Let n(r) = r**3 + 9*r**2 + 12*r - 10. Let c be n(-7). Factor -8 + 8 - 4*y**5 + c*y**4 + 2*y**3 - 4*y**2 + 2*y**3.
-4*y**2*(y - 1)**2*(y + 1)
What is r in 2*r - 1/2*r**3 + 1/2*r**4 - 3*r**2 + 4 = 0?
-2, -1, 2
Let d(y) be the first derivative of 2*y**7/21 + y**6/30 - y**5/5 - y**4/12 - 9*y + 2. Let f(r) be the first derivative of d(r). Suppose f(m) = 0. Calculate m.
-1, -1/4, 0, 1
Let b = -23579/12600 - -118/63. Let v(o) be the third derivative of 0 - b*o**6 + 0*o**3 + 0*o**4 + 0*o + 13*o**2 + 1/150*o**5. Factor v(i).
-i**2*(i - 2)/5
Let w(d) be the first derivative of -d**5 + 5*d**4/2 + 5*d**3 - 20*d**2 + 20*d + 150. Let w(s) = 0. Calculate s.
-2, 1, 2
Let z(a) = a**4 + 12*a**3 + 4*a**2 - 6*a - 5. Let k(s) = -s**4 - 10*s**3 - 3*s**2 + 5*s + 4. Let f(j) = -6*k(j) - 5*z(j). Factor f(y).
(y - 1)**2*(y + 1)**2
Let l(o) be the second derivative of o**5/70 + 115*o. Find u such that l(u) = 0.
0
Let c(a) be the first derivative of -6/5*a + 1/5*a**3 + 35 - 3/10*a**2. Factor c(n).
3*(n - 2)*(n + 1)/5
Solve 3/4*n**5 + 21*n - 6 + 75/4*n**3 - 57/2*n**2 - 6*n**4 = 0.
1, 2
Let d(k) be the second derivative of 19*k**6/375 - 17*k**5/250 - k**4/75 + 195*k + 1. Suppose d(f) = 0. Calculate f.
-2/19, 0, 1
Factor 174/11*i**2 + 354/11*i**3 + 186/11*i**4 + 6/11*i**5 + 0 + 0*i.
6*i**2*(i + 1)**2*(i + 29)/11
Solve 458*h + 5*h**2 + 514*h - 712*h - 265 = 0.
-53, 1
Let d(u) = 19*u - 52. Let l be d(4). Let b be (9/(-7) - -1)*l/(-48). Factor 0 - b*x**2 + 1/7*x.
-x*(x - 1)/7
Let i = -2099 - -2101. Factor -4/3 - 20/3*b - 16/3*b**i.
-4*(b + 1)*(4*b + 1)/3
Let k(g) be the first derivative of g**9/2520 + g**8/1050 + g**7/2100 + 8*g**3/3 - 2. Let y(b) be the third derivative of k(b). Factor y(o).
2*o**3*(o + 1)*(3*o + 1)/5
Factor -6092*b + b**2 + 105 + 6060*b + 151.
(b - 16)**2
Let y(q) = -q**3 + 2*q**2 + q + 1. Let f be y(3). Let m be (-10)/52 - ((-5)/(-2))/f. Factor 14/13*p - 18/13*p**2 + m.
-2*(p - 1)*(9*p + 2)/13
Let u = 175 + -172. Factor 12*h + 3 + 3*h**u - 11*h**2 + 19*h - 26*h.
(h - 3)*(h - 1)*(3*h + 1)
Let r(m) be the first derivative of m**6/195 - m**5/65 + m**4/78 - 13*m + 22. Let p(l) be the first derivative of r(l). Let p(z) = 0. Calculate z.
0, 1
Factor -1291*i**3 + 8*i**2 + 1290*i**3 + 43*i**2.
-i**2*(i - 51)
Let n(f) be the first derivative of 2*f**5/25 + 3*f**4/10 + 2*f**3/15 - 3*f**2/5 - 4*f/5 + 27. Factor n(d).
2*(d - 1)*(d + 1)**2*(d + 2)/5
Let -12*n**2 + 43*n - 22*n + 13*n**2 = 0. What is n?
-21, 0
What is a in 1685*a + 3125 - 585*a - 2*a**3 + 2*a**3 + 5*a**3 + 1775*a - 245*a**2 = 0?
-1, 25
Let p(c) = c**2. Let i be p(0). Let j(h) be the second derivative of -h**2 - h**3 + i - h - 1/10*h**5 - 1/2*h**4. Factor j(m).
-2*(m + 1)**3
Factor -72/11*d**2 - 2/11*d**4 - 2*d**3 + 128/11 - 32/11*d.
