 be 3/r - (-3)/15. Factor -g**3 + 0*g**2 + 1/2*g**4 + g - z.
(g - 1)**3*(g + 1)/2
Let p(d) = -d**3 + 9*d**2 - 6*d - 16. Let z be p(8). Suppose -2/3*s**2 + z*s + 2/3 = 0. What is s?
-1, 1
Let a(c) be the second derivative of 0 - 3/2*c**4 + 2*c**3 + 3/5*c**5 - 3/2*c**2 - 1/10*c**6 + c. Determine u, given that a(u) = 0.
1
Let p(x) = -5*x - 33. Let i be p(-7). Factor 0*n - 2/9 + 2/9*n**i.
2*(n - 1)*(n + 1)/9
Suppose -2*f + 56 = -4*f. Let t be 8/f + (-10)/(-7). Factor -2/7*p**4 + 12/7*p**3 - t + 24/7*p - 26/7*p**2.
-2*(p - 2)**2*(p - 1)**2/7
Suppose 71 + 51 = 4*k - f, 4*k - 4*f - 116 = 0. Let m be k/6 + (-3)/(-9). Factor m*d**2 + d + 8*d**3 + 7/2*d**4 + 0.
d*(d + 1)**2*(7*d + 2)/2
Let c(u) = -2*u**3 - 10*u**2 + 10*u + 2. Let n(l) = l**3 + 7*l**2 - 7*l - 1. Let o(m) = -5*c(m) - 8*n(m). Factor o(p).
2*(p - 1)**3
Let z(b) be the second derivative of 3*b - 1/27*b**3 - 1/90*b**5 + 0 + 0*b**2 + 1/27*b**4. What is w in z(w) = 0?
0, 1
Let a(l) be the second derivative of -2*l - 1/6*l**4 + 0*l**2 + 0 - 1/6*l**3 - 1/20*l**5. Factor a(t).
-t*(t + 1)**2
Let z(n) = -7*n**3 + 16*n**2 - 9*n. Let y(l) = -36*l**3 + 80*l**2 - 44*l. Let t(m) = -3*y(m) + 16*z(m). Find f, given that t(f) = 0.
0, 1, 3
Let s(f) be the second derivative of -3*f - 1/16*f**4 - 1/8*f**3 - 1/80*f**5 + 0 - 1/8*f**2. Factor s(y).
-(y + 1)**3/4
Let t(z) = 9*z**2 - 12*z - 12. Let b(k) = -k**2 + k + 1. Let x(h) = -12*b(h) - t(h). Determine w, given that x(w) = 0.
0
Let a(v) be the second derivative of 5*v**7/14 - 7*v**6/6 + v**5/2 + 5*v**4/2 - 25*v**3/6 + 5*v**2/2 - v + 3. Determine n so that a(n) = 0.
-1, 1/3, 1
Let d(v) be the second derivative of v**6/40 - v**5/20 - 5*v**4/8 - 3*v**3/2 + 3*v**2/2 - v. Let t(y) be the first derivative of d(y). What is k in t(k) = 0?
-1, 3
Let u be 1 + 10/(-14) + (-72)/(-126). Factor 6/7*n + 2/7*n**3 - u*n**2 - 2/7.
2*(n - 1)**3/7
Let r(c) be the second derivative of c**4/66 - 8*c**3/33 + 16*c**2/11 + 6*c. Find s, given that r(s) = 0.
4
Let i(r) be the second derivative of -r**5/50 - r**4/15 - r**3/15 + 6*r. Let i(z) = 0. What is z?
-1, 0
Let g be ((-4 - -1) + 2)*12. Let w be 16/(-300)*30/g. Factor -w*v**2 - 4/15*v - 2/15.
-2*(v + 1)**2/15
Let i(a) = -a + 3. Let l be i(-4). Let y(s) = s - 7. Let n be y(l). Find j, given that 0*j**4 + n + 0*j + 0*j**2 - 1/2*j**3 + 1/2*j**5 = 0.
-1, 0, 1
Let a be (39/9 - 4)*1/1. Suppose 1/3*y**2 - 2/3*y + a = 0. What is y?
1
Suppose -8*z + 8 = -4*z - 3*c, 6 = 3*z + 5*c. Let a be (z/24)/((-24)/(-320)). Factor -14/9*p**2 - 2/3*p**3 - a*p - 2/9.
-2*(p + 1)**2*(3*p + 1)/9
Let -1/2*r**2 + 1/2 - 1/2*r + 1/2*r**3 = 0. Calculate r.
-1, 1
Let j(i) = -i**2 + 7*i - 10. Let b be j(4). Let t(w) be the second derivative of 3*w - 1/48*w**4 + 1/80*w**5 + 1/8*w**b - 1/24*w**3 + 0. Factor t(v).
