1
Let u(y) be the first derivative of 4*y**3/7 - 4*y**2/7 - 13. Suppose u(w) = 0. What is w?
0, 2/3
Let q(l) be the second derivative of -1/80*l**5 + 3*l + 0 + 1/48*l**4 + 1/12*l**3 + 0*l**2. Factor q(i).
-i*(i - 2)*(i + 1)/4
Suppose -y = -0*y - 6. Let z(a) be the second derivative of 1/21*a**3 + 1/49*a**7 + 1/21*a**4 + 0 - 2/35*a**5 - a - 2/105*a**y + 0*a**2. Solve z(w) = 0 for w.
-1, -1/3, 0, 1
Let k(x) be the second derivative of -x**7/168 - x**6/60 + x**5/80 + x**4/24 + 3*x. Solve k(t) = 0 for t.
-2, -1, 0, 1
Factor -6*n + 4*n**4 - 3*n**2 - 3 - n**4 + 3 + 6*n**3.
3*n*(n - 1)*(n + 1)*(n + 2)
Let g(f) be the first derivative of -56*f**5/5 + 71*f**4/2 - 64*f**3/3 + 4*f**2 - 41. Let g(r) = 0. What is r?
0, 1/4, 2/7, 2
Suppose 4*f - 6 = 3*f - 3*t, 4*f + 21 = 3*t. Let z(g) = 3*g**2 - 3*g - 3. Let k(y) = 9*y**2 - 9*y - 8. Let o(a) = f*k(a) + 8*z(a). Factor o(x).
-3*x*(x - 1)
Let y(n) be the second derivative of 0*n**2 + 0*n**3 + 1/18*n**4 + 0 - 3*n. Factor y(f).
2*f**2/3
Let g(d) = 3*d**3 - 3*d**2 + d. Let b(m) = -m**3 - m + 1. Let i(a) = -4*b(a) - g(a). Let l(z) be the first derivative of i(z). Factor l(x).
3*(x + 1)**2
Let g(o) be the first derivative of o**5/25 + o**4/20 - 7*o**3/15 - o**2/10 + 6*o/5 + 40. Determine j, given that g(j) = 0.
-3, -1, 1, 2
Let r be (-6)/(-1)*(-5)/(-6). Let s(k) be the second derivative of -1/36*k**4 + 0 + 3*k + 0*k**2 + 1/60*k**r + 0*k**3. Solve s(g) = 0.
0, 1
Let b(v) be the second derivative of -v**5/10 + v**4/6 + 2*v**3/3 + 7*v. Let b(w) = 0. What is w?
-1, 0, 2
Let b = -11 + 11. Let m(o) be the second derivative of -2*o - 1/54*o**4 + 0 + b*o**3 + 1/9*o**2. Determine y so that m(y) = 0.
-1, 1
Let j(t) be the third derivative of -t**9/15120 - t**8/13440 + t**7/5040 - t**4/12 - t**2. Let z(i) be the second derivative of j(i). Factor z(u).
-u**2*(u + 1)*(2*u - 1)/2
Let r(f) be the third derivative of f**5/24 + 5*f**4/48 - 5*f**3/6 - f**2. Factor r(v).
5*(v - 1)*(v + 2)/2
Let u(w) be the second derivative of w**6/40 - 3*w**5/40 - w**4/4 + w**3/4 + 9*w**2/8 - 8*w. Let u(c) = 0. What is c?
-1, 1, 3
Suppose 0 = 5*n - m - 17 - 2, 6 = -2*n - 3*m. Let g(q) = q**2 - 11*q - 8. Let w(s) = -10*s - 8. Let x(f) = n*w(f) - 2*g(f). Find c such that x(c) = 0.
-2
Let u(h) = h**3 - 9*h**2 + 8. Let q be (-3)/(-3 + 24/9). Let y be u(q). Suppose 26/3*c**2 - y*c + 2/3*c**4 + 8/3 - 4*c**3 = 0. Calculate c.
1, 2
Let k(m) be the second derivative of 49*m**7/2 + 196*m**6/5 - 483*m**5/20 - 67*m**4/2 + 34*m**3 - 12*m**2 + 25*m. Let k(t) = 0. Calculate t.
-1, 2/7
Factor 8*b**3 + 12*b**2 - 2*b**3 - 5*b**2 - 5*b**2.
2*b**2*(3*b + 1)
Let 0 + 2/5*y**2 - 2/5*y = 0. Calculate y.
0, 1
Solve -2/7*f**2 + 20/7 + 18/7*f = 0.
-1, 10
Let a(r) be the first derivative of 4*r**6 - 28*r**5/5 + 4*r**3/3 + 26. Find q such that a(q) = 0.
