 -4/7 - 18/7*g - 26/7*g**3 + 48/7*g**2.
-2*(g - 1)**2*(13*g + 2)/7
Let v(x) be the third derivative of -x**7/3780 + x**6/1620 - 5*x**3/6 - 6*x**2. Let w(a) be the first derivative of v(a). Factor w(f).
-2*f**2*(f - 1)/9
Factor -10 - 9/2*f**2 - 12*f - 1/2*f**3.
-(f + 2)**2*(f + 5)/2
Let q(l) be the third derivative of l**6/120 - l**5/10 + l**4/2 + 7*l**3/6 - 4*l**2. Let i(o) be the first derivative of q(o). Suppose i(u) = 0. What is u?
2
Let p(d) = -d**3 + 5*d**2 + 6*d + 5. Let f be p(6). Let w(o) = 3*o**2 - 6*o + 5. Let g(z) = z**2 - z + 1. Let c(q) = f*g(q) - w(q). Solve c(b) = 0 for b.
-1/2, 0
Let j be (-3)/(-3) - (4 - 5). Suppose 3*t + 4 = -p, -j*t - p - 4 = -3*t. Factor -8/5*l**3 - 4/5*l + t + 2*l**2 + 2/5*l**4.
2*l*(l - 2)*(l - 1)**2/5
Let d(r) be the third derivative of r**5/120 - r**4/24 + r**3/12 - 8*r**2. Factor d(b).
(b - 1)**2/2
Let w(o) be the second derivative of -2*o + 0 + 0*o**2 + 1/20*o**5 + 1/12*o**4 - 1/3*o**3. Determine y, given that w(y) = 0.
-2, 0, 1
Let g(y) = 3*y - 25. Let a be g(10). Suppose -2*x - 4*u = -a - 13, 0 = x - u. Solve -2/3*k**4 + 0*k + 0 + 0*k**x + 2/3*k**2 = 0 for k.
-1, 0, 1
Let c(x) be the second derivative of -x**5/120 + x**4/48 + 3*x**2/2 - x. Let i(j) be the first derivative of c(j). Find v such that i(v) = 0.
0, 1
Find j such that 60*j - 24*j**2 + 353*j**3 - 718*j**3 - 32 + 361*j**3 = 0.
-8, 1
Let q(d) = d**2 + 5*d - 12. Let n(v) = -2*v**2 - 10*v + 25. Let r(x) = -6*n(x) - 13*q(x). Factor r(a).
-(a - 1)*(a + 6)
Let c(y) = -y - 1. Let b(a) = -2*a**2 - 5*a - 11. Let w(x) = 2*b(x) - 18*c(x). Let w(h) = 0. Calculate h.
1
Let f(l) = -4*l**2 + 5*l + 5. Let w(r) = -4*r**2 + 4*r + 4. Let c(n) = 4*f(n) - 5*w(n). Suppose c(h) = 0. Calculate h.
0
Suppose 7*g + 1 - 15 = 0. Factor -6*b + 3 + 9/4*b**g.
3*(b - 2)*(3*b - 2)/4
Suppose 16*x**3 - 53*x**2 - 52*x**2 - 20*x + 4*x**5 - 8 + 16*x**4 + 97*x**2 = 0. What is x?
-2, -1, 1
Let s(x) be the first derivative of x**9/3024 - x**8/840 + x**7/840 - 4*x**3/3 - 2. Let j(h) be the third derivative of s(h). Factor j(c).
c**3*(c - 1)**2
Factor 4/5 - 3/5*w - 1/5*w**2.
-(w - 1)*(w + 4)/5
Suppose 261*y**2 + 10 + 25*y**3 - 100*y**2 + 45*y - 101*y**2 = 0. What is y?
-1, -2/5
Find q such that 2*q + 99 - q**2 - 99 + 2*q**2 - q**3 = 0.
-1, 0, 2
Let q(p) be the third derivative of 0 + 1/108*p**4 + 2/27*p**3 - 1/540*p**6 + 0*p - 1/135*p**5 - 2*p**2. Solve q(i) = 0 for i.
-2, -1, 1
Let r(z) = -z - 3. Let v be r(-2). Let b = 2 - v. Solve 3*i**b + 0*i**3 - i**3 - i**3 = 0 for i.
0
Let j(b) be the first derivative of 2 - 2*b**2 - 2*b - 2/3*b**3. Solve j(o) = 0 for o.
-1
Suppose -4*q + 55 = -17. Let c be 10/45 + 4/q. Factor -c + 2/9*r**2 - 2/9*r.
2*(r - 2)*(r + 1)/9
What is k in 5*k**2 - 36*k**3 + 3*k + 31*k**3 - 3*k = 0?
