1/3*l**2 - 7*l**3.
-l*(l - 1)**3*(5*l - 2)/3
Suppose 0 = 5*o - 3*o. Suppose -4*h + 2*t = -14, h = -o*h - 4*t - 10. Let -3/4*g**h + 1/2*g**4 + 1/4*g - 1/4*g**3 + 1/4 = 0. What is g?
-1, -1/2, 1
Let d(h) be the third derivative of 0*h**3 + 2/105*h**7 + 3*h**2 + 0*h + 0*h**5 + 0*h**6 + 0 + 0*h**4. Factor d(q).
4*q**4
Let h be 650/70 + (-21)/3. Suppose -12/7*b**4 + 2/7*b + 12/7*b**2 + h*b**3 + 0 - 18/7*b**5 = 0. What is b?
-1, -1/3, 0, 1
Suppose 14 = 2*c + 2*j, c + 4*c = -4*j + 31. Factor -3*h**5 - 15*h**c - 1 + 3*h**2 + 7*h**4 + 13*h**3 - 9*h**2 + 5*h.
-(h - 1)**3*(h + 1)*(3*h - 1)
Let p(r) be the second derivative of r**7/21 - r**5/5 + r**3/3 + 15*r. Let p(t) = 0. Calculate t.
-1, 0, 1
Let s = 7451326/945 + -7885. Let m(f) be the third derivative of -3*f**2 + 0*f**4 + 0*f**6 + 0*f + 0*f**3 + 0 - 1/270*f**5 + s*f**7. Factor m(v).
2*v**2*(v - 1)*(v + 1)/9
Let -36 - i**2 + 2*i - 12*i + 48 - i**2 = 0. Calculate i.
-6, 1
Let q be 4 - (5 - 7)*(-3)/6. Suppose -2/3*p**2 - 1/3*p + 0 - 1/3*p**q = 0. What is p?
-1, 0
Suppose 5*p - 2*p = -18. Let n(o) = o**3 + 6*o**2 + 3. Let k be n(p). Find h, given that 0*h + 0 - h**2 - 2*h**4 - 1/2*h**5 - 5/2*h**k = 0.
-2, -1, 0
Let j(h) be the third derivative of h**8/10080 + h**7/840 + h**6/180 - h**5/12 - 6*h**2. Let v(l) be the third derivative of j(l). Factor v(z).
2*(z + 1)*(z + 2)
Let j be 1/6 - 121/(-462). Let r = j + -2/21. Factor -r*o**4 - 4/3*o**3 - 4/3*o - 2*o**2 - 1/3.
-(o + 1)**4/3
Suppose 0*x - 2/7*x**3 - 6/7*x**4 + 0 + 0*x**2 = 0. Calculate x.
-1/3, 0
Let a be ((-5 - 2) + 3)/(-2). Let j(c) be the first derivative of 2/21*c**3 - 3/7*c**a + 1 + 4/7*c. Factor j(s).
2*(s - 2)*(s - 1)/7
Suppose 0 = m + 3*m - 24. Factor -m*p**3 + 12*p - 12 - 11*p**4 - 7*p**4 + 9*p**2 + 15*p**4.
-3*(p - 1)**2*(p + 2)**2
Let q(n) be the first derivative of -12*n**5/5 - 11*n**4 - 16*n**3 - 8*n**2 + 27. Factor q(g).
-4*g*(g + 1)*(g + 2)*(3*g + 2)
Let c(u) = -8*u**2 - u - 3. Let i be (-16)/24 - 17/(-3). Let q(x) = -15*x**2 - x - 5. Let a(j) = i*c(j) - 3*q(j). Factor a(o).
o*(5*o - 2)
Let z = 11 + -9. Let 6*r**z + r**4 + 1 + 9*r**3 - 14*r**3 + r**3 - 4*r = 0. Calculate r.
1
Let p(i) be the second derivative of 2*i + 0 + 0*i**4 - 1/45*i**6 + 1/15*i**5 + 0*i**3 + 0*i**2. Factor p(n).
-2*n**3*(n - 2)/3
Let i(a) be the first derivative of -3*a**6 + 24*a**5/5 - 2*a**4 + 22. Factor i(v).
-2*v**3*(3*v - 2)**2
Let n(q) be the third derivative of -q**8/1512 - 2*q**7/945 - q**6/540 + 2*q**2. Suppose n(l) = 0. Calculate l.
-1, 0
Let k(z) be the third derivative of -z**7/630 - z**6/180 + z**4/36 + z**3/18 + 20*z**2. Find v such that k(v) = 0.
-1, 1
Solve 3*w**2 - 49*w**4 - 4 - 40*w**3 + 45*w**3 - 20*w + 65*w**3 = 0.
-2/7, 1
Let p(i) be the second derivative of -i**7/8820 + i**5/420 + i**4/12 - 10*i. Let g(r) be the third derivative of p(r). Solve g(f) = 0 for f.
