h that u(d) = 0.
0
Let m(f) be the third derivative of -f**5/180 - f**4/72 + 11*f**2. Let m(k) = 0. Calculate k.
-1, 0
Let f be 2/(-40) - 13/(-52). Let j(l) be the first derivative of 2 + 2/15*l**3 + 0*l - f*l**2. Solve j(a) = 0 for a.
0, 1
Let b(y) = 1 + 2*y + 3*y**3 - 3 + 1. Let c be b(1). Solve -6*t**2 + 4*t**3 + 4*t**2 + t**4 - 3*t**c = 0 for t.
0, 1
Let m = -8 + 13. Factor 0*d**3 + 6*d**2 + 0*d**2 - 4*d**3 - 5*d**3 + 3*d**m.
3*d**2*(d - 1)**2*(d + 2)
Let s(l) be the second derivative of l**4/15 - l**3/15 - 3*l**2/5 + 15*l. Factor s(b).
2*(b + 1)*(2*b - 3)/5
Suppose 4*j - 18 = 14. What is l in 2*l + j*l**2 + 3*l**3 + 4 + 0*l**3 - l**3 + 8*l = 0?
-2, -1
Let u(k) be the second derivative of 1/8*k**3 + 2*k + 0 - 1/24*k**4 + 1/4*k**2 - 3/80*k**5. Factor u(y).
-(y - 1)*(y + 1)*(3*y + 2)/4
Factor -4 - 18*p**2 - 14*p**2 + 1 + 29*p**2 + 6*p.
-3*(p - 1)**2
Let a be 1/(1/(-2) - -1). Factor -a*d**2 - 1 + d + 0*d + d + d**2.
-(d - 1)**2
Suppose -2*c + 24 = -24. Factor 11*z**4 + 3*z**4 + 6*z**2 - z + c*z**3 - 3*z.
2*z*(z + 1)**2*(7*z - 2)
Let h(i) be the second derivative of -i**9/25200 + i**8/11200 - 5*i**4/6 - 4*i. Let l(g) be the third derivative of h(g). Factor l(p).
-3*p**3*(p - 1)/5
Find y, given that 3/2 - 9/4*y**2 + 15/4*y = 0.
-1/3, 2
Suppose -2*k + 8 = 0, -2*m + 39 = k - 5. Let x be (-2)/((-5)/(m/16)). Factor -1/4 + x*h - 1/4*h**2.
-(h - 1)**2/4
Let v(b) = -2*b**2 - 34*b - 50. Let h(a) = 5*a**2 + 67*a + 101. Let s(w) = -6*h(w) - 13*v(w). Find m, given that s(m) = 0.
-1, 11
Let l(z) be the second derivative of z**6/1620 - z**3/6 + 3*z. Let x(h) be the second derivative of l(h). Find u such that x(u) = 0.
0
Let h = 144 + -1006/7. Factor -4/7 + h*j**2 - 2/7*j.
2*(j - 2)*(j + 1)/7
Let i(a) be the first derivative of -a**5/15 - 5*a**4/12 - 8*a**3/9 - 2*a**2/3 + 4. Let i(x) = 0. What is x?
-2, -1, 0
Suppose 0 = -t + 14 - 12. Let m be (t/6)/((-55)/(-66)). Factor -m*c**2 - 4/5*c + 0.
-2*c*(c + 2)/5
Let y(t) be the first derivative of -t**6/6 - 2*t**5/5 + t**4/2 + 4*t**3/3 - t**2/2 - 2*t + 40. Solve y(x) = 0.
-2, -1, 1
Factor -1/6*c**3 - 1/3*c + 0 - 1/2*c**2.
-c*(c + 1)*(c + 2)/6
Let o(d) be the first derivative of d**5/5 - d**3 + d**2 - 63. Factor o(a).
a*(a - 1)**2*(a + 2)
Let k(w) be the second derivative of -2/15*w**6 - 3*w + 18*w**3 + 0*w**2 + 9/5*w**5 - 9*w**4 + 0. Determine p, given that k(p) = 0.
0, 3
Let l = -338 - -341. Factor -1/3*b**2 + 0*b + 1/3*b**l + 0.
b**2*(b - 1)/3
Suppose -x + 6*x = -0*x. Let p(o) be the first derivative of -1/2*o**2 + 1/4*o**4 + 0*o + x*o**3 - 2. Factor p(l).
l*(l - 1)*(l + 1)
Let l(i) = -i**3 + 5*i**2 - 4*i - 1. Let h be l(4). Let w = -1 - h. Find u, given that -u - u - 2*u**2 + w*u = 0.
-1, 0
Suppose n + n = 0. Suppose n*o = 2*o. Let o*k + 0 - 1/3*k**3 + 0*k**2 = 0. What is k?