0, 1
Let r = 92/39 - 310/429. Let r + 12/11*v + 2/11*v**2 = 0. Calculate v.
-3
Let d(b) be the third derivative of -b**6/240 - 3*b**5/40 - 9*b**4/16 - 2*b**3/3 + 4*b**2. Let w(z) be the first derivative of d(z). What is y in w(y) = 0?
-3
Let v(l) be the first derivative of l**6/6 - 2*l**5/5 + l**4/4 + 13. Factor v(f).
f**3*(f - 1)**2
Let s(z) be the second derivative of 0*z**2 + 1/40*z**5 - 1/24*z**4 - 6*z + 0 + 0*z**3. Factor s(c).
c**2*(c - 1)/2
Let o(k) = 15*k**3 - 36*k**2 + 3*k + 36. Let d(u) = u**3 - u**2 + 1. Let q(m) = -18*d(m) + o(m). Factor q(s).
-3*(s - 1)*(s + 1)*(s + 6)
Let d(r) be the second derivative of 8*r**2 + 15*r**4 + 4*r + 0 + 44/3*r**3 + 9/5*r**6 + 81/10*r**5. Factor d(k).
2*(k + 1)*(3*k + 2)**3
Let v(q) be the first derivative of q**6/57 + 6*q**5/95 + 3*q**4/38 + 2*q**3/57 - 8. Factor v(d).
2*d**2*(d + 1)**3/19
Solve -o**2 - 682*o**5 - 5*o**2 - 3*o**3 + 6*o**4 + 685*o**5 = 0 for o.
-2, -1, 0, 1
Let c(s) = 3*s**4 + 7*s**3 - 5. Let b(h) = 8*h**4 + 20*h**3 - 14. Let m(x) = 5*b(x) - 14*c(x). Suppose m(k) = 0. Calculate k.
0, 1
Let d = -469/3074 + 9/53. Let z = d - -229/174. Factor 0*g + 0 - 5/3*g**3 + z*g**4 + 1/3*g**2.
g**2*(g - 1)*(4*g - 1)/3
Let j be (0 + -1)/(2/4). Let z(o) = -5*o**4 - 4*o**3 - 5*o**2. Let p(u) = 36*u**4 + 27*u**3 + 36*u**2. Let x(m) = j*p(m) - 15*z(m). Factor x(y).
3*y**2*(y + 1)**2
Let d(l) be the first derivative of l**8/672 - l**7/210 - l**6/240 + l**5/60 - l**2 + 3. Let i(o) be the second derivative of d(o). Factor i(u).
u**2*(u - 2)*(u - 1)*(u + 1)/2
Let i(z) be the first derivative of -8*z**4/7 - 16*z**3/7 + 15*z**2/7 - 4*z/7 - 3. Factor i(k).
-2*(k + 2)*(4*k - 1)**2/7
Let r(u) be the second derivative of -u**7/126 - u**6/15 + 2*u**5/15 + u**4/6 - 7*u**3/18 + 66*u. Suppose r(p) = 0. Calculate p.
-7, -1, 0, 1
Determine h so that 0 + 2/5*h**3 + 2/5*h**4 - 2/5*h - 2/5*h**2 = 0.
-1, 0, 1
Let n(c) be the first derivative of 4*c**3/3 - 2*c**2 - 4. Determine u so that n(u) = 0.
0, 1
Let y(b) be the first derivative of b**5/180 + b**4/72 - b**3/9 - 3*b**2/2 + 1. Let x(a) be the second derivative of y(a). Let x(l) = 0. Calculate l.
-2, 1
Let l(s) be the second derivative of -s**4/42 + s**3/7 - 2*s**2/7 + 6*s. Determine m, given that l(m) = 0.
1, 2
Let r(s) be the second derivative of -2/7*s**2 + s + 0 - 1/14*s**4 + 1/3*s**3. Suppose r(a) = 0. What is a?
1/3, 2
Let k be (-1)/2 - (-182)/28. Solve 7 - 3*j**2 + 4*j**2 - k + 2*j = 0.
-1
Suppose -q + 78 = 2*q. Let t be (q/65)/(18/50). Factor t*r - 2/9 + 20/9*r**3 - 10/9*r**4 - 20/9*r**2 + 2/9*r**5.
2*(r - 1)**5/9
Let l be (38/2)/(168/48). Factor -2/7*b**5 + 8/7 - 32/7*b + 50/7*b**2 - l*b**3 + 2*b**4.
-2*(b - 2)**2*(b - 1)**3/7
Suppose -20 = -5*o + o. Solve 3*r**2 + 4*r**3 - 2 - 2*r + 3*r**5 + r**2 - 5*r**o - 2*r**4 = 0 for r.
