 2
Let s(k) be the second derivative of k**5/10 + 17*k**4/18 + 10*k**3/9 - 5*k. Factor s(p).
2*p*(p + 5)*(3*p + 2)/3
Let q be (20 - 25) + (-2 - -10). Determine l, given that 0*l + 0 + 0*l**2 - 2/7*l**4 - 2/7*l**q = 0.
-1, 0
What is h in -11*h**3 - 18*h**2 - 10*h**4 - 13*h**3 + 14*h - 18*h = 0?
-1, -2/5, 0
Let -2/15*u**2 + 0 - 4/15*u = 0. Calculate u.
-2, 0
Factor 0 - 8/11*y**4 + 2/11*y**5 - 8/11*y**2 + 2/11*y + 12/11*y**3.
2*y*(y - 1)**4/11
Let v(a) = a**2 + a - 5. Let q(y) = 1. Let l(s) = -3*q(s) - v(s). Determine p so that l(p) = 0.
-2, 1
Let a(g) = -g**2 - 8*g - 11. Let w(v) = v**2 + 1. Let h(p) = a(p) + 2*w(p). Factor h(m).
(m - 9)*(m + 1)
Let s be (-2*2)/(8/(-16)). Let h be 6/24*s/6. What is z in -4/3*z**2 + 2/3*z**3 + 2/3*z**4 - 1/3*z**5 + 2/3 - h*z = 0?
-1, 1, 2
Let m(v) = 2*v + 35. Let q be m(-17). Let c(t) be the first derivative of 0*t**2 + 3/2*t**4 + 0*t + 0*t**5 + 4/3*t**3 + q - 1/3*t**6. Factor c(y).
-2*y**2*(y - 2)*(y + 1)**2
Let f = -3 + 3. Factor f*c**4 - 4*c**3 - 3*c**5 + 6*c**4 + c**3.
-3*c**3*(c - 1)**2
Let d(v) = v**4 - v**3 + v**2 + v - 1. Let n(b) = -3*b**5 + 32*b**4 - 86*b**3 + 86*b**2 + 5*b - 5. Let c(t) = -5*d(t) + n(t). Factor c(k).
-3*k**2*(k - 3)**3
Let q(m) be the first derivative of 0*m - 2/45*m**5 - 4/27*m**3 - 3 + 0*m**2 + 1/6*m**4. Suppose q(d) = 0. Calculate d.
0, 1, 2
Let o(t) be the second derivative of 1/231*t**7 + 5*t + 0*t**2 + 0 - 1/33*t**3 + 0*t**5 - 1/33*t**4 + 2/165*t**6. Solve o(q) = 0.
-1, 0, 1
Suppose -23*g + 67*g = 0. Factor m**2 + g + 2/3*m + 1/3*m**3.
m*(m + 1)*(m + 2)/3
Let m(s) = -5*s**4 + 19*s**3 + 17*s**2 - 17. Let k(o) = o**4 - 3*o**3 - 3*o**2 + 3. Let v(f) = -34*k(f) - 6*m(f). Factor v(u).
-4*u**3*(u + 3)
Let r(y) be the first derivative of -y**5/150 + y**4/60 + 2*y**3/15 - y**2 - 7. Let j(l) be the second derivative of r(l). Factor j(v).
-2*(v - 2)*(v + 1)/5
Factor 1/5*l**5 - 2/5*l**4 + 0*l + 0 - 7/5*l**3 - 4/5*l**2.
l**2*(l - 4)*(l + 1)**2/5
Let j = -17 - -17. Let g(y) be the third derivative of 0 + 0*y + 2/135*y**5 - y**2 + 4/945*y**7 + 1/1512*y**8 + 1/108*y**4 + 1/90*y**6 + j*y**3. Factor g(f).
2*f*(f + 1)**4/9
Let o be ((-6)/5)/(2/(-65)). Suppose -14 + o = 5*b. Factor 1/3*m**b + 2*m**3 + 1/3*m + 0 + 4/3*m**2 + 4/3*m**4.
m*(m + 1)**4/3
Let g(s) be the first derivative of s**5/42 + s**4/12 + 2*s**3/21 - 3*s**2 + 4. Let t(d) be the second derivative of g(d). Factor t(h).
2*(h + 1)*(5*h + 2)/7
Let l(w) be the third derivative of -7/240*w**5 + 2*w**2 + 1/1344*w**8 + 0*w + 0 - 1/168*w**7 + 1/48*w**4 + 0*w**3 + 3/160*w**6. Factor l(y).
y*(y - 2)*(y - 1)**3/4
Let t(g) be the second derivative of g**6/20 + 3*g**5/10 - g**4/4 - 3*g**3 + 27*g**2/4 + 14*g. Factor t(y).