-1/3, 0, 1/2, 1
Factor -6/5*h - 3/5*h**2 + 0.
-3*h*(h + 2)/5
What is y in 0 + 0*y + 3/4*y**5 + 3/4*y**3 + 3/2*y**4 + 0*y**2 = 0?
-1, 0
Let g(v) be the third derivative of -v**5/120 + v**4/4 - 3*v**3 - 23*v**2. Find s such that g(s) = 0.
6
Let b(o) be the second derivative of -o**9/1890 - o**8/672 - o**7/1260 + 2*o**4/3 - 4*o. Let q(l) be the third derivative of b(l). Let q(w) = 0. What is w?
-1, -1/4, 0
Let m(b) = b**4 - 2*b**3 + 2*b**2 - b + 3. Let c(y) = 2*y**4 - 4*y**3 + 3*y**2 - y + 5. Let i(x) = 3*c(x) - 5*m(x). Factor i(p).
p*(p - 2)*(p - 1)*(p + 1)
Let s(n) = 9 + 2*n + 0*n - n + 0*n. Let i be s(-7). Let -2*d**2 + 3*d**i - 9 - 3*d**2 + 1 - 8*d = 0. Calculate d.
-2
Let k(v) be the third derivative of -v**8/112 - v**7/35 + v**5/10 + v**4/8 + 3*v**2. Determine z, given that k(z) = 0.
-1, 0, 1
Suppose 0 = -2*d + 9 - 1. Let i(t) be the third derivative of 2*t**2 + 1/9*t**3 + 0 + 1/90*t**5 + 0*t - 1/18*t**d. Factor i(x).
2*(x - 1)**2/3
Let a = 77 - 769/10. Let l(v) be the first derivative of 0*v**3 - a*v**5 + 1/2*v**2 + 1/2*v - 1 - 1/4*v**4. Factor l(x).
-(x - 1)*(x + 1)**3/2
Let q(a) = 6*a**2 - 6*a. Let h(v) = 7*v**2 - 7*v. Suppose 0 = y + 5*n + 21, 0 = 4*n + n + 25. Let s(z) = y*h(z) - 5*q(z). Solve s(u) = 0.
0, 1
Find i such that 6 + 2*i**2 - 1 + 4*i - 5 - 4*i**3 - 2*i**4 = 0.
-2, -1, 0, 1
Let 5*d**2 + 25*d + 10 + 8*d**3 - 10*d**3 - 8*d**3 = 0. Calculate d.
-1, -1/2, 2
Suppose -6*x + 20 = -3*x - 5*h, -5*x = -2*h - 8. Let p = x + 2. Let -8/9 - 8/9*l - 2/9*l**p = 0. Calculate l.
-2
Suppose -4*h = -3*v + 12, -5*h = -h + 3*v - 12. Let o(s) be the third derivative of 0*s**4 + 0*s**3 + 0 + 1/150*s**5 + h*s + s**2. Suppose o(t) = 0. What is t?
0
Factor -15*r + 4*r**2 + 3*r**3 + 18*r + 9*r**3 - 11*r.
4*r*(r + 1)*(3*r - 2)
Factor 1/4*z**2 - 3/4*z + 1/2.
(z - 2)*(z - 1)/4
Let c = -23 - -26. Factor -s**3 - 4*s**2 - 7*s**4 - 7*s**3 + c*s**4.
-4*s**2*(s + 1)**2
Let t(i) = -13*i + 275. Let f be t(21). Find j such that 3*j**f + 5/3*j**4 - 2/3 - 13/3*j**3 + 1/3*j = 0.
-2/5, 1
Let j(a) be the third derivative of -a**8/50400 - a**7/6300 + a**5/20 + 4*a**2. Let z(r) be the third derivative of j(r). Suppose z(c) = 0. Calculate c.
-2, 0
Let b be (-21355)/(-14025) + (-1)/5. Let s = 2/187 + b. Factor 0*v**2 + s + 2*v - 2/3*v**3.
-2*(v - 2)*(v + 1)**2/3
Let q(r) be the third derivative of 1/120*r**4 + 0*r - 1/600*r**6 + 0 + 0*r**3 - r**2 + 0*r**5. Solve q(b) = 0 for b.
-1, 0, 1
Let t(l) = 9*l**4 + 41*l**3 - 49*l - 17. Let i(g) = -g**4 - 5*g**3 + 6*g + 2. Let u(n) = 51*i(n) + 6*t(n). Factor u(x).
3*x*(x - 2)**2*(x + 1)
Let i(b) = -3*b + 3. Let x be i(-4). Let f be 8/x - (-4)/(-20). Let 0*q + 4/3*q**3 + f*q**2 - 4/3*q**5 - 1/3*q**4 + 0 = 0. What is q?