-1, 1
Let o(a) = -14*a**5 + 34*a**4 + 6*a**3 - 34*a**2 + 2*a - 6. Let w(h) = -h**5 - h**4 + h**3 + h**2 + h + 1. Let q(v) = o(v) + 6*w(v). What is j in q(j) = 0?
-1, 0, 2/5, 1
Let q(v) be the first derivative of -12*v**3/5 + 33*v**2/10 - 6*v/5 - 4. Factor q(r).
-3*(3*r - 2)*(4*r - 1)/5
Let t(n) be the third derivative of -n**7/105 + 2*n**6/45 - 7*n**5/90 + n**4/18 - n**2. Solve t(s) = 0 for s.
0, 2/3, 1
Let j(q) be the first derivative of -2*q**3/57 + 4*q**2/19 + 10*q/19 - 1. Factor j(t).
-2*(t - 5)*(t + 1)/19
Let q(i) = -3*i**2 - 10*i + 24. Let n(x) = 3*x**2 + 9*x - 24. Let y(m) = 4*n(m) + 3*q(m). Factor y(d).
3*(d - 2)*(d + 4)
Suppose -5*s - 4*x - 20 = 0, 4*s = 2*x - 40 - 2. Let h(u) = 2*u**2 + 17*u + 11. Let r be h(s). Factor -2/9*f**4 + 2/9*f**2 + 0*f**r + 0 + 0*f.
-2*f**2*(f - 1)*(f + 1)/9
Let k(r) = 13*r**4 - 9*r**3 - 4*r**2 - 2*r. Let j(g) = 38*g**4 - 27*g**3 - 11*g**2 - 7*g. Let i = 18 - 11. Let d(y) = i*k(y) - 2*j(y). Solve d(v) = 0 for v.
-2/5, 0, 1
Let q(m) be the second derivative of m**7/21 + m**6/3 + m**5 + 5*m**4/3 + 5*m**3/3 + m**2 - 5*m. Factor q(s).
2*(s + 1)**5
Let g(q) be the first derivative of 1/3*q**3 + 3*q**2 + 9*q - 1. Determine o, given that g(o) = 0.
-3
Let p(q) be the first derivative of -5*q**6/6 + 6*q**5 - 15*q**4 + 50*q**3/3 - 15*q**2/2 + 8. Factor p(z).
-5*z*(z - 3)*(z - 1)**3
Let d(y) be the first derivative of -1/9*y**3 + 1/3*y**2 - 3 + y. Factor d(p).
-(p - 3)*(p + 1)/3
Let u = 37 + -35. What is b in -10/3*b**u + 8/3 + 16/3*b = 0?
-2/5, 2
Let j = 19/24 + 193/120. Factor -22/5*a + 6/5*a**2 + j.
2*(a - 3)*(3*a - 2)/5
Factor 0*f + 1/3*f**2 + 0 - 1/3*f**3.
-f**2*(f - 1)/3
Let m(t) be the second derivative of 0*t**4 + 1/10*t**5 + 5*t + 0 - 1/3*t**3 + 0*t**2. Factor m(v).
2*v*(v - 1)*(v + 1)
Let v(g) be the third derivative of 0*g + 1/315*g**7 + 0*g**5 - 1/18*g**4 - 3*g**2 + 1/90*g**6 - 1/9*g**3 + 0. Determine b so that v(b) = 0.
-1, 1
Let j be 1/(9/(-5) + 2). Suppose -2*k - 1 = 3, 5*k - j = -5*t. Solve -14/11*l**t - 18/11*l + 32/11*l**5 - 46/11*l**2 - 2/11 + 48/11*l**4 = 0.
-1, -1/4, 1
Let b(s) be the second derivative of s**7/2940 - s**6/1260 - s**3/2 + 3*s. Let q(o) be the second derivative of b(o). Suppose q(r) = 0. What is r?
0, 1
Let u(w) be the third derivative of w**6/40 + w**5/20 - w**4/8 - w**3/2 + 9*w**2. Factor u(h).
3*(h - 1)*(h + 1)**2
Let s = -112 - -116. Factor -r**2 + 0 + 1/3*r + r**s - 1/3*r**3.
r*(r - 1)*(r + 1)*(3*r - 1)/3
Let n(t) be the third derivative of 0 + 1/60*t**4 + 0*t + 1/300*t**5 - 8*t**2 + 0*t**3. Factor n(h).
h*(h + 2)/5
Suppose -6*y + 4 = -14. Suppose 8*o**y - 51*o + 51*o + 8*o**3 - 4*o**2 = 0. Calculate o.