-2*(d - 1)*(d + 4)**3/11
Suppose 0 = -j + 3*j - 2*p - 58, 2*p = j - 25. Solve j*i**3 + 7*i**4 - 27*i**3 + 5*i**4 + 15*i**4 + 21*i**5 = 0.
-1, -2/7, 0
Let t be ((-3)/2)/(3/(-6)). Suppose 0 = -2*p - 10 - 0, 0 = 3*n + 3*p + t. Solve m - 2*m**2 + n*m**3 + 4*m**2 + m**3 - 4*m**3 = 0 for m.
-1, 0
Suppose -y - 5*f = y - 11, -14 = -4*y - 2*f. Let p(n) = -12*n + 12. Let d(c) = -c**2 + 1. Let a(q) = y*d(q) - p(q). Factor a(j).
-3*(j - 3)*(j - 1)
Let i(d) be the first derivative of -5*d**4/4 - 19*d**3 - 11*d**2 - 359. Determine x so that i(x) = 0.
-11, -2/5, 0
Let m = -1410 + 1412. Suppose -3/2*t**m + 21/4*t - 21/4*t**3 + 3/2 = 0. Calculate t.
-1, -2/7, 1
Factor -22*u**2 + 23*u**2 - 45*u + 45*u - 59*u - 68*u.
u*(u - 127)
Let x(o) be the first derivative of 31 + 4*o**2 + 8*o + 2/3*o**3. Factor x(j).
2*(j + 2)**2
Let q(m) = 2*m**2 + 35*m + 54. Let n(o) = -o**2 - 18*o - 26. Let y(w) = -7*n(w) - 3*q(w). What is z in y(z) = 0?
-20, -1
Let n = -85 - -87. Let m(k) be the second derivative of 0 + k + 0*k**n + 0*k**3 - 1/70*k**5 - 1/21*k**4. Solve m(c) = 0.
-2, 0
Let w be ((-5)/(-5))/((-2)/(-6)). Let 5*m + 22 - m**2 - 7*m**2 - 4*m**w + 10 + 11*m = 0. Calculate m.
-2, 2
Let v(d) = d**2 - d - 1. Let g be (-1)/(3/(-1) + 4). Let u(z) = -12*z - 9. Let q(p) = g*u(p) + 3*v(p). Solve q(r) = 0 for r.
-2, -1
Let j(a) be the second derivative of -19*a**4/24 + 13*a**3/4 - a**2/2 + 548*a. What is i in j(i) = 0?
1/19, 2
Let x(r) be the third derivative of 0*r + 0*r**3 + 0 + 0*r**4 + 1/18*r**5 + 1/72*r**6 - 33*r**2. Determine p, given that x(p) = 0.
-2, 0
Suppose 0 + 3/8*w**5 - 75/8*w**2 + 105/8*w**3 - 33/8*w**4 + 0*w = 0. What is w?
0, 1, 5
Let z(o) = o**2 - 27*o + 44. Let c be z(27). Suppose c = a + 42. Suppose -1/4*q**4 - 1/4*q**a + 1/2 - 3/4*q**3 + 3/4*q = 0. Calculate q.
-2, -1, 1
Let r(l) be the third derivative of -2*l**2 + 0*l + 0 - 13/10*l**5 + 10/9*l**4 + 9/20*l**6 - 4/9*l**3. Factor r(v).
2*(v - 1)*(9*v - 2)**2/3
Let n(s) be the third derivative of 2/315*s**5 + 0*s**3 + 1/210*s**6 + 0 + 1/252*s**4 + 1/3528*s**8 + 0*s - 12*s**2 + 4/2205*s**7. What is b in n(b) = 0?
-1, 0
Let b(p) = 3*p**5 + p**4 + 2*p**3 + 2*p**2. Let m(d) = -7*d**5 - 2*d**4 - 5*d**3 - 5*d**2. Let x(w) = -5*b(w) - 2*m(w). Solve x(t) = 0 for t.
-1, 0
Let r = -303 + 306. Let j(f) be the third derivative of 8*f**2 + 0 + 0*f + 2/3*f**r - 1/3*f**5 + 1/6*f**4 + 1/10*f**6. Let j(q) = 0. What is q?
-1/3, 1
Let g(v) be the first derivative of -2*v**6/3 + v**5 + 3*v**4/4 - 5*v**3/3 + v**2/2 - 198. Solve g(m) = 0 for m.
-1, 0, 1/4, 1
Let k(j) be the first derivative of -2*j**5/5 + 3*j**4/2 - 4*j**3/3 + 169. Determine d so that k(d) = 0.
0, 1, 2
Let g = 1161/5 - 8359/36. Let b(x) be the third derivative of 0 + 3*x**2 - g*x**6 - 1/30*x**5 - 1/9*x**3 - 1/12*x**4 + 0*x. What is s in b(s) = 0?
