 4/7*c**2 + 1. Solve n(a) = 0 for a.
-2, 0
Let t(k) be the third derivative of k**5/80 + 5*k**4/32 + 3*k**3/4 + 25*k**2. Suppose t(r) = 0. Calculate r.
-3, -2
Suppose 6*s = s + 15. Factor -12*r - 9 - 6*r**2 + s*r**2 + 0*r.
-3*(r + 1)*(r + 3)
Let s = -1509838/9 - -167515. Let b = s + 245. Factor 0 + 0*l - 2/9*l**3 + 2/9*l**5 - 2/9*l**4 + b*l**2.
2*l**2*(l - 1)**2*(l + 1)/9
Let q = 1/36630 - 373649/842490. Let s = -1/23 - q. Find k such that 2/5*k**3 - 2/5*k + 2/5 - s*k**2 = 0.
-1, 1
Find f such that -2*f**2 - 2*f**2 - 2*f + 0*f + 6*f = 0.
0, 1
Let a be 8/(-32) + (-89)/(-36) + -2. Let s(k) be the first derivative of 1/18*k**4 + a*k + 1/3*k**2 + 2/9*k**3 - 3. Factor s(p).
2*(p + 1)**3/9
Let j(g) be the second derivative of -g**7/11340 + g**6/1620 - g**5/540 - g**4/4 - 2*g. Let x(k) be the third derivative of j(k). Suppose x(r) = 0. Calculate r.
1
Let c(w) be the second derivative of 5*w**4/12 + 5*w**3/3 - 13*w. Factor c(f).
5*f*(f + 2)
Let r(t) be the first derivative of -t**2 + 0*t**4 + 0*t**3 + 0*t - 1 - 1/30*t**5. Let o(v) be the second derivative of r(v). Solve o(x) = 0.
0
Let j(x) be the third derivative of -x**9/120960 - x**8/20160 + x**5/20 + 7*x**2. Let i(s) be the third derivative of j(s). Solve i(t) = 0 for t.
-2, 0
Let u(c) = -5*c**5 - 10*c**4 - 7*c**3 + c**2 - 3. Let h(m) = -m**5 - m**4 + m**2 - 1. Let t(r) = 3*h(r) - u(r). Find l such that t(l) = 0.
-2, -1, -1/2, 0
Let d be 116/(-174) + (-20)/(-21). Let 3/7*b + 1/7*b**2 + d = 0. Calculate b.
-2, -1
Let z(h) be the first derivative of -2*h**3/3 + 2*h + 8. What is r in z(r) = 0?
-1, 1
Let m(y) be the first derivative of -y**8/168 - y**7/35 - y**6/20 - y**5/30 + 3*y**2 - 7. Let d(u) be the second derivative of m(u). Factor d(z).
-2*z**2*(z + 1)**3
Factor 4*r**2 - 8*r**3 - 44 + 0*r**3 + 44 + 4*r**4.
4*r**2*(r - 1)**2
Let h be (-1)/(-2)*(3 + 25/(-15)). Factor 0 + h*p + 2/3*p**3 - 4/3*p**2.
2*p*(p - 1)**2/3
Let l(p) be the second derivative of -8*p**6/15 - 6*p**5/5 + 21*p**4/4 - 13*p**3/3 + 3*p**2/2 + 15*p. Suppose l(d) = 0. Calculate d.
-3, 1/4, 1
Let -2/3*u + 1/3 + 1/3*u**2 = 0. What is u?
1
Suppose -3 - 5 = -4*c. Factor -v + 3*v**c + 3*v - v**2.
2*v*(v + 1)
Let y(b) be the second derivative of 3/5*b**5 + 13/6*b**4 + 1/15*b**6 + 4*b**2 + 6*b + 4*b**3 + 0. Let y(r) = 0. Calculate r.
-2, -1
Let d be (-3)/(0 - 0 - 1). Suppose -d*q = -2*n - 19, 2*n = 4*q - 8*q + 2. Factor -2*z**q + 7*z**5 - z**5 + 0*z**3 - 4*z**5.
2*z**3*(z - 1)*(z + 1)
Let n(y) be the second derivative of y**7/3780 - y**5/180 - y**4/3 - 8*y. Let d(z) be the third derivative of n(z). Factor d(f).
2*(f - 1)*(f + 1)/3
Let x(z) be the second derivative of z**5/60 - z**4/6 + 2*z**3/3 - 3*z**2/2 + 3*z. Let w(l) be the first derivative of x(l). Factor w(v).
(v - 2)**2
Let p = -24 + 34. Suppose 0*l - 9 = 3*l, 5*l = -z - p. Find i such that i**2 - 1/2*i**z - 1/2 - 1/2*i - 1/2*i**4 + i**3 = 0.
