et l(v) = -6*v**3 + 38*v**2 - 40*v + 24. Let r = 5 + 3. Let w(f) = r*d(f) + 5*l(f). Factor w(n).
2*(n - 2)**2*(n - 1)
Let y be ((-4 + 10)*1)/2. Let k(g) be the second derivative of 1/12*g**4 + 0 + g - 1/6*g**y - 1/60*g**5 + 1/6*g**2. Solve k(h) = 0 for h.
1
Let p be (-1*1)/((-14)/42). Let -28*u**p + 19*u**3 + 12*u**3 + 3*u**4 = 0. Calculate u.
-1, 0
Let i be 26/(9/(-3) - -5). Let k = 16 - i. What is s in 0*s + 1/5*s**k + 0 + 1/5*s**5 + 0*s**2 + 2/5*s**4 = 0?
-1, 0
Let j be 1/((-5)/(-4))*5. Let w be (3 - 5)/(-8) - 0. Factor -6*f**4 + 0 + 3/2*f**2 + w*f**3 + 1/4*f + j*f**5.
f*(f - 1)**2*(4*f + 1)**2/4
Let z = 97/255 + 1/51. Let s(p) be the first derivative of 1/3*p**6 - p**4 + 2*p + z*p**5 + 2 - 4/3*p**3 + p**2. Factor s(f).
2*(f - 1)**2*(f + 1)**3
Let -19/8*z - 3/4 + 19/8*z**3 - 7/8*z**4 + 13/8*z**2 = 0. Calculate z.
-1, -2/7, 1, 3
Let g(c) = -9*c - 9. Let y(t) = -t**2 - 11*t - 10. Let p(i) = 4*i**2 + 45*i + 41. Let s(z) = -2*p(z) - 9*y(z). Let o(a) = -2*g(a) - 3*s(a). Factor o(m).
-3*(m + 1)*(m + 2)
Suppose -a + p = -25, -106 = -2*a - 2*p - 44. Suppose -5*u - 8 = -a. Factor 0 + 14/9*c**u + 0*c - 2*c**3 + 4/9*c**2.
2*c**2*(c - 1)*(7*c - 2)/9
Suppose -5*c = -14 - 1. Factor -3 + 8*w**2 - 2*w**c + 4*w**5 + 2 + w - 7*w**4 - 3*w.
(w - 1)**3*(w + 1)*(4*w + 1)
Let g(s) be the first derivative of s**5/5 - s**4/2 + 23. Suppose g(r) = 0. What is r?
0, 2
Let d be (1 + 0)/(3 + -4). Let c be 2*-1*1/d. Find f, given that -1/4*f**c + 1/2*f - 1/4 = 0.
1
Let z be -2 + 3 + (-25)/30. Let d(p) be the second derivative of 109/80*p**5 + 21/20*p**6 + 0 + 7/24*p**7 + 3/4*p**4 + p + 0*p**2 + z*p**3. Factor d(i).
i*(i + 1)**2*(7*i + 2)**2/4
Let y = 21 - 18. Suppose 2*x - y*x = -3. Factor 0*t + 2/5*t**x + 0 - 2/5*t**2.
2*t**2*(t - 1)/5
Suppose 4 = 3*b - 2*b. Factor b*o + 4*o**4 + o**3 + 5*o**2 - 1 - o - 8*o**4 - 4*o**3.
-(o - 1)*(o + 1)**2*(4*o - 1)
Solve 1/3*s + 0*s**2 - 1/3*s**3 + 0 = 0 for s.
-1, 0, 1
Let v(b) be the first derivative of -b**3/9 - 2*b**2/3 + 5*b/3 - 14. Factor v(x).
-(x - 1)*(x + 5)/3
Let g(f) be the second derivative of -f**6/540 + f**4/108 - 5*f**2/2 - f. Let z(k) be the first derivative of g(k). Solve z(n) = 0 for n.
-1, 0, 1
Let h be 0/(-3*(-2)/(-6)). Let x be (-5)/(-10)*h/2. Suppose 0 + 1/2*i**5 + 0*i**4 + x*i + 0*i**2 - 1/2*i**3 = 0. Calculate i.
-1, 0, 1
Find x such that 14/13*x**3 + 10/13*x + 0 + 22/13*x**2 + 2/13*x**4 = 0.
-5, -1, 0
Let s = 722/15 + -48. Let p(q) be the first derivative of 2 - q**4 + 0*q - 8/3*q**3 - s*q**5 - 8/3*q**2. Let p(k) = 0. What is k?
-2, 0
Let w(r) be the third derivative of -r**8/5040 + r**7/2520 + r**6/1080 - r**5/360 - r**3/3 + 2*r**2. Let p(s) be the first derivative of w(s). Solve p(v) = 0.
-1, 0, 1
Let q(b) be the first derivative of 1 + 1/7*b**2 + 4/7*b - 2/21*b**3. Find p such that q(p) = 0.