-1
Let n(s) be the third derivative of s**6/540 + s**5/270 - 5*s**4/108 + s**3/9 + s**2 - 8. Factor n(p).
2*(p - 1)**2*(p + 3)/9
Let u(g) be the third derivative of -2/105*g**7 - 32/3*g**3 + 4/15*g**6 + 0 - 8/5*g**5 - 9*g**2 + 16/3*g**4 + 0*g. Suppose u(t) = 0. What is t?
2
Let n be 11/4 - 819/364. Factor -3 + 5/2*l + n*l**2.
(l - 1)*(l + 6)/2
Let w = 76 + -72. Determine b, given that 0 + 3/5*b**2 + 2/5*b + 0*b**3 - 1/5*b**w = 0.
-1, 0, 2
Find d, given that -70*d + 57*d - 18 + 33*d - 2*d**2 = 0.
1, 9
Let 4/3*m**3 + 0 - 4/3*m + 0*m**2 = 0. Calculate m.
-1, 0, 1
Let i(x) be the second derivative of x**9/1620 - x**8/20160 - x**7/3780 - 43*x**4/12 - 24*x. Let p(v) be the third derivative of i(v). Let p(o) = 0. What is o?
-1/4, 0, 2/7
Determine s so that 4/5*s**3 + 0 + 8/5*s**2 - 4/5*s**4 + 0*s = 0.
-1, 0, 2
Factor -88 - 6*a**2 + 3*a - 6*a + 7*a**2.
(a - 11)*(a + 8)
Let g be (1/2)/((-9)/(-54)). Let t be 6*3/18*g. Factor -t*v**2 + 5*v**2 + 12 + 20 + 0*v**2 - 16*v.
2*(v - 4)**2
Let f(m) = -19*m**2 - 35*m - 14. Suppose 10 - 25 = 5*v, -v + 12 = 3*s. Let o(z) = -20*z**2 - 35*z - 15. Let l(q) = s*f(q) - 4*o(q). Find u such that l(u) = 0.
-2, -1/3
Let i(f) be the third derivative of 8/135*f**5 + 7/540*f**6 + 1/27*f**4 + 0*f + 0*f**3 + 0 + 18*f**2. Suppose i(d) = 0. What is d?
-2, -2/7, 0
Let d be (-5 - 1) + 3/((-6)/(-17)). Let l(i) be the first derivative of -5*i**2 + d*i**4 + 2*i + 1 - 8/5*i**5 + 2*i**3. Find r, given that l(r) = 0.
-1, 1/4, 1
Let n = 23 + -79. Let l be 4/((n/(-12))/(2/6)). Factor 0 - 2/7*j**4 + 0*j**3 + l*j**2 + 0*j.
-2*j**2*(j - 1)*(j + 1)/7
Let v = -83 + 83. Let x(a) be the second derivative of 0*a**3 + 3*a + 0*a**2 + v - 1/6*a**4 - 1/10*a**5. Factor x(c).
-2*c**2*(c + 1)
Let n be (9 - 9)/(1 + -3). Suppose 3*r = 3*d + 9, -4*r - 2*d + 6 = -n*r. Factor 1 + 2*f + 3*f**2 + 4 - 6 - 4*f**r.
-(f - 1)**2
Let n(v) be the third derivative of v**7/1470 + v**6/140 + 3*v**5/140 + v**4/42 + 91*v**2 - 2. Suppose n(b) = 0. Calculate b.
-4, -1, 0
Suppose 1 = 2*n - n - r, -r = 2*n + 1. Suppose l - 6*l + 15 = n. Determine u, given that -4*u - u**3 + 1 - l + 7*u + 0*u**3 = 0.
-2, 1
Let c(v) be the third derivative of 25*v**8/336 + 11*v**7/21 - 13*v**6/6 - 46*v**5/3 + 160*v**4/3 + 320*v**3/3 - 339*v**2. Solve c(b) = 0 for b.
-4, -2/5, 2
Let w be ((-10)/(-6))/(11/429). Factor -98*u**2 + w*u + 45*u**3 - 5 - 5 - 2*u**2.
5*(u - 1)**2*(9*u - 2)
What is w in -15/7*w**2 + 3/7*w + 0 = 0?
0, 1/5
Let q(s) be the second derivative of 0*s**3 + 0*s**2 + 0 - 17*s + 1/5*s**5 - 1/3*s**4. Factor q(b).
4*b**2*(b - 1)
Suppose 3*t - 9*t + 36 = 0. Let u(f) be the second derivative of -1/20*f**5 + 0 + 1/18*f**t - 1/3*f**4 - 2/9*f**3 + 3*f + 0*f**2. Factor u(l).
l*(l - 2)*(l + 1)*(5*l + 2)/