(k) = 3*k**2 - 63*k + 117. Let t(m) = m**2 - 16*m + 29. Let g(a) = 2*d(a) - 9*t(a). Factor g(u).
-3*(u - 3)**2
Let a(z) be the second derivative of -z**5/25 + 2*z**4/15 + 2*z**3/15 - 4*z**2/5 + 8*z - 3. Factor a(o).
-4*(o - 2)*(o - 1)*(o + 1)/5
Let m(u) be the second derivative of -u**7/378 + u**6/54 - u**5/30 - u**4/54 + 7*u**3/54 - u**2/6 + 11*u. What is r in m(r) = 0?
-1, 1, 3
Let h = -17 - -21. Suppose -4*n = -2*n - h. Factor -1/4*q + 0 + 1/4*q**n.
q*(q - 1)/4
Let x be 22/24 - 4/16. Factor -2/9*a**2 + 8/9*a - x.
-2*(a - 3)*(a - 1)/9
Let m(a) be the third derivative of a**8/40320 - a**6/1440 + a**5/15 + 2*a**2. Let y(u) be the third derivative of m(u). Suppose y(q) = 0. What is q?
-1, 1
Let u(b) be the first derivative of b**3/12 + b**2/2 + 10. Determine n so that u(n) = 0.
-4, 0
Let m(j) be the first derivative of -2 + 0*j**3 + 2*j**2 - j**4 - 2*j + 2/5*j**5. Factor m(p).
2*(p - 1)**3*(p + 1)
Factor 0 + 1/5*r**5 - 4/5*r**3 + 3/5*r + 2/5*r**2 - 2/5*r**4.
r*(r - 3)*(r - 1)*(r + 1)**2/5
Let s(k) = k**3 - k**2 - k. Let r = -7 + 5. Let z(i) be the second derivative of -i**4/6 + 2*i**3/3 + 2*i. Let q(g) = r*s(g) - z(g). Solve q(u) = 0 for u.
0, 1
Factor 1/6*i**3 + 0 + 1/2*i + 2/3*i**2.
i*(i + 1)*(i + 3)/6
Let s(l) = -l**3 - 8*l**2 - 7*l + 2. Let j be s(-7). Determine y so that 109*y**3 + y**5 + 6*y**4 + 8 - 111*y**3 - 14*y**j + 2*y**5 - y**5 = 0.
-2, -1, 1
Let z**4 - 4*z**3 - 2*z**3 - 5*z**4 + 22*z**3 = 0. What is z?
0, 4
Let f(k) be the third derivative of 0*k**3 - 1/20*k**4 + 0*k + 0 - 1/150*k**5 + 5*k**2. Let f(s) = 0. Calculate s.
-3, 0
Suppose 0 = -7*t + 3*t - 32. Let h be (-1)/4 + (-162)/t. Solve 10*o + 2*o**5 + 2 + 9*o**4 + 20*o**2 + 0*o**4 + h*o**3 + o**4 = 0.
-1
Let a be 0/(-1 - (-4)/2). Suppose a = -0*n + 2*n - 4. Factor 7/2*z**2 - n + 6*z.
(z + 2)*(7*z - 2)/2
Suppose -2*n = 3*r + 6, 18 = 2*r - 5*n + 3. Suppose r = i - 0*i + 2*h - 8, 0 = -4*h + 16. Factor -t**4 + t - t**5 + i*t**2 + 2*t**2 - t**4.
-t*(t - 1)*(t + 1)**3
Let x(h) be the third derivative of -h**7/840 - h**6/240 + h**4/6 + 2*h**2. Let l(f) be the second derivative of x(f). What is w in l(w) = 0?
-1, 0
Let n(r) be the second derivative of r**8/1344 - r**6/480 + r**2/2 - r. Let d(j) be the first derivative of n(j). Factor d(q).
q**3*(q - 1)*(q + 1)/4
Let w(r) be the second derivative of 0 + 0*r**3 + 0*r**2 + 1/10*r**5 + 2/21*r**4 + 4*r. Factor w(v).
2*v**2*(7*v + 4)/7
Factor -8/7*a - 2/7*a**2 + 0.
-2*a*(a + 4)/7
Let u = -649/9 - -72. Let s = u - -4/9. Suppose s + 0*i + 0*i**3 - 2/3*i**2 + 1/3*i**4 = 0. Calculate i.
-1, 1
Let m(l) be the second derivative of 0*l**2 + 1/105*l**6 + 0 + 1/14*l**4 - 3*l + 3/70*l**5 + 1/21*l**3. Determine o, given that m(o) = 0.
-1, 0
Suppose 3*c = 3*v - 15, 2*v - 22 = -2*c + 6*c. Let q = c - -8. Suppose b**2 + 0*b**2 + q*b**2 - 2*b**2 = 0. What is b?