-1, 1
Let w(r) = -r**3 + r**2 - r - 1. Let b(i) = 4*i**3 - 12*i**2 + 16*i - 4. Let l(u) = 2*b(u) + 4*w(u). Factor l(h).
4*(h - 3)*(h - 1)**2
Let w be (12/10)/((-1)/((-105)/28)). Determine u so that -w*u**4 - 14*u**2 + 0 - 4*u - 15*u**3 = 0.
-2, -2/3, 0
Suppose 0 = -3*n + 2*m - 1 + 3, -4*n = m + 1. Suppose 2*s = -6, n = -i - 5*s - 4 - 7. Factor 2*u + u**4 - 3*u + 3*u**2 + 2*u**i - 2*u**4 - 3*u**3.
u*(u - 1)**3
Let k(t) = -t - 1. Let z(j) = 16*j**2 - 6*j - 2. Let p(a) = 2*k(a) - z(a). Factor p(i).
-4*i*(4*i - 1)
Let m(n) = -n**3 + n**2 - n + 1. Let a(j) = -j**4 + 8*j**3 - 5*j**2 + 4*j - 6. Let g(w) = -5*a(w) - 30*m(w). Determine u, given that g(u) = 0.
-1, 0, 1, 2
Let n(t) be the first derivative of t**3/8 - 3*t**2/16 + 13. Factor n(r).
3*r*(r - 1)/8
Let h be ((-4)/(-6))/(3/9). Let z be 1/((12/14)/(88/154)). Factor -2*d**2 - 2/3*d**3 - h*d - z.
-2*(d + 1)**3/3
What is a in -2938*a**5 + 18*a**2 - 18 + 48*a**4 - 22*a**3 + 2929*a**5 + 33*a - 50*a**3 = 0?
-2/3, 1, 3
Let h = 5 + -1. Factor d - h*d + 1 + 2*d**3 + 3*d**2 - 3*d**3.
-(d - 1)**3
Let g = 8 + -3. Factor g*r**4 - 3*r**4 - 3*r**5 + r**5 + 3*r**5 + r**3.
r**3*(r + 1)**2
Let s = 15 - 22. Let p = 10 + s. Factor -b**p - 1/2*b**5 + 3/2*b + 1/2 + b**2 - 3/2*b**4.
-(b - 1)*(b + 1)**4/2
Let l be (-16)/(-15) - (-3 + (-34)/(-10)). Factor -l*q**3 + 4/3*q**2 + 0 - 2/3*q.
-2*q*(q - 1)**2/3
Suppose -a + 6*a + 90 = 0. Let l be -3*92/a - 2. Factor 6*b**3 + l*b**2 + 26/3*b + 4/3.
2*(b + 1)**2*(9*b + 2)/3
Let o(a) be the first derivative of a**3/6 + a**2/4 + 1. Suppose o(d) = 0. Calculate d.
-1, 0
Let l(o) = 3*o**5 - 6*o**4. Let y = 15 - 12. Let u(j) = -j**5 + j**4. Let w(s) = y*l(s) + 12*u(s). Determine f, given that w(f) = 0.
-2, 0
Factor -4*y**2 + 4*y**4 - 620 + 620.
4*y**2*(y - 1)*(y + 1)
Let r be 8/(-14) - 102/(-105). Suppose -8/5*m + r*m**2 + 8/5 = 0. What is m?
2
Suppose 6*p - 14 = -2. Factor -4/3*q**2 + 0*q**4 + 2/3*q**5 + 0 + 0*q - p*q**3.
2*q**2*(q - 2)*(q + 1)**2/3
Let k(r) = -r**3 + r**2 + r + 6. Let n be k(0). Suppose -n*o = -o. Solve 2/7*p**2 + o*p + 0 = 0 for p.
0
Let r(i) = i**3 - i**2 - i - 1. Let o(f) = -f**2 - 5*f + 7. Let p be o(-6). Let a(q) = 4*q**2 + 2*q + 2. Let z(s) = p*a(s) + 2*r(s). Factor z(c).
2*c**2*(c + 1)
Let p = -4 - -6. Suppose m - 4*m = 2*h - 23, 0 = p*m + 3*h - 22. Solve 0*u**2 - 6*u**2 + m*u**2 - u = 0 for u.
-1, 0
Let i = 28 + -10. Let y be -6 + 5 + 22/i. Factor y*a + 2/9*a**2 - 2/9*a**3 - 2/9.
-2*(a - 1)**2*(a + 1)/9
Let k(s) be the third derivative of -s**6/1080 + s**5/90 - s**4/18 + s**3/2 + 7*s**2. Let u(q) be the first derivative of k(q). Let u(z) = 0. Calculate z.
2
Let y(o) be the third derivative of o**6/1260 - o**5/420 + o**3/6 - 2*o**2. Let w(n) be the first derivative of y(n). Factor w(v).