3*(y - 1)**2*(y + 3)**2/2
Suppose 0 = -3*g + 4*g - 14. Let y = 14 - g. Factor -4/7*j**4 + y*j**2 + 0 + 2/7*j**5 + 2/7*j**3 + 0*j.
2*j**3*(j - 1)**2/7
Let p(v) be the first derivative of -v**4/16 + v**3/6 - v**2/8 - 13. Suppose p(q) = 0. What is q?
0, 1
Let r(h) = 2*h**2 - 3*h. Let g be r(2). Factor 3*a**g + 3*a + 2*a**2 - 5*a - 4*a**2.
a*(a - 2)
Let t(u) = 16*u**2 - 116*u + 44. Let w(f) = 3*f**2 - 21*f + 8. Let c(z) = 5*t(z) - 28*w(z). Factor c(h).
-4*(h - 1)**2
Let l(r) be the first derivative of r**8/3360 + r**7/840 - r**5/120 - r**4/48 - r**3 - 2. Let x(y) be the third derivative of l(y). Let x(a) = 0. Calculate a.
-1, 1
Solve 2/5*q**5 + 0*q**3 + 2/5*q**4 + 0 + 0*q + 0*q**2 = 0.
-1, 0
Let d be (4/6)/((-1)/(-3)). Suppose -3*b - 4*w + 19 = -8, -16 = -d*b - 2*w. Factor -b - 2*y**2 + 3 + y**2 - 4*y - y**2.
-2*(y + 1)**2
Let 1/5*a**2 + 3/5 + 4/5*a = 0. What is a?
-3, -1
Suppose 2*v + v = v. Let c(z) = z**2 + 3*z - 1. Let d be c(-4). Factor 0*h**4 + 0*h - 2/11*h**5 + 0*h**2 + v + 2/11*h**d.
-2*h**3*(h - 1)*(h + 1)/11
Suppose 0 = -5*u + 4*n + 33, -u - 3*u - 3*n = -14. Suppose 2*j - u = -1. Factor 1/4*x**j + 0 + 0*x.
x**2/4
Find z such that -4*z**2 - z**2 - 13155 + 13125 + 25*z = 0.
2, 3
Suppose 3*h - 4*m = 5*h + 4, -h = 4*m - 2. Let x(k) = -k**3 - 6*k**2 + k + 8. Let j be x(h). Solve -2*r**j - 6*r - r**2 - 3*r**2 + 3*r**2 = 0 for r.
-2, 0
Let l(n) = -5*n**3 - 3*n**2 + 6*n + 4. Let u(t) = 16*t**3 + 10*t**2 - 18*t - 12. Let k(m) = -10*l(m) - 3*u(m). Find y such that k(y) = 0.
-1, 2
Suppose -3*o - 7*n = -2*n - 1, 3*o + 2*n = 4. Let r be (11/5 - o)*4. Factor -r - 2/5*d**2 - 6/5*d.
-2*(d + 1)*(d + 2)/5
Solve 26*q + 5*q**2 - 46*q - 35*q + 55 - 5*q = 0 for q.
1, 11
What is z in 12/5*z**2 + 48/5*z + 64/5 + 1/5*z**3 = 0?
-4
Let s be 1 - 3 - (-5)/2. Let x(q) be the first derivative of q**2 + 4/3*q**3 + 2 + s*q**4 + 0*q. Solve x(g) = 0.
-1, 0
Let k be ((-6)/(-10))/((-72)/(-240)). Find i, given that -1/3*i**3 + 1/3*i - 1/3*i**k + 1/3 = 0.
-1, 1
Let y = 2499/1565 - -1/313. Factor 0 - 2/5*m - 12/5*m**3 + y*m**4 + 8/5*m**2 - 2/5*m**5.
-2*m*(m - 1)**4/5
Let m(k) = 7*k**3 - 6*k**2 - 5*k - 5. Let t(d) = 4*d**3 - 3*d**2 - 3*d - 3. Let q be 1/(2/(-10) - 0). Let r(u) = q*t(u) + 3*m(u). Factor r(w).
w**2*(w - 3)
Find a, given that -5 - 2*a + 3*a**2 + 5*a - 1 = 0.
-2, 1
Let z(p) = 4*p**4 - 14*p**3 - 18*p**2 + 22*p + 16. Let v(j) = -4*j**4 + 15*j**3 + 19*j**2 - 23*j - 16. Let m(n) = -6*v(n) - 7*z(n). Factor m(c).
-4*(c - 2)**2*(c + 1)**2
Let y(w) be the first derivative of -w**6/40 + w**5/10 - w**4/8 + 11*w**2/2 - 8. Let a(v) be the second derivative of y(v). Factor a(u).
-3*u*(u - 1)**2
Determine j, given that -1/7*j + 0 - 25/7*j**4 - 5*j**3 - 11/7*j**2 = 0.