0
Suppose 14 = -0*u - u. Let r(a) = -19*a**2 - 10*a + 9. Let w(g) = 56*g**2 + 30*g - 26. Let l(j) = u*r(j) - 5*w(j). Determine y so that l(y) = 0.
-1, 2/7
Let x = -446 - -4018/9. Factor x + 2/9*d**2 + 2/3*d.
2*(d + 1)*(d + 2)/9
Let g(u) be the second derivative of u**5/20 + u**4/4 - 2*u**2 - 51*u. Factor g(n).
(n - 1)*(n + 2)**2
Let q(f) = 16*f**2 - 4 - 7*f - 4*f - 5*f**2. Let t(c) = -21*c**2 + 23*c + 8. Let a(u) = 5*q(u) + 3*t(u). Determine p so that a(p) = 0.
-1/4, 2
Suppose -9*q + 12*q = 0. Let k(r) be the first derivative of 1/10*r**4 - 1 - 3/5*r**2 - 4/5*r + q*r**3. Factor k(i).
2*(i - 2)*(i + 1)**2/5
Find h, given that 0*h**2 + 2/3*h + 0 - 2/3*h**3 = 0.
-1, 0, 1
Let u(v) be the third derivative of -v**5/15 - 2*v**4/3 + 10*v**3/3 + 18*v**2. Factor u(i).
-4*(i - 1)*(i + 5)
Let n(v) be the third derivative of v**7/1260 - v**6/720 - v**5/180 + 9*v**2. Factor n(q).
q**2*(q - 2)*(q + 1)/6
Let k = -4 - -7. Suppose -4*x**3 - 4*x**2 - 2 - 5*x + 0*x**3 + k*x**3 = 0. What is x?
-2, -1
Let t(c) = -c**3 - 15*c**2 - 14*c + 5. Let m be t(-14). Factor -4/11*f**2 - 6/11*f**3 + 0*f + 0 + 2/11*f**m + 0*f**4.
2*f**2*(f - 2)*(f + 1)**2/11
Factor -6/11*l**4 + 6/11*l**2 + 0 - 6/11*l + 6/11*l**3.
-6*l*(l - 1)**2*(l + 1)/11
Let n(t) be the third derivative of t**6/180 + t**5/45 + t**4/36 + 5*t**2. Suppose n(p) = 0. Calculate p.
-1, 0
Let q(h) be the second derivative of 3*h**5/20 - h**3/2 + 2*h. Suppose q(n) = 0. Calculate n.
-1, 0, 1
Suppose 1 + 5/4*c**2 + 1/4*c**3 + 2*c = 0. Calculate c.
-2, -1
Let r(m) be the third derivative of -6*m**2 + 1/210*m**7 + 1/72*m**4 + 0*m + 1/252*m**8 - 1/60*m**5 - 1/72*m**6 + 0 + 0*m**3. Let r(g) = 0. Calculate g.
-1, 0, 1/4, 1
Let k(z) = 14*z**2 - 20*z + 14. Suppose 3*q - 3*g - 18 = q, g = -5*q + 11. Let x(i) = -5*i**2 + 7*i - 5. Let p(u) = q*k(u) + 8*x(u). Factor p(n).
2*(n - 1)**2
Let p(f) be the first derivative of -3/14*f**4 + 4 + 0*f + 0*f**2 + 4/21*f**3. Find o such that p(o) = 0.
0, 2/3
Let g(s) = -s**2 - 10*s + 1. Let t be g(-10). Let v(u) be the first derivative of 0*u - 1/2*u**4 - t + 4/3*u**3 - u**2. Factor v(j).
-2*j*(j - 1)**2
Let h be -2 + 7 - 76/16. Let a(t) be the first derivative of 1/5*t**5 + h*t**4 - 1/3*t**3 + 0*t + 2 - 1/2*t**2. Factor a(o).
o*(o - 1)*(o + 1)**2
Suppose l = -l + 10. Suppose -2/3*g + 2/3*g**l + 0*g**3 + 4/3*g**4 + 0 - 4/3*g**2 = 0. Calculate g.
-1, 0, 1
Let q = 2420600/331 - 7313. Let r = q + 3319/993. Factor -4/3 - r*f**2 - 14/3*f.
-2*(f + 1)*(5*f + 2)/3
Let p(l) = -l**3 + l**2 - 1. Let c(n) = -6*n**3 + 4*n**2 + 2*n - 4. Let q = 11 + -3. Let i = -4 + q. Let b(k) = i*p(k) - c(k). Factor b(t).
