j**6/4 - 3*j**5/5 - j**4/2 - 3*j + 3. Let b(g) be the first derivative of s(g). Factor b(d).
-3*d**2*(d + 1)*(d + 2)**2/2
Suppose -t - 4*t = 0. Let j(y) be the second derivative of -2/3*y**3 + 0 + y + 1/6*y**4 + t*y**2. Factor j(l).
2*l*(l - 2)
Let c be (-8)/(-36) - 170/(-45). Let n(m) be the second derivative of 0 + c*m - 1/6*m**4 - 2*m**2 - m**3. Factor n(q).
-2*(q + 1)*(q + 2)
Let l(k) = k**2 + k + 1. Let t(j) = 9*j - 15. Let x(d) = 3*l(d) - 3*t(d). What is m in x(m) = 0?
4
Let d be (-110)/(-70) - 3/(-7). Factor 2/7*s**d + 0 + 2/7*s.
2*s*(s + 1)/7
Let o(r) be the second derivative of r**6/90 - 7*r**5/60 + 5*r**4/12 - 13*r**3/18 + 2*r**2/3 - 33*r. Let o(m) = 0. Calculate m.
1, 4
Let p(b) = b - 5. Let f be p(7). Suppose -4 + 10 = 2*a. Determine j so that 4/7*j**a + 8/7*j - 10/7*j**f - 2/7 = 0.
1/2, 1
Let a(l) be the second derivative of l**4/16 + 7*l. Find q, given that a(q) = 0.
0
Let a(u) = -u**4 - u**2 + 1. Let x(y) = -3*y**4 - 7*y**3 - 2. Let p(d) = -2*a(d) - x(d). Factor p(h).
h**2*(h + 1)*(5*h + 2)
Factor 2/3*s + 1/3*s**3 - s**2 + 0.
s*(s - 2)*(s - 1)/3
Let i be -2 + -1*(1 + -6). Suppose 0*c - 2 + 2*c**2 + i*c - 3*c = 0. Calculate c.
-1, 1
Let k be (-1)/(-3*8/6). Let r(b) be the first derivative of -k*b**3 - 1/20*b**5 - 1/8*b**2 - 3/16*b**4 + 0*b + 2. Find y, given that r(y) = 0.
-1, 0
Let r = 11/12 - -7/4. Determine o so that 0 - 2/3*o + 2/3*o**3 - 8/3*o**4 + r*o**2 = 0.
-1, 0, 1/4, 1
Let i(w) = -w + 2. Let b be i(0). Let z be -1*((-8)/6 + 1). Find a, given that -2/3*a - 1/3 - z*a**b = 0.
-1
Suppose 0 = 5*w - 4*w. Suppose 20 = -v + 4*d, 2*v + 2*d + 2*d - 20 = w. Solve 2/3*u**2 + 0*u + 2/3*u**3 + v = 0 for u.
-1, 0
Let q(x) = -x**4 + x**3 - x**2 - x + 1. Let w(r) = -6*r**4 + 13*r**3 - 11*r**2 - r + 3. Let l(s) = 4*q(s) - 2*w(s). Factor l(d).
2*(d - 1)**3*(4*d + 1)
Factor 0 - 1/2*o**3 + o**2 - o**4 + 1/2*o.
-o*(o - 1)*(o + 1)*(2*o + 1)/2
Let d(w) be the first derivative of -w**6/57 - 4*w**5/95 + 3*w**4/38 + 36. Factor d(m).
-2*m**3*(m - 1)*(m + 3)/19
Let c be 5/(-10) + 8/14. Let l(a) be the first derivative of -2 - c*a**4 + 2/21*a**3 + 0*a + 0*a**2. Factor l(p).
-2*p**2*(p - 1)/7
Factor 8*h - 5*h - 5*h**2 - 5 + 7*h.
-5*(h - 1)**2
Suppose -9*g + 3*g - 3*g = 0. Factor 3/2*u**3 + g + 3*u**2 + 3/2*u.
3*u*(u + 1)**2/2
Let s(m) = 2*m - 8. Let r be s(8). Factor -3*q + 0*q - 8*q**4 - 7*q + 4*q**5 + 6*q + r*q**2.
4*q*(q - 1)**3*(q + 1)
Let y(w) = -10*w**4 + 5*w**3 + 14*w**2 - 3*w - 2. Let r(o) = -39*o**4 + 21*o**3 + 57*o**2 - 12*o - 9. Let u(c) = -2*r(c) + 9*y(c). What is i in u(i) = 0?
-1, 0, 1/4, 1
Suppose -16*n = -4*n. Solve -2/9*p**4 + 0*p + 0 + n*p**3 + 0*p**2 = 0.
0
Suppose -3 = w - 6. Let g(y) be the first derivative of -2/3*y**3 + 0*y**2 + 2/3*y + 1/3*y**4 + w. Factor g(l).
