0 + 1/5*o + 1/5*o**2 = 0?
-1, 0
Suppose f - 41 = 4. Suppose -f = 3*u - 8*u. What is z in 0 + 5*z**2 + u*z - z + z**3 + 4 = 0?
-2, -1
Factor -w**3 + 0*w - 5/4*w**2 + 0.
-w**2*(4*w + 5)/4
Let d = 31 - 21. Factor v**5 + 20*v**3 + 2 - 20*v**2 - 10*v**4 + v**5 - 4 + d*v.
2*(v - 1)**5
Let q(f) = f**3 + 2*f**2 - 1. Let a be q(1). Factor -u**4 + 4*u**3 - 3*u**2 + 6*u**4 + 5*u**a - 3*u**4.
2*u**2*(u + 1)**2
Let l(p) be the third derivative of -p**5/12 + p**4/6 + p**3/3 - 3*p**2. Let c(t) = 4*t**2 - 4*t - 2. Let f(x) = -7*c(x) - 6*l(x). Suppose f(d) = 0. What is d?
-1
Let u(g) be the second derivative of g**7/84 - g**6/60 - 3*g**5/40 + g**4/24 + g**3/6 - 6*g. Determine h so that u(h) = 0.
-1, 0, 1, 2
Let l = 1537/4257 - -1/387. Factor -l*f + 6/11*f**2 + 0*f**3 + 0 - 2/11*f**4.
-2*f*(f - 1)**2*(f + 2)/11
Find f such that -2/5*f**2 + 0 + 4*f = 0.
0, 10
Suppose -2*l + 5 - 41 = 0. Let f be (-4)/l - 4/18. Factor 0 + 0*u + 1/4*u**4 + 0*u**2 + f*u**3.
u**4/4
Factor 2/5*i**3 - 2/5*i - 6/5*i**2 + 6/5.
2*(i - 3)*(i - 1)*(i + 1)/5
Let i(g) be the first derivative of g**4/4 + 3*g**3/2 + 3*g**2 - 9*g + 8. Let q(n) be the first derivative of i(n). Suppose q(j) = 0. What is j?
-2, -1
Let u(f) = f**2 - 6*f - 14. Let n be u(8). Let h be -3 - 1*(-95)/25. Solve 2/5*x + h + 2/5*x**4 - 6/5*x**n - 2/5*x**3 = 0.
-1, 1, 2
Suppose 4*i - 2 = -r, 0*i = 2*i + 3*r - 6. Determine n, given that -3/4*n**3 - 3/4*n - 3/2*n**2 + i = 0.
-1, 0
Let 0*w + 0 - 160/9*w**3 + 8/3*w**2 + 98/9*w**5 + 238/9*w**4 = 0. What is w?
-3, 0, 2/7
Let y(b) be the first derivative of -b**4/20 + 9*b**3/5 - 243*b**2/10 + 729*b/5 + 45. Factor y(i).
-(i - 9)**3/5
Let d be 4 - (1 - -1)*1. Solve -2*t**3 + t**4 + t**2 + 0*t**d + 0*t**3 = 0.
0, 1
Let t(y) be the second derivative of 1/21*y**7 + 0*y**3 + 0*y**2 + 0 + 0*y**4 + 1/10*y**5 + 2/15*y**6 + 2*y. Solve t(k) = 0.
-1, 0
Let f(a) = 0 - 11*a - 5 + a**2 + 15. Let o be f(10). Factor 1/3*r**2 + o*r + 0 + 2/3*r**3 - r**4.
-r**2*(r - 1)*(3*r + 1)/3
Let y(g) be the second derivative of 3*g**5/35 - 2*g**4/21 - 38*g**3/21 - 12*g**2/7 - 6*g. Factor y(a).
4*(a - 3)*(a + 2)*(3*a + 1)/7
Let a(q) be the third derivative of -1/210*q**6 + 1/1176*q**8 + 0*q**5 + 0*q + 6*q**2 + 1/84*q**4 + 0*q**7 + 0 + 0*q**3. Solve a(z) = 0 for z.
-1, 0, 1
Let p be 8/(-2)*(-3)/6. Suppose -2 + 6 + 18*y**p - 17*y + 39*y = 0. Calculate y.
-1, -2/9
Suppose i - 5*x = -6*x + 2, -3*x + 6 = 0. Let w(q) be the second derivative of 0 - 3/40*q**5 + q + i*q**4 + 1/4*q**3 + 0*q**2. Factor w(c).
-3*c*(c - 1)*(c + 1)/2
Suppose 522*s + 20*s**3 - 5*s**4 + 20*s**2 - 5*s**5 - 522*s = 0. What is s?
-2, -1, 0, 2
Let m = -47 + 47. Let l(v) be the third derivative of 2*v**2 + 7/90*v**5 - 1/18*v**4 + m*v**3 + 0 + 0*v. Factor l(c).
2*c*(7*c - 2)/3
Let h(i) = i**4 + i**3 - i**2 + i + 1. Let l(g) = 7*g**4 + g**3 - 11*g**2 + 5*g + 5. Let v(s) = -10*h(s) + 2*l(s). Determine p so that v(p) = 0.
-1, 0, 3
Let r be 33/22 - 2/(-4). Factor 7/5*c - 7/5*c**3 + 2/5*c**r - 2/5.
-(c - 1)*(c + 1)*(7*c - 2)/5
Let r(p) = 0 + 4 - 3*p + 3*p + p**2 + 3*p. Let h(i) = -i - 1. Let s(x) = 12*h(x) + 3*r(x). Factor s(w).
3*w*(w - 1)
Let x = -11 + 13. Let t(k) be the first derivative of 0*k**4 + 0*k**x - 2/3*k + 4/9*k**3 - 2/15*k**5 - 2. Factor t(m).