2*t*(t - 1)*(t + 1)
Let w(i) be the first derivative of 0*i**3 + 3 - 1/240*i**5 + 0*i**4 + i**2 + 1/480*i**6 + 0*i. Let h(n) be the second derivative of w(n). Factor h(l).
l**2*(l - 1)/4
Suppose 3*z = -4*a - 3, 1 + 8 = -3*a. Let m(q) be the third derivative of 1/12*q**4 + 0 + 0*q - 1/18*q**5 + q**2 + 2/9*q**z. Let m(i) = 0. Calculate i.
-2/5, 1
Let z(o) be the first derivative of 0*o**2 + 0*o - 1/3*o**4 + 2/9*o**3 + 1 + 2/15*o**5. Factor z(s).
2*s**2*(s - 1)**2/3
Let s(k) be the third derivative of k**6/30 - 4*k**5/15 + 7*k**2. Find q, given that s(q) = 0.
0, 4
Let s(b) be the third derivative of 21*b**8/32 + 13*b**7/10 - 97*b**6/30 - 6*b**5/5 + 3*b**4 + 8*b**3/3 - 13*b**2. Solve s(m) = 0.
-2, -2/7, 2/3
Let a be 5/720*356 - (-6)/(-27). Find r such that a - 3/2*r + 1/4*r**2 = 0.
3
Let m(l) be the second derivative of 0 - 3/70*l**5 + 1/14*l**4 + 0*l**2 - l + 1/105*l**6 - 1/21*l**3. Find d such that m(d) = 0.
0, 1
Let u = -27 + 29. Factor 8/5 + 14/5*m**u - 3/5*m**3 - 4*m.
-(m - 2)**2*(3*m - 2)/5
Let p(z) = -3*z - 7. Let o be p(-5). Suppose 5*f + o = 7*f. Solve 0*s**2 - 1/4*s**f + 1/2*s**3 - 1/2*s + 1/4 = 0.
-1, 1
Factor -32*u + 81*u - 39*u - 5 - 5*u**2.
-5*(u - 1)**2
Factor -16/3*x**3 - 20/3*x**2 + 0 - 8/3*x - 4/3*x**4.
-4*x*(x + 1)**2*(x + 2)/3
Let l(u) be the third derivative of 0 - 1/3*u**3 + 1/120*u**5 + 9*u**2 - 1/30*u**6 + 0*u + 1/140*u**7 + 1/6*u**4. Determine f so that l(f) = 0.
-1, 2/3, 1, 2
Let z(y) be the third derivative of -y**5/135 - y**4/108 + y**3/27 - y**2. Determine o so that z(o) = 0.
-1, 1/2
Factor -2/9*p**3 - 2/9*p**2 + 2/9 + 2/9*p.
-2*(p - 1)*(p + 1)**2/9
Let z(o) be the second derivative of o**4/12 + 4*o**3/3 + 8*o**2 - 2*o. Factor z(t).
(t + 4)**2
Let z(j) be the first derivative of 18*j**5/35 + j**4/2 - 4*j**3/21 + 5. Determine m so that z(m) = 0.
-1, 0, 2/9
Let p be 1*(25/20)/(-5)*-2. Factor 0 + 3/2*u - p*u**2.
-u*(u - 3)/2
Let s(p) be the first derivative of 4/7*p + 5/7*p**2 + 2/7*p**3 - 1 - 1/14*p**4 - 2/35*p**5. Factor s(x).
-2*(x - 2)*(x + 1)**3/7
Factor 16/5 - 24/5*n - 2/5*n**3 + 12/5*n**2.
-2*(n - 2)**3/5
Let t = 92 - 63. Let h = -27 + t. Factor -2/5 - 2/5*c**h + 4/5*c.
-2*(c - 1)**2/5
Factor -20*q**4 + 2*q**2 - 16*q**3 - 8*q**5 - 3*q**2 - 3*q**2.
-4*q**2*(q + 1)**2*(2*q + 1)
Let s(m) be the first derivative of 2*m**5/65 + 3*m**4/26 - 4*m**2/13 - 30. Suppose s(g) = 0. What is g?
-2, 0, 1
Suppose -7 + 5 + 7*y - 8 + y**2 + 2*y = 0. What is y?
-10, 1
Let j(y) be the third derivative of y**8/840 - y**7/105 + y**6/75 + 51*y**2. Factor j(r).
2*r**3*(r - 4)*(r - 1)/5
Suppose 2*p = -0*p + 4. Solve -2/3*f + 0 - 2/3*f**p = 0.
-1, 0
Let f(h) be the third derivative of h**7/735 + h**6/105 + h**5/35 + h**4/21 + h**3/21 + 6*h**2. Factor f(n).
2*(n + 1)**4/7
Let b(h) = -h**2 - 6*h - 3. Let z = 5 + -9. Let v be b(z). Factor o + v*o + 2*o**2 - 