0, 1/4
Let f = 0 - 0. Suppose 4*p - 10 = -5*c + 3*c, 3*p - 18 = -5*c. Factor f + 1/2*x**2 + 1/4*x**c + 1/4*x.
x*(x + 1)**2/4
Let y(d) = 7*d**2 - 1. Let f(b) = -b**2. Let j(w) = -6*f(w) - y(w). Factor j(k).
-(k - 1)*(k + 1)
Let q(a) = 17 - 29*a**4 - 5*a**2 - 34*a**5 + 25*a + 11*a**5 - 2*a. Let g(v) = 4*v**5 + 5*v**4 + v**2 - 4*v - 3. Let d(c) = -34*g(c) - 6*q(c). Factor d(z).
2*z*(z - 1)*(z + 1)**3
Let v(x) be the second derivative of -x**4/66 - x**3/33 + 2*x**2/11 - 6*x. Factor v(n).
-2*(n - 1)*(n + 2)/11
Determine s so that -388/7*s**2 + 288/7*s**3 + 144/7*s - 64/7*s**4 - 16/7 = 0.
1/4, 2
Let y = -9 + 12. Let d = -7 + y. Let i(w) = -12*w**3 + 3*w**2 + 15*w - 15. Let r(k) = -3*k**3 + k**2 + 4*k - 4. Let f(q) = d*i(q) + 15*r(q). Factor f(u).
3*u**2*(u + 1)
Let d(w) = 8*w - 8. Let z(y) = 2*y - 2. Let h(q) = -4*d(q) + 18*z(q). Let v be h(2). Factor 0*k**2 + 2/3*k**3 - 4/3*k**v + 0 + 2/3*k**5 + 0*k.
2*k**3*(k - 1)**2/3
Let k(x) be the second derivative of x**8/28 + 2*x**7/15 + x**6/6 + x**5/15 - 9*x**2/2 - 3*x. Let n(j) be the first derivative of k(j). Factor n(p).
4*p**2*(p + 1)**2*(3*p + 1)
Suppose 5*u + 270 = -15. Let a be u/(-12) + 1/4. Factor -25*q**4 + 13*q + 32*q**3 - 5*q**2 - 2 + 6*q**a - 28*q**2 + 9*q**3.
(q - 1)**3*(2*q - 1)*(3*q - 2)
Suppose -6 - 2 = 2*f. Let b(i) = -12*i**2 + 12*i - 3. Let c(u) = u**3 + 12*u**2 - 11*u + 2. Let p(a) = f*b(a) - 3*c(a). Determine s so that p(s) = 0.
1, 2
Let a(k) be the second derivative of 9/20*k**5 - 1/4*k**4 + 0*k**2 - 3/10*k**6 + 1/14*k**7 + 0 + 0*k**3 + 3*k. Factor a(c).
3*c**2*(c - 1)**3
Let j be 56/(-40) + 4/10. Let x be 4/(-16)*(j + 0). Factor x*t + 1/4*t**2 + 0.
t*(t + 1)/4
Find p, given that 130*p**4 - 803*p**5 + 903*p**5 - 32*p**2 - 16*p + 70*p**4 + 84*p**3 = 0.
-1, -2/5, 0, 2/5
Let k(t) be the second derivative of 3*t**5/160 - t**3/4 - 20*t. Suppose k(r) = 0. Calculate r.
-2, 0, 2
Let j = 66 + -45. Suppose j*z = 19*z. Factor 0 + 2/5*q**3 - 2/5*q**2 + z*q.
2*q**2*(q - 1)/5
Let z(d) = d**3 - d**2 - 2*d - 3. Let h be z(3). Factor -2*t**2 + t + 12*t - h*t.
-2*t*(t - 2)
Factor 628*x - 312*x - x**2 - 318*x.
-x*(x + 2)
Let 107*u**2 - 54*u**2 + 4 - 54*u**2 = 0. Calculate u.
-2, 2
Let d be 4/(-7) - (-24)/42. Find s, given that -1/4*s**4 - 1/4*s**5 + 0*s**2 + 0 + 0*s + d*s**3 = 0.
-1, 0
Suppose 3*s - 15 = -3. Suppose -3*n**3 - 2*n + 3*n**5 - 2*n + s*n = 0. Calculate n.
-1, 0, 1
Let r(s) be the second derivative of -9/10*s**5 - 1/3*s**4 + 0 + 0*s**2 + 0*s**3 - 5*s. Factor r(g).
-2*g**2*(9*g + 2)
Suppose -2*t = -2 - 2. Suppose -5 + 5 - 2*i**t = 0. Calculate i.
0
Suppose 4*w = 5*w + 12. Let o be w/(-40) + 2/10. Factor 0*t + o*t**5 + 0*t**2 + 0*t**4 - 1/2*t**3 + 0.
t**3*(t - 1)*(t + 1)/2
Suppose 0 = -2*c - 3*l + 3 - 1, -2*l + 5 = 5*c. Suppose 5*m - 11 = -c. Factor 0*j**2 + 8*j**3 +