-1, -1/5, 0
Let n(g) be the second derivative of -g**6/900 - g**5/300 - g**3/6 - 2*g. Let b(r) be the second derivative of n(r). Factor b(d).
-2*d*(d + 1)/5
Let d be 8/(-1 + 3) - 2. Suppose 0 = -k - d*k + 24. Factor -4*g - 4*g**3 - k*g**2 - 1 - 2*g - g**2.
-(g + 1)**2*(4*g + 1)
Let d(c) be the third derivative of 2*c**7/525 - c**6/150 - 2*c**5/75 + 14*c**2. Let d(j) = 0. What is j?
-1, 0, 2
Let h(f) = f**2 - f. Let s(b) = -b + 0 - 2 - b + 4*b**2. Let n = 1 - 7. Let q(o) = n*h(o) + s(o). Factor q(t).
-2*(t - 1)**2
Let v(y) = -2*y - 4. Let b(t) = t**2 + t - 4. Let w be b(0). Let c be v(w). Find r, given that -2 - r**c - r**4 + 3*r**2 + r**2 = 0.
-1, 1
Suppose -v + 3 = -1. Let 15*g**2 - 3*g**5 + 31*g**4 + 12*g**5 + 33*g**3 - 2*g**v + 2*g = 0. What is g?
-1, -2/9, 0
Let o(h) be the third derivative of h**5/360 + h**4/72 - 2*h**3/9 + 17*h**2. Factor o(t).
(t - 2)*(t + 4)/6
Let h(a) be the third derivative of 0*a + 7*a**2 + 0 - 1/75*a**5 - 1/12*a**4 - 2/15*a**3. Factor h(y).
-2*(y + 2)*(2*y + 1)/5
Let u(z) be the third derivative of -z**9/12096 - 17*z**8/20160 - z**7/315 - z**6/180 - z**5/60 + z**2. Let q(v) be the third derivative of u(v). Factor q(h).
-(h + 1)*(h + 2)*(5*h + 2)
Let p(d) = 5*d**2 - 3*d. Let r(j) = 3*j + 10. Let o be r(-5). Let x(t) = -3*t**2 + 2*t. Let g(k) = o*p(k) - 8*x(k). Let g(v) = 0. Calculate v.
-1, 0
Let a(p) = -12*p**2 + 14*p - 7. Let q(w) = 11*w**2 - 13*w + 6. Let g(v) = -4*a(v) - 5*q(v). Determine u, given that g(u) = 0.
2/7, 1
Suppose 5 - 1 = 2*f. Let v(c) be the first derivative of -1 - 3/7*c**f - 36/35*c**5 - 4/7*c + 8/7*c**3 + 3/7*c**6 + 1/7*c**4. Find h, given that v(h) = 0.
-2/3, -1/3, 1
Let y(m) be the second derivative of -2*m**6/75 + m**5/25 + m**4/15 - 2*m**3/15 - 10*m. Suppose y(c) = 0. Calculate c.
-1, 0, 1
Let 2/5*r**3 - 2/5*r**5 + 2/5*r**2 - 2/5*r**4 + 0 + 0*r = 0. What is r?
-1, 0, 1
Let u(n) be the third derivative of 0 - 1/56*n**8 + 0*n**3 + 1/30*n**6 + 2/15*n**5 + 0*n - 4/105*n**7 + n**2 + 1/12*n**4. Suppose u(c) = 0. What is c?
-1, -1/3, 0, 1
Let d = 22 - 18. Let s(v) be the third derivative of -1/60*v**6 - 1/30*v**5 + 0*v**d + 1/168*v**8 + 0 + 0*v + 0*v**3 + 1/105*v**7 - 3*v**2. Factor s(i).
2*i**2*(i - 1)*(i + 1)**2
Let d(m) be the third derivative of 5/48*m**4 + 2*m**2 + 0 + 1/30*m**5 + 1/240*m**6 + 1/6*m**3 + 0*m. Factor d(t).
(t + 1)**2*(t + 2)/2
Suppose -l = -3*k + 7, 3*k + 2*l = -k + 16. Let z = 0 + k. Factor r**2 + 4*r**4 - 4*r**3 + 5*r**z + 4*r**3.
r**2*(r + 1)*(4*r + 1)
Let z(x) be the first derivative of -x**4/4 - x**3/3 - 11. Find w such that z(w) = 0.
-1, 0
Let m be (-1)/((-1 - -2)/(-3)). Let w be (m/9)/(3/45). Let b(j) = -j**2. Let z(p) = p**2. Let r(c) = w*b(c) + 7*z(c). Suppose r(k) = 0. What is k?
0
Let k(h) be the second derivative of 1/70*h**5 - 2*h + 0 + 0*h**4 - 2/105*h**6 + 0*h**2 - 1/49*h**7 + 0*h**3. Factor k(r).
-2*r**3*(r + 1)*(3*r 