2*(l - 1)**2*(2*l + 1)/3
Factor -2/5*p**3 + 0*p**2 + 0 - 2/5*p**5 + 4/5*p**4 + 0*p.
-2*p**3*(p - 1)**2/5
Let q(n) = -5*n**4 + 3*n**2. Let h = -5 - -7. Let c(v) = 11*v**4 - 6*v**2. Let x(z) = h*c(z) + 5*q(z). Solve x(r) = 0 for r.
-1, 0, 1
Let u be 8/(-14) - -1 - 6/42. Factor 4/7 - 2/7*g**2 + u*g.
-2*(g - 2)*(g + 1)/7
Let o be (8 + 15/(-2))/((-1)/(-4)). Factor 0 + 0*z + 2/3*z**2 + 2/3*z**5 + 2*z**3 + o*z**4.
2*z**2*(z + 1)**3/3
Let w = 6 - 4. Let 3 - 3 - g**2 + g**4 - g**5 + w*g**5 - g**3 = 0. Calculate g.
-1, 0, 1
Let i(o) = o + 5. Let q be i(-5). Determine x so that -24*x**3 + 25*x**3 + 12*x + q - 6*x**2 - 8 = 0.
2
Factor 4 + 1/4*t**2 + 2*t.
(t + 4)**2/4
Let a(v) be the third derivative of -v**5/15 - v**4/3 - 2*v**3/3 - v**2 + 2*v. Solve a(x) = 0 for x.
-1
Let b(k) be the second derivative of -2*k**6/3 + 13*k**5/5 + 2*k**4 + k. Suppose b(n) = 0. Calculate n.
-2/5, 0, 3
Let j(h) be the first derivative of -h**5/20 + 4*h + 2. Let w(c) be the first derivative of j(c). Factor w(i).
-i**3
Let a(u) be the first derivative of -3/8*u**4 - 1/6*u**3 + u - 1/10*u**5 + 3 + 3/4*u**2. Factor a(x).
-(x - 1)*(x + 1)**2*(x + 2)/2
Suppose 2*s + 2*s + 40 = 0. Let b = s - -10. What is t in b*t + 0 + 2/7*t**2 = 0?
0
Let m(t) be the second derivative of t**8/26880 - t**7/10080 - t**6/1440 + t**4/6 - t. Let o(w) be the third derivative of m(w). Factor o(v).
v*(v - 2)*(v + 1)/4
Factor 1/4*s**5 - s**4 + 0 + s**3 + 0*s + 0*s**2.
s**3*(s - 2)**2/4
Let n(q) be the second derivative of 0*q**3 + 0*q**2 + 1/6*q**4 - q + 0. Factor n(x).
2*x**2
Suppose -i = -n - 0*n - 7, -2*n + 3*i - 16 = 0. Let f be -2*(4 + (n - 0)). Factor 2/3*p**3 + 0 - 2/3*p - 2/3*p**4 + 2/3*p**f.
-2*p*(p - 1)**2*(p + 1)/3
Let u = 7/22 - -9/110. Factor 2/5*m**2 + 4/5*m + u.
2*(m + 1)**2/5
Suppose -5*t + 13 + 42 = -5*o, 0 = 3*t - 2*o - 37. Suppose t*a = 19*a. Factor a - 1/3*l**2 - 1/3*l.
-l*(l + 1)/3
Let k(c) be the third derivative of 5*c**8/336 - c**7/7 + 7*c**6/12 - 4*c**5/3 + 15*c**4/8 - 5*c**3/3 - 19*c**2. Find b such that k(b) = 0.
1, 2
Let w be ((-2)/(-3))/(6 + -4). Let c(b) be the second derivative of -w*b**3 - 2*b**2 + 0 - 2*b + 1/6*b**4. Solve c(a) = 0 for a.
-1, 2
Let l(z) = -z**3 + 14*z**2 + 16*z - 13. Let r be l(15). Determine g, given that 0 + 2/5*g - g**3 + 3/5*g**r = 0.
-2/5, 0, 1
Let f(z) = 51*z**2 + z - 50. Let y(k) = 10*k**2 - 10. Let s(u) = 2*f(u) - 11*y(u). Factor s(v).
-2*(v + 1)*(4*v - 5)
Let b(m) = m + 1. Let z(w) = -4*w**2 + 12*w + 12. Let k(a) = -12*b(a) + z(a). Factor k(p).
-4*p**2
Let j = -168 + 171. Factor h**2 + 0 + 1/3*h**4 - 1/3*h - h**j.
h*(h - 1)**3/3
Let y(r) be the third derivative of -1/30*r**5 - 1/35*r**7 - r**2 + 0*r**4 + 0*r + 0 + 0*r**3 - 1/20*r**6 - 1/168*r**8. Factor y(q).
-2*q**2*(q + 1)**3
Let c be (7 + -6)*4/7. Factor -18/7*v**3 + 10/7*v**2 + 2*v**4 - 2/7*v - c*v**5 + 0.