-1, 2
Let i be 345/18 - (-9)/6. Suppose 0 + 6*k**2 + i*k**4 + 2/3*k + 8*k**5 + 18*k**3 = 0. Calculate k.
-1, -1/3, -1/4, 0
Let s(c) = -13*c**4 + 19*c**3 + 3*c**2 - 11*c + 11. Let p(j) = 6*j + 3*j**3 - 2*j**2 + 4*j**4 - 13*j**3 + 3*j**4 - 6. Let m(w) = -11*p(w) - 6*s(w). Factor m(d).
d**2*(d - 2)**2
Let c(y) be the first derivative of -y**3/5 - 6*y**2/5 + 19. Solve c(a) = 0 for a.
-4, 0
What is f in 1/4*f**3 + 0 - 1/4*f - 1/4*f**4 + 1/4*f**2 = 0?
-1, 0, 1
Let d(b) be the third derivative of 1/504*b**8 + 0*b**4 + 1/60*b**6 + 0*b + 1/105*b**7 - 2*b**2 + 0 + 0*b**3 + 1/90*b**5. Factor d(k).
2*k**2*(k + 1)**3/3
Let q(k) be the third derivative of 1/12*k**4 - 4/105*k**7 - 4*k**2 + 0 - 1/5*k**5 + 0*k**3 + 3/20*k**6 + 0*k. Determine z, given that q(z) = 0.
0, 1/4, 1
Find o such that 8*o + 1 - 48*o**3 - 4*o - 32*o**2 + 3 = 0.
-1/2, 1/3
Let l(s) = -8*s**2 + 56*s + 36. Let x(q) = 3*q**2 - 19*q - 12. Let r(j) = -5*l(j) - 14*x(j). Solve r(o) = 0 for o.
-6, -1
Let v = 0 + 7. Let h = -7 + v. Solve h*b**2 - 4/3 + 2/3*b**3 - 2*b = 0.
-1, 2
Let i be (2 - 0) + (-33)/(-11). Let d(j) be the second derivative of -3/80*j**i + 0 - 1/4*j**3 - 3/16*j**4 - j + 0*j**2. Factor d(c).
-3*c*(c + 1)*(c + 2)/4
Let l(k) = -2*k**3 - 3*k**2 + 2*k - 3. Let h(c) = 6*c**3 + 8*c**2 - 6*c + 8. Let z(v) = 3*h(v) + 8*l(v). Suppose z(x) = 0. What is x?
-1, 0, 1
Let b(z) be the third derivative of z**5/42 - z**4/12 + 2*z**3/21 + 8*z**2 - 4*z. Factor b(l).
2*(l - 1)*(5*l - 2)/7
Let a(x) = 6*x**3 + x**2 - 2*x + 1. Let t be a(1). Let y(s) = 3*s**2 + 7*s - 5. Let r(d) = d**2 + 3*d - 2. Let o(g) = t*y(g) - 15*r(g). Solve o(j) = 0.
0, 1
Let m(l) = l**3 + l**2 - l + 1. Let w(t) = 9*t**4 - 33*t**3 - 3*t**2 + 21*t - 18. Let y(n) = 12*m(n) + w(n). Suppose y(a) = 0. What is a?
-2/3, 1
Let f be 60 + -62 - ((-28)/6 + 2). Determine c, given that 8/3 + 0*c + 2/3*c**5 - 14/3*c**2 - f*c**3 + 2*c**4 = 0.
-2, -1, 1
Determine m so that 6/5*m - 1/10*m**2 - 18/5 = 0.
6
What is d in 5/2*d - 1/4 - 25/4*d**2 = 0?
1/5
Let x = 92 - 89. Factor 3/5*h + 0*h**2 + 24/5*h**4 - 18/5*h**x + 0 - 9/5*h**5.
-3*h*(h - 1)**3*(3*h + 1)/5
Factor 67/7*m**3 + 171/7*m**2 + 216/7*m + 1/7*m**5 + 13/7*m**4 + 108/7.
(m + 2)**2*(m + 3)**3/7
Let r(w) be the third derivative of -w**8/70560 + w**7/8820 - w**6/2520 - w**5/30 - 4*w**2. Let a(i) be the third derivative of r(i). Factor a(l).
-2*(l - 1)**2/7
Suppose 95*q**4 + 1 + 3 + 110*q**3 + 30*q**5 - 4 + 10*q + 55*q**2 = 0. Calculate q.
-1, -2/3, -1/2, 0
Let l(r) be the first derivative of -r**3/9 - 2*r**2/3 + 5*r/3 + 14. Find g such that l(g) = 0.
-5, 1
Let h(p) = p**3 - 8*p**2 - 10*p + 13. Let j be h(9). Factor -2*b + j*b - 4*b + 3*b**2 - b**3 + 0*b**2.