-2*(m - 1)**2*(m + 1)**2/3
Let n(c) be the third derivative of 0 - 1/15*c**5 + 1/60*c**6 - c**2 + 1/105*c**7 + 0*c + 0*c**3 + 0*c**4. Factor n(z).
2*z**2*(z - 1)*(z + 2)
Let y = 233/4 - 58. Factor y*r**3 - 3/4*r**2 + 3/4*r - 1/4.
(r - 1)**3/4
Let a(i) be the third derivative of i**7/7560 + i**6/1080 + i**5/360 + i**4/24 - 3*i**2. Let x(p) be the second derivative of a(p). Factor x(k).
(k + 1)**2/3
Let k(l) be the first derivative of -l**6/15 + 6*l**5/25 - l**4/5 + 2. Factor k(j).
-2*j**3*(j - 2)*(j - 1)/5
Let x(n) = 2*n**2 - 5*n - 3. Let f be x(4). Let o be 29/f - (-8)/(-36). Factor w**4 - 7/2*w**o - 5/2*w + 9/2*w**2 + 1/2.
(w - 1)**3*(2*w - 1)/2
Let l = -262/5 + 53. Factor 6/5*z**3 - 3/5*z + 3/5 + 3/5*z**4 - 6/5*z**2 - l*z**5.
-3*(z - 1)**3*(z + 1)**2/5
Let i = -585 - -1757/3. Factor -i*s**4 + 8/3*s**3 + 0*s - 8/3*s**2 + 0.
-2*s**2*(s - 2)**2/3
Let 0*o + 0 + 5/2*o**3 + 5*o**2 - 5/2*o**4 = 0. Calculate o.
-1, 0, 2
Let c(o) = -o**3 - 3*o**2 + 4*o + 5. Let s be c(-4). Let l(v) be the third derivative of 0*v + 0 - v**2 - 1/30*v**4 + 1/15*v**3 + 1/150*v**s. Factor l(h).
2*(h - 1)**2/5
Let g = -120 + 120. Let c(x) be the first derivative of -1 - 3/10*x**2 + 1/10*x**6 - 6/25*x**5 + 2/5*x**3 + 0*x**4 + g*x. Factor c(w).
3*w*(w - 1)**3*(w + 1)/5
Let x(b) = -b**2 + b + 9. Suppose -9*i + 10 + 17 = 0. Let c be x(i). Suppose -14/3*t**c + 14/3*t - 2/3*t**2 + 2*t**4 - 4/3 = 0. Calculate t.
-1, 1/3, 1, 2
Let n(l) be the first derivative of 7/2*l**2 - 2*l + 5/6*l**3 - 5 - l**5 - 71/16*l**4 + 25/24*l**6. Solve n(b) = 0.
-1, 2/5, 2
Suppose -9*h + 2 = -8*h. Find n, given that -2 - 1/2*n**2 - h*n = 0.
-2
Let v(g) be the second derivative of 5*g**5/12 + 35*g**4/18 + 22*g**3/9 + 4*g**2/3 - 28*g. Let v(z) = 0. What is z?
-2, -2/5
Let f = -4 + 6. Suppose -f*p + 6 = -0. Factor -2/7 - 2/7*q**5 - 20/7*q**2 - 10/7*q - 10/7*q**4 - 20/7*q**p.
-2*(q + 1)**5/7
Let g be 3/2*(-100)/(-75). Determine d, given that 2/13 + 2/13*d**4 + 2/13*d**5 + 2/13*d - 4/13*d**g - 4/13*d**3 = 0.
-1, 1
Let c(f) be the first derivative of 7*f**6/3 - 4*f**5/5 - 7*f**4/2 + 4*f**3/3 - 6. Solve c(z) = 0.
-1, 0, 2/7, 1
Let f(r) be the first derivative of r**8/672 - r**7/420 - r**6/240 + r**5/120 - r**2 + 4. Let m(u) be the second derivative of f(u). Factor m(n).
n**2*(n - 1)**2*(n + 1)/2
Let l(n) be the second derivative of -1/21*n**4 + 1/21*n**3 - 2*n + 1/70*n**5 + 0*n**2 + 0. Find r such that l(r) = 0.
0, 1
Suppose 7*t = 2*t - 25. Let q(u) = -2*u - 7. Let n be q(t). Factor 0*x**2 + 2*x**2 - n*x**2.
-x**2
Let s(a) = a + 15. Let i be s(-9). Let z(d) be the first derivative of 1/5*d**5 + 0*d + 1/6*d**i - 1/4*d**4 + 2 - 1/3*d**3 + 0*d**2. Let z(q) = 0. Calculate q.
-1, 0, 1
Let k be 1*(1 - 2) - -4. Factor 0*c**5 + 20*c**k + 5*c**5 - 4 + c**5 + 20*c**4 - 10*c.
2*(c + 1)**4*(3*c - 2)
Suppose -2/5*p**2 + 0*p + 0 + 1/5*p**3 = 0. Calculate p.
0, 2
Let s be (0 - 11)*(-2 + 3). Let m = s - -16. Factor 2*u + 3*u**m - u - 2*u**5 - 2*u**3.
u*(u - 1)**2*(u + 1)**2
Let n(o) be the second derivative of o**7/42 - o**5/10 + o**3/6 + 10*o. Find z such that n(z) = 0.
-1, 0, 1
Let j(m) be the first derivative of -m**4 - 20*m**3/3 - 16*m**2 - 16*m + 7. Determine d so that j(d) = 0.
-2, -1
Let y(o) be the second derivative of -o**7/105 + o**6/