(v - 1)**2*(v + 1)/4
Let p(u) = 15*u**2 - 25*u - 5. Let h(k) = -23*k**2 + 38*k + 8. Let m(x) = 5*h(x) + 8*p(x). Factor m(l).
5*l*(l - 2)
Let d(a) = 9*a**3 - 9*a**2 + 21. Let j(q) = -2*q**3 + 2*q**2 - 5. Let h(g) = 5*d(g) + 21*j(g). Let h(f) = 0. Calculate f.
0, 1
Let a(b) = -3*b**2 - 11*b - 8. Suppose 3*q - 6*q - 15 = 2*c, -5*c = 0. Let v(p) = -2*p**2 - 7*p - 5. Let y(x) = q*a(x) + 8*v(x). Factor y(m).
-m*(m + 1)
Let u(s) = s**3 + 2*s**2 + 2*s + 1. Let j be u(-1). Factor 18*g**3 - 20*g**3 + 2 + j*g**2 - 2*g**2 + 0*g + 2*g.
-2*(g - 1)*(g + 1)**2
Let x(l) be the first derivative of l**6/360 - l**5/60 + l**4/24 - 4*l**3/3 + 1. Let m(z) be the third derivative of x(z). Let m(q) = 0. Calculate q.
1
Factor 2/9*q**2 + 2/9 + 4/9*q.
2*(q + 1)**2/9
Let j(p) be the first derivative of -p**6/21 + 2*p**5/7 - 3*p**4/7 - 8*p**3/21 + 8*p**2/7 + 13. What is m in j(m) = 0?
-1, 0, 2
Suppose 2*g - 3 = -0*g - y, 0 = 3*g - y - 17. Let h(q) = q**2 - 22*q - 31. Let a(z) = -21*z - 30. Let i(d) = g*a(d) - 3*h(d). Solve i(k) = 0.
-3
Let f(x) be the first derivative of 3*x**4/10 - 7*x**3/5 - 3*x**2/2 + 12*x/5 + 20. Solve f(s) = 0.
-1, 1/2, 4
Let g(u) = u**3 + 8*u**2 + 5. Let i be g(-8). What is v in 0 + 0*v + 1/4*v**2 + v**3 - v**i - 1/4*v**4 = 0?
-1, -1/4, 0, 1
Let k(f) be the second derivative of -1/21*f**3 - 2/7*f**2 + 1/42*f**4 + 0 - 7*f. Factor k(j).
2*(j - 2)*(j + 1)/7
Let r(q) = -q**3 + 2*q**2 - q + 2. Let a(m) = -m**3 + m**2 + 1. Let g(k) = 2*a(k) - r(k). Factor g(d).
-d*(d - 1)*(d + 1)
Factor -4/9 - 8/9*d**2 - 10/9*d - 2/9*d**3.
-2*(d + 1)**2*(d + 2)/9
Factor 3/2*g**2 + 1/2*g**3 + 3/2*g + 1/2.
(g + 1)**3/2
Let z = -718 - -721. Factor 0 + p**z + 1/2*p**4 + 0*p + 1/2*p**2.
p**2*(p + 1)**2/2
Let u = 53/141 - 2/47. Suppose 6*r - 2*r - 8 = 4*y, r + 4*y + 8 = 0. Factor r - 2/3*v + u*v**2.
v*(v - 2)/3
Factor -22/7*m + 10/7 - 2/7*m**3 + 2*m**2.
-2*(m - 5)*(m - 1)**2/7
Let v(m) be the third derivative of -1/30*m**5 + 0*m - 3*m**2 + 0 + 0*m**3 + 1/12*m**4. Find s, given that v(s) = 0.
0, 1
Factor 2/5*b**3 - 4/5*b**2 + 0 + 2/5*b**4 + 0*b.
2*b**2*(b - 1)*(b + 2)/5
Suppose 4*q + 557 - 573 = 0. Let 7/2*p**3 + 0*p + 0 - p**2 - q*p**4 + 3/2*p**5 = 0. What is p?
0, 2/3, 1
Let a(j) = j**3 - 5*j**2 - 8*j + 3. Let n be a(7). Find d, given that -45 - 2*d + n - 2*d**5 + 4*d**3 = 0.
-1, 0, 1
Let l = -456/175 + 133604/1575. Let g = l + -244/3. Factor -4/3*t**3 + g*t**2 - 2/9*t + 8/9*t**4 + 0 - 2/9*t**5.
-2*t*(t - 1)**4/9
Let m(q) be the second derivative of 3*q**5/20 + 5*q**4/2 - 23*q**3/2 + 18*q**2 - 30*q. Factor m(w).
3*(w - 1)**2*(w + 12)
Let m(z) be the first derivative of 0*z + 1 - 1/3*z**2 - 1/24*z**4 + 2/9*z**3. Factor m(g).