-2*v*(v - 1)**3*(2*v - 1)/7
Let o(w) be the third derivative of -7*w**6/660 - w**5/165 + 7*w**2. Factor o(z).
-2*z**2*(7*z + 2)/11
Let -10*a + 4 + 1/4*a**4 - 5/2*a**3 + 33/4*a**2 = 0. Calculate a.
1, 4
Let h(p) = 2*p**3 - 10*p**2 + 8*p. Let i(j) = -j**2 + j. Let z(a) = 2*h(a) - 28*i(a). Determine x, given that z(x) = 0.
-3, 0, 1
Suppose -21*k + 17*k = 16. Let w be 2/k*(-8)/10. Factor 0 + 8/5*d**2 + w*d**3 + 8/5*d.
2*d*(d + 2)**2/5
Let j be (-12)/(-16)*16/126. Let s(h) be the first derivative of 4/7*h**2 - 2 - j*h**3 + 2/7*h - 2/7*h**4. Factor s(p).
-2*(p - 1)*(p + 1)*(4*p + 1)/7
Let s(z) be the second derivative of -z**6/10 - z**5/2 - 7*z**4/12 + 2*z**3/3 + 2*z**2 - 11*z. Factor s(x).
-(x + 1)**2*(x + 2)*(3*x - 2)
Let m = 14 - 20. Let j = -1 - m. What is b in -2*b**2 - 3*b**2 + b + j*b**2 + b**2 = 0?
-1, 0
Solve -14/9*h - 4/9*h**2 + 4/9 + 14/9*h**3 = 0 for h.
-1, 2/7, 1
Let o = -5 - 2. Let c = o + 11. Factor 2*q + 12*q**3 + 2*q**5 - 8*q**2 - 5*q**c - 6*q**4 + 3*q**4.
2*q*(q - 1)**4
Let c(l) = -2*l**4 + 19*l**3 - l**2 - 5*l + 3. Let j(h) = h**4 - 9*h**3 + h**2 + 3*h - 2. Let i(m) = -3*c(m) - 7*j(m). Suppose i(s) = 0. Calculate s.
-1, 1, 5
Let a(m) = -m**2 + 6*m. Let b be a(6). Let l be (b/2)/(1/1). Suppose -4/7*o**3 + 0 - 2/7*o**2 + l*o - 2/7*o**4 = 0. What is o?
-1, 0
Let o(f) be the first derivative of f**3/9 + f**2/6 + 4. Factor o(t).
t*(t + 1)/3
Factor 1/2*g**2 - 3/4*g - 1/4*g**5 - 1/2 + g**3 + 0*g**4.
-(g - 2)*(g - 1)*(g + 1)**3/4
Suppose -3*x = g - 2*g + 8, 0 = 5*g - 2*x - 14. Factor 3*i**3 - 11*i**g - 9*i**2 + 0*i**2 - 27 + 45*i - i**2.
3*(i - 3)**2*(i - 1)
Let h = 30 + -20. Let i(f) = -f**2 + 9*f + 14. Let l be i(h). Factor -2*v**3 + l*v**2 - v - 3*v + 2*v.
-2*v*(v - 1)**2
Let z(k) be the second derivative of k**7/14 - k**6/5 + 3*k**5/20 + 9*k. Factor z(r).
3*r**3*(r - 1)**2
Factor -2/9*b**3 + 2/9*b + 0 - 2/9*b**2 + 2/9*b**4.
2*b*(b - 1)**2*(b + 1)/9
Let c(n) be the third derivative of 0 + 0*n**4 + 0*n**6 + 1/1680*n**7 + 0*n**5 + 3*n**2 - 1/3*n**3 + 0*n. Let b(d) be the first derivative of c(d). Factor b(f).
f**3/2
Let t(m) be the first derivative of -2*m**2 + 0*m**2 + 3*m**3 - 8*m + 2 - m**3 + 2*m**3. Factor t(w).
4*(w - 1)*(3*w + 2)
Suppose -k + 2 = -3*v - 0, 2*k + 4*v - 4 = 0. Let b be (3/(-4) - -1) + 0. Factor -k*a**2 - b - 7/4*a + 4*a**3.
(a - 1)*(4*a + 1)**2/4
Let c(z) = -z + 3. Let t be c(2). Let i be t - 7/(147/(-45)). Suppose 6*p**3 + 4/7*p + i*p**2 + 34/7*p**4 + 10/7*p**5 + 0 = 0. Calculate p.
-1, -2/5, 0
Let a(k) be the third derivative of k**5/12 - k**4/8 - k**3/3 + 10*k**2. Solve a(c) = 0 for c.
-2/5, 1
Let p be (-6 + 8)/(3 + 14/(-6)). Let q(d) be the first derivative of 1/2*d**4 - 4/3*d**p + d