-1, 1
Let q(z) be the first derivative of z - 4. Let p = 0 - -1. Let w(k) = 81*k**2 - 36*k + 7. Let a(g) = p*w(g) - 3*q(g). Factor a(o).
(9*o - 2)**2
Let w(d) be the second derivative of d**7/14 - d**6/10 - 3*d**5/20 + d**4/4 - 2*d. Determine o, given that w(o) = 0.
-1, 0, 1
Factor 9/4*k - 27/8 - 3/8*k**2.
-3*(k - 3)**2/8
Let n be (4/(-36))/((-3)/9). Let p(y) be the first derivative of -1/18*y**6 + 2/9*y**3 - 1/5*y**5 + 1 + 1/2*y**2 + n*y - 1/6*y**4. Suppose p(w) = 0. What is w?
-1, 1
Let u = -20 + 22. Let j be (-12)/(-4)*(-2)/(-18). Factor 0 - j*q**u + 1/3*q.
-q*(q - 1)/3
Factor -2/9*j**4 + 0*j - 2/9*j**3 + 0 + 0*j**2.
-2*j**3*(j + 1)/9
Let l = 12 - 10. Find h, given that -12*h - 12 - 8*h**2 + 0*h**l + 5*h**2 = 0.
-2
Suppose 6 = -3*p + 5*p. Solve 3*k**2 + p*k**3 - 3*k - 3*k - 3 + 3*k = 0 for k.
-1, 1
Suppose 2*x - 50 = 4*f, -x - 4*f - 65 = -4*x. Solve -1 + 8*a**5 - 12*a**4 + 11*a**3 - x*a**3 + 1 - 4*a + 12*a**2 = 0.
-1, 0, 1/2, 1
Let j(i) be the third derivative of 0*i + 2*i**2 - 1/120*i**6 + 0*i**5 + 0*i**4 + 0 + 0*i**3 - 1/105*i**7 - 1/336*i**8. Factor j(q).
-q**3*(q + 1)**2
Let o be 32/24*(-1)/(-2). Let i(p) be the first derivative of -2/9*p**3 + o*p + 1/6*p**4 + 1 - 1/3*p**2. Let i(f) = 0. What is f?
-1, 1
Let n(z) be the second derivative of 0 + 1/3*z**4 + 1/3*z**3 + 1/21*z**7 - 1/5*z**5 - z**2 - 3*z - 1/15*z**6. Find y such that n(y) = 0.
-1, 1
Let t(o) be the first derivative of 0*o**3 + 1/20*o**5 + 0*o + 0*o**2 + 1/8*o**4 + 2. Determine m, given that t(m) = 0.
-2, 0
Suppose 5*t + 4*l = -20, 12*l + 5 = -5*t + 11*l. Find v, given that t*v + 0 - 1/2*v**2 = 0.
0
Let 4/9 - 2/9*l**2 - 2/9*l = 0. Calculate l.
-2, 1
Suppose -6*l + 3*l = 0. Let t(v) be the third derivative of 0 + 0*v**4 - 1/30*v**5 + l*v + 1/3*v**3 - v**2. Suppose t(a) = 0. What is a?
-1, 1
Solve z**4 - 15*z**2 + z + 3*z**3 - 9*z**2 + 27*z**2 = 0 for z.
-1, 0
Let f(i) = i**2 - 5*i - 3. Let s be f(6). Factor 3*y**4 + 2*y**2 + 2*y**2 - 3*y + 2*y**3 + y**s - 7*y**2.
3*y*(y - 1)*(y + 1)**2
Let d = 93 + -274/3. Let 8/3*p**4 - 1/3 + d*p - 1/3*p**3 - 4/3*p**5 - 7/3*p**2 = 0. What is p?
-1, 1/2, 1
Let d(z) = z - 6. Let p be d(12). Let w(l) be the third derivative of 1/96*l**4 + 0*l + 1/120*l**5 + 0*l**3 + 0 - l**2 + 1/480*l**p. Factor w(j).
j*(j + 1)**2/4
Suppose 4*p = 12 + 4. Suppose -2*m - 5 = -p*n + n, -m = 2*n - 15. Let -d**m + 4*d**2 - 4*d**4 + 3*d - 5*d + 3*d**5 = 0. Calculate d.
-1, 0, 1
Let a be (-44)/(-10) - (-2)/(-5). Factor 2*h**4 + 2*h**2 - 4*h**2 - 4*h**a + 4*h**3.
-2*h**2*(h - 1)**2
Let r be -3*((-24)/9)/(-4). Let u = r - -4. Determine c so that -4 - 6*c - c**u - 2*c**2 + c**2 = 0.
-2, -1
Suppose -10/9*z**3 + 2/3 + 10/9*z - 2/3*z**2 = 0. What is z?
-1, -3/5, 1
Let p(h) be the second derivative