-1, -1/4, 0, 1
Suppose -4*y - 17 = -5, 2*o - 4*y = 14. Factor -1/4*z**2 - o + z.
-(z - 2)**2/4
Let m(x) = -x + 5. Let u be m(5). Suppose 9*w - 5*w = u. Determine g, given that w + 1/2*g**3 + 1/2*g - g**2 = 0.
0, 1
Let x be 106/48 - (-14)/(-7). Let d(t) be the first derivative of -x*t**6 - 2/5*t**5 + 0*t**2 + 0*t + 2 - 1/16*t**4 + 1/6*t**3. Find i such that d(i) = 0.
-1, 0, 2/5
Let m(j) = j**3 - 4*j**2 - j + 5. Let p be m(4). Suppose 5*q - 2 - 8 = 0. Let -x**2 + 5*x**q - 5*x**2 + p = 0. What is x?
-1, 1
Let s(y) = -y**2 + 7. Let j(p) = -2*p**2 + p + 7. Let t(g) = -3*j(g) + 2*s(g). Factor t(w).
(w + 1)*(4*w - 7)
Let p(w) be the second derivative of 2*w**7/21 - 2*w**6/15 - w**5/5 + w**4/3 + 55*w. Factor p(i).
4*i**2*(i - 1)**2*(i + 1)
Let l = -215/2 - -108. Let 0*b**4 + 1/4*b**5 - l*b**3 + 0 + 1/4*b + 0*b**2 = 0. Calculate b.
-1, 0, 1
Let p be 12/5 + (-12)/30. Suppose s = -0*s + p. Suppose 0 - 2/9*w + 2*w**3 + s*w**4 - 2/9*w**2 = 0. What is w?
-1, -1/3, 0, 1/3
Suppose 2*o = -3*o. Let q(x) be the third derivative of o + 3/28*x**4 + 0*x - 2/21*x**3 - 1/30*x**5 + x**2. Determine u so that q(u) = 0.
2/7, 1
Suppose -2*g - c = 2*c - 1, 4*c - 20 = -5*g. Suppose 0*v - g = -4*v. Let -4/9*o + 0 - 2/9*o**v = 0. What is o?
-2, 0
Let t(x) = 36*x**4 + 30*x**3 + 21*x**2 - 21*x. Let i(j) = 7*j**4 + 6*j**3 + 4*j**2 - 4*j. Let g(w) = -21*i(w) + 4*t(w). Suppose g(p) = 0. What is p?
-2, 0
Let g(a) be the first derivative of -2*a**3/3 - a**2 + 4*a + 4. Factor g(f).
-2*(f - 1)*(f + 2)
Let q(i) be the third derivative of 1/60*i**6 + 0*i**3 + 0*i**5 + i**2 + 0 + 2/105*i**7 + 0*i + 1/168*i**8 + 0*i**4. Determine v so that q(v) = 0.
-1, 0
Find w such that 5*w**2 - w**2 + 3*w**4 - w + 7*w**3 + 2*w + w**2 = 0.
-1, -1/3, 0
Let t(p) be the first derivative of -2*p**6 - 4*p**5/5 + 9*p**4 - 4*p**3 - 4*p**2 - 24. Suppose t(n) = 0. What is n?
-2, -1/3, 0, 1
Let x(i) be the second derivative of i**6/255 + i**5/34 - 7*i**4/34 + 23*i**3/51 - 8*i**2/17 - 22*i. Factor x(s).
2*(s - 1)**3*(s + 8)/17
Suppose 5*y = 2*v - v + 11, -4*y = 5*v - 32. Find u, given that 2*u - v + 1 + 2*u**2 - 1 = 0.
-2, 1
Let z(s) be the third derivative of s**6/660 + s**5/30 - 25*s**4/132 + 13*s**3/33 - 44*s**2. Find f such that z(f) = 0.
-13, 1
Let y(i) be the second derivative of 0 + i + 1/12*i**4 + 1/3*i**3 + 1/2*i**2. Factor y(d).
(d + 1)**2
Let a(u) be the first derivative of -1/6*u**6 + 0*u**2 + 1/15*u**5 + 11 + 0*u + 0*u**3 + 1/6*u**4. Let a(n) = 0. What is n?
-2/3, 0, 1
Let k(d) be the second derivative of 1/55*d**5 + 0 + 1/165*d**6 + 0*d**3 + 0*d**2 + d + 1/66*d**4. Factor k(q).
2*q**2*(q + 1)**2/11
Let t(p) = -4*p**2 + 6*p + 10. Let v(g) = 5*g**2 - 6*g - 11. Let q(d) = -7*d**3 + d**2 - d + 1. Let h be q(1). Let l(m) = h*v(m) - 7*t(m). Factor l(c).
-2*(c + 