-g*(g - 2)**2/6
Let l(c) = 9*c**3 - 5*c**2 - 14*c + 4. Let b(f) = 125*f**3 - 70*f**2 - 195*f + 55. Let o(i) = 4*b(i) - 55*l(i). Factor o(s).
5*s*(s - 2)*(s + 1)
Suppose 25 = l - 6*l. Let x = l - -9. Determine z, given that -12 - 15*z**2 - 3*z - 51*z**3 - 9*z**x + 16*z**2 + 27*z**5 + 27*z + 20*z**2 = 0.
-1, 2/3, 1
Let g(w) = 22*w**4 - 6*w**3 - 16*w**2 + 14*w + 12. Let q(a) = 2*a**4 - a**2. Let h(j) = 2*g(j) - 20*q(j). Solve h(t) = 0.
-1, 2, 3
Let p be 6*1 - 3/(-3). Let q be (-2)/p - (-1762)/42. Factor 8/3*o + 0 - 20*o**2 + 50*o**3 - q*o**4.
-o*(5*o - 2)**3/3
Let l(f) be the third derivative of f**7/12600 + f**6/1800 + f**5/600 - f**4/24 + 2*f**2. Let x(s) be the second derivative of l(s). Factor x(j).
(j + 1)**2/5
Factor 4/3*z - 4/3*z**3 + 2/3*z**2 + 0 - 2/3*z**4.
-2*z*(z - 1)*(z + 1)*(z + 2)/3
Factor 6*a - a**2 - 18 + 6 + 4*a**2 - 3*a**3 + 6*a.
-3*(a - 2)*(a - 1)*(a + 2)
Let f(n) = n**3 - 9*n**2 + 8*n + 10. Let q be f(8). Suppose 0 = 5*o - 0 - q. Factor 5*i**o - 3*i**2 - i**3 - i - 1 - i**2 + 2*i.
-(i - 1)**2*(i + 1)
Let k(o) be the first derivative of -3*o - 8/3*o**2 - o**4 - 4 - 1/45*o**6 - 20/9*o**3 - 7/30*o**5. Let z(n) be the first derivative of k(n). Factor z(w).
-2*(w + 1)*(w + 2)**3/3
Suppose 4*i - 66 = -26. Factor 0 + 21*p**2 + 10*p + 4 + i*p.
(3*p + 2)*(7*p + 2)
Suppose 0 = 4*w - 2*k, -w - 4*k - 18 = -9*k. Solve 3*f**w - 3/2 + 3/4*f**5 - 3/2*f**3 + 3/4*f - 3/2*f**4 = 0.
-1, 1, 2
Let v(r) be the third derivative of -r**8/560 + r**7/350 + 7*r**2. Factor v(h).
-3*h**4*(h - 1)/5
Suppose -6 = -3*x + x. Factor 0 - 9/2*z**2 + 7/2*z**x + z.
z*(z - 1)*(7*z - 2)/2
Suppose 3*u + 2*m = 22, 6*m - 3*m = 2*u - 6. Suppose 5*f - u = 2*f. Suppose -1 + 2*n - f*n**2 + 0 - 3*n**2 + 4*n**2 = 0. Calculate n.
1
Let u = 15 + -9. Suppose 2*r - 4*r = -u. Determine y so that 10*y**3 + 2*y**2 + y - 3*y**r - 2*y + 4*y**4 = 0.
-1, 0, 1/4
Let c(h) be the second derivative of 1/120*h**6 + 0 + 0*h**4 - 3/80*h**5 + 4*h + 0*h**2 + 1/6*h**3. Let c(w) = 0. What is w?
-1, 0, 2
Let s(i) be the third derivative of -i**8/5880 - i**7/1470 - i**6/1260 - i**3/3 - i**2. Let j(n) be the first derivative of s(n). Let j(d) = 0. Calculate d.
-1, 0
Suppose -4*o**2 + 7*o**2 + 5 - 3*o - 5 = 0. What is o?
0, 1
Let v(r) = 9*r**3 + r**2 - r - 5. Let o(s) = -35*s**3 - 5*s**2 + 5*s + 20. Let n(y) = -4*o(y) - 15*v(y). Let n(a) = 0. Calculate a.
-1, 1
Let k(h) be the third derivative of -h**5/24 + 5*h**4/24 + 14*h**2. Factor k(v).
-5*v*(v - 2)/2
Let z(c) be the first derivative of 3*c**4 + 16*c**3/3 + 2*c**2 - 9. Factor z(a).
4*a*(a + 1)*(3*a + 1)
Let o(w) be the second derivative of 2*w**7/21 - 2*w**6/5 + 3*w**5/5 - w**4/3 - 12*w. Find f such that o(f) = 0.
0, 1
Let b(z) be the first derivative of 1 - 4*z - 1/27*z**4 + 1/27*z**3 + 1/90*z**5 + 0*z**2. Let f(n) be the first derivative of b(n). Factor f(v).
2*v*(v - 1)*