-b*(b - 2)*(b - 1)
Let m(z) be the second derivative of -z**6/30 + z**5/4 - 3*z**4/4 + 7*z**3/6 - z**2 - 7*z. Factor m(t).
-(t - 2)*(t - 1)**3
Let t(r) be the second derivative of r**10/6720 - r**9/2016 + r**8/1920 - r**7/5040 - r**4/4 - 3*r. Let v(a) be the third derivative of t(a). Factor v(l).
l**2*(l - 1)*(3*l - 1)**2/2
Let f(g) be the first derivative of 5*g**4/12 + 5*g**3/9 - 5*g**2/6 - 5*g/3 - 17. Factor f(y).
5*(y - 1)*(y + 1)**2/3
Let a(l) be the first derivative of l**4/3 + 5*l**3/9 + l**2/6 - 5. Determine s so that a(s) = 0.
-1, -1/4, 0
Let t = 105/4 + -26. Suppose -3*d = -2*n + 7, -3*n - 7*d + 1 = -2*d. Factor 0*a**n + t*a**3 - 1/4*a**4 + 0*a + 0.
-a**3*(a - 1)/4
Let y(d) = d**3 + d. Let r(t) = -25*t**3 - 50*t**2 - 29*t - 2. Let w(q) = -2*r(q) - 2*y(q). Solve w(l) = 0.
-1, -1/12
Solve 1/2*f**3 + 0*f**4 - 1/2*f**5 + 0 + 0*f**2 + 0*f = 0 for f.
-1, 0, 1
Find t such that -48*t + 12*t**3 - 10*t**4 - 47*t + 110*t**2 + 23*t**3 - 30 - 10*t**4 = 0.
-2, -1/4, 1, 3
Let q(b) = b. Let c be q(2). Let d(v) be the first derivative of 0*v + 5/3*v**3 + v**c + v**4 + 2 + 1/5*v**5. Factor d(z).
z*(z + 1)**2*(z + 2)
Let g = 63 + -29. Let c = -32 + g. Factor 0 + 0*f - 5/6*f**4 + 1/2*f**5 + 1/3*f**3 + 0*f**c.
f**3*(f - 1)*(3*f - 2)/6
Factor 1/5*s**2 + 49/5 - 14/5*s.
(s - 7)**2/5
Let o = 2005/4 + -504. Let u = 7/12 - o. Solve -2*r**3 + 0 - 2/3*r - 10/3*r**4 + u*r**2 + 8/3*r**5 = 0.
-1, 0, 1/4, 1
Let n(t) be the third derivative of t**9/30240 - t**8/6720 + t**7/5040 + t**4/12 + 6*t**2. Let q(s) be the second derivative of n(s). Factor q(c).
c**2*(c - 1)**2/2
Let i(g) be the first derivative of 8*g**5/35 + 4*g**4/7 - 2*g**3/7 - 5*g**2/7 + 4*g/7 + 19. Let i(r) = 0. What is r?
-2, -1, 1/2
Let z(r) be the third derivative of -r**5/270 + r**4/54 - 12*r**2. Solve z(a) = 0 for a.
0, 2
Let l(f) be the first derivative of 1/3*f**6 + 1 + 2*f + f**2 + 2/5*f**5 - f**4 - 4/3*f**3. Factor l(d).
2*(d - 1)**2*(d + 1)**3
Let a(m) be the first derivative of m**4/10 + 8*m**3/15 + 4*m**2/5 - 7. Suppose a(p) = 0. Calculate p.
-2, 0
Suppose 6*o + 3*o**3 + 4*o - 13*o = 0. What is o?
-1, 0, 1
Let b(n) be the first derivative of 2*n**3/21 - n**2/7 - 7. Factor b(d).
2*d*(d - 1)/7
Let w = 16 + -10. Let h be w/(-16)*8/(-4). Factor 1/2*n + 0 + 1/4*n**3 + h*n**2.
n*(n + 1)*(n + 2)/4
Let o be (5 + 0)*9/15. Suppose -4 = -0*h - h + 5*a, 4*h = o*a + 16. Find n such that -h*n + 5*n**2 - 3*n + 5*n = 0.
0, 2/5
Suppose 3*c + 7*b - 6*b = 3, -4*b = -c + 14. Let a(t) be the first derivative of -t**c + 2/5*t**5 + 2 - 4/3*t**3 - 1/3*t**6 + 2*t + t**4. What is j in a(j) = 0?
-1, 1
Factor -2/9*d**4 + 0*d**3 + 0 + 4/9*d + 2/3*d**2.
-2*d*(d - 2)*(d + 1)**2/9
Let j = 9 + -5. Suppose 0 = 3*f - j*f + 3. Solve -46/3*b**3 - 1/3 - 11*b**4 - f*b**5 - 3*b - 10*b**2 = 0.
-1, -1/3