2*v*(v - 1)/7
Suppose 4*y + 4*w + 24 = 4, w + 5 = 2*y. Suppose 4*v = -y*v - u, 4*v - 5*u = 0. Suppose 0*b + 1/4*b**4 + 1/2*b**3 + 0*b**2 - 3/4*b**5 + v = 0. Calculate b.
-2/3, 0, 1
Suppose 4*y - 4 = 3*y. Suppose y*h + 0*h = 88. Factor -22*g**2 - 18*g**4 - 48*g**3 - 2 + 7*g - h*g**2 - 23*g.
-2*(g + 1)**2*(3*g + 1)**2
Suppose 3*w + 4 - 19 = 0. Factor 1 - w*u - u**2 + 2*u + 3*u.
-(u - 1)*(u + 1)
Let i(z) be the second derivative of 5*z**4/48 - z**3/3 - z**2/2 + 3*z. Factor i(a).
(a - 2)*(5*a + 2)/4
Determine z, given that -30*z + 32*z - 4*z**3 - 2*z**5 + 4*z**5 = 0.
-1, 0, 1
Solve u**2 - u - u**4 + u**3 + 0*u + 0*u = 0 for u.
-1, 0, 1
Let a(b) = 2*b**5 - 2*b**4 + b**3. Let d(j) = j**5. Let f be (-7)/9 + (-4)/18. Let h = 21 - 20. Let s(v) = f*a(v) + h*d(v). Factor s(x).
-x**3*(x - 1)**2
Let p(x) be the second derivative of -x**7/3780 - x**6/180 - x**5/20 - x**4/3 + 4*x. Let k(c) be the third derivative of p(c). Factor k(o).
-2*(o + 3)**2/3
Solve -2*s**3 + s**4 - 5*s**4 + 15*s - 13*s + 3*s**4 + 1 = 0.
-1, 1
Let q(j) be the second derivative of j**6/6 + 5*j**5/4 + 15*j**4/4 + 35*j**3/6 + 5*j**2 - 26*j. Let q(n) = 0. Calculate n.
-2, -1
Let o be 1*(6/(-2))/(-21). Determine w, given that 1/7*w**2 - o*w + 0 = 0.
0, 1
Let c(t) be the second derivative of t**6/150 + 3*t**5/100 + t**4/30 + 7*t. Factor c(n).
n**2*(n + 1)*(n + 2)/5
Let i(d) = -3*d + 14. Let y be i(-10). Let t = y - 42. Factor 1/2 + 3*b**2 - 2*b - t*b**3 + 1/2*b**4.
(b - 1)**4/2
Let q(b) = -4*b**5 - 4*b**4 + 8*b**3 + 3*b**2 - 4*b - 9. Let r(u) = -2*u**5 - 2*u**4 + 4*u**3 + u**2 - 2*u - 5. Let n(p) = -6*q(p) + 10*r(p). Factor n(z).
4*(z - 1)**2*(z + 1)**3
Let r(y) be the first derivative of -2*y**3/15 + 2*y**2/5 + 6*y/5 + 4. Factor r(i).
-2*(i - 3)*(i + 1)/5
Determine x so that 1 + 108*x + 81*x**3 - 162*x**2 - 22 - 3 = 0.
2/3
Find g, given that 40/3*g**3 + 100*g**2 + 1000/3*g + 1250/3 + 2/3*g**4 = 0.
-5
Suppose 3*f - 6 = -o, 3*o - f + 2 = -0*f. Let u = -9 - -9. What is p in -1/5*p**3 - 2/5*p**4 - 1/5*p**5 + u*p**2 + 0 + o*p = 0?
-1, 0
Let y(w) be the second derivative of w**4/12 + 4*w**3/3 - 7*w**2/2 - 2*w. Let v be y(-9). Solve 5 + 6*h + 6*h**3 - 5 - 16*h**v + 4 = 0.
-1/3, 1, 2
Let h be 284/18 + 22/99. Let s(t) = 4*t**4 - 13*t**3 + 9*t**2. Let g(n) = -12*n**4 + 40*n**3 - 28*n**2. Let j(k) = h*s(k) + 5*g(k). Factor j(u).
4*u**2*(u - 1)**2
Let f be 15/10 + (-6)/(-4). Factor -11*i**3 + i**2 + 3*i**2 + 5*i**4 - 6*i**3 + 7*i**5 + i**f.
i**2*(i - 1)*(i + 2)*(7*i - 2)
Suppose -3*q = 2*i - 2 - 8, 2*q - 5*i + 6 = 0. Let l = 20/23 - 88/207. Factor -l*s + 2/3*s**q - 2/9.
2*(s - 1)*(3*s + 1)/9
Let 0 - 1/9*z**2 - 2/9*z = 0. What is z