0
Let s = 704/9 + -78. Solve -2/3*o**3 - s*o + 2/9*o**4 + 2/3*o**2 + 0 = 0 for o.
0, 1
Let m(v) = 2*v**3. Let t be m(-2). Let i = -14 - t. Factor 1/4*n**i - 1/4 + 0*n.
(n - 1)*(n + 1)/4
Suppose -2*k + 6 = -2. Let f be (-1 - 0) + (5 - k). Factor l**4 + f*l**2 - 2*l**2 + l**4.
2*l**2*(l - 1)*(l + 1)
Let t(k) be the third derivative of -k**8/5760 + k**7/1120 - k**6/720 + k**5/15 - k**2. Let v(u) be the third derivative of t(u). Let v(j) = 0. What is j?
2/7, 1
Let m(r) = 27*r**5 + 77*r**4 + 61*r**3 + 11*r**2 - 6*r. Let f(i) = 108*i**5 + 309*i**4 + 243*i**3 + 45*i**2 - 24*i. Let u(c) = 2*f(c) - 9*m(c). Factor u(a).
-3*a*(a + 1)**3*(9*a - 2)
Let k(h) = h**2 - h + 4. Let b be k(0). Find a such that -3*a**3 + 9*a**4 + 12*a - b - 2*a**3 - 7*a**3 - 5*a**2 = 0.
-1, 2/3, 1
Factor -5/3*u**5 - 10/3*u**4 + 10/3*u**2 + 0 + 5/3*u + 0*u**3.
-5*u*(u - 1)*(u + 1)**3/3
Let x be 0 - (-7 - 438/(-66)). Factor -2/11*s + 4/11 - x*s**2 + 2/11*s**3.
2*(s - 2)*(s - 1)*(s + 1)/11
Let k(z) be the second derivative of z**4/36 - z**3/9 - z**2/2 + 8*z. Factor k(b).
(b - 3)*(b + 1)/3
Suppose -3*f + 4*k - 2*k + 19 = 0, 23 = f - 4*k. Let t = -9 - -14. Solve l**t + l**4 - 3 + f = 0 for l.
-1, 0
Let t(m) = 3*m**3 - 2 + 2*m**3 + 4*m**2 + 4*m - 7*m**3. Let i(f) = -4*f**3 + 3 + 21*f**2 - 6*f**3 - 13 + 21*f. Let o(p) = -2*i(p) + 11*t(p). Factor o(s).
-2*(s - 1)**2*(s + 1)
Let b(o) = -5*o**4 - 8*o**3 + o**2 + 12*o - 3. Let n(p) = 14*p**4 + 24*p**3 - 2*p**2 - 36*p + 8. Let q(v) = -8*b(v) - 3*n(v). Solve q(t) = 0.
-3, -2, 0, 1
Suppose -2*v - 91 = -27. Let a(n) = 76*n**2 - 56*n - 32. Let j(x) = -7*x**2 + 5*x + 3. Let d(b) = v*j(b) - 3*a(b). Factor d(p).
-4*p*(p - 2)
Let d be (2 - (-15)/(-6))*-8. Solve d*t**3 - 2*t**3 + 0*t**3 - 4*t**2 - t - t + 4 = 0 for t.
-1, 1, 2
Let k(i) be the third derivative of 0 - 3/32*i**4 + 1/20*i**5 + 1/12*i**3 + 0*i - 2*i**2 - 1/120*i**6. Factor k(a).
-(a - 2)*(2*a - 1)**2/4
Let b(v) be the first derivative of 1/10*v**4 - 4/15*v**3 + 1/5*v**2 + 0*v - 6. Solve b(l) = 0.
0, 1
Suppose 4*z = -4*i - 16, 2*i - 2*z + z = 4. Let n(s) be the first derivative of -1/9*s**3 - 1 + 1/6*s**2 + i*s. Let n(l) = 0. What is l?
0, 1
Let p(s) be the first derivative of -s**5/70 + s**3/21 + 5*s + 3. Let j(n) be the first derivative of p(n). Factor j(y).
-2*y*(y - 1)*(y + 1)/7
Let y be 24/15 - (-4)/10. Suppose 0 = -2*v + 4*w, v - 5 = -y*v + w. Suppose 0*x**4 + 0*x**v + 0*x + 0*x**3 - 2/3*x**5 + 0 = 0. Calculate x.
0
Let k = -7 + 13. Suppose -g - 3 = -k. Solve 8 + 8*a**2 - 98*a**g + 38*a**2 - 4*a**2 + 48*a = 0.
-2/7, 1
Factor -8/7*o**3 + 0*o + 0 - 2/7*o**5 + 0*o**2 - 10/7*o**4.
-2*o**3*(o + 1)*(o + 4)/7
Let f(u) be the third derivative of 3*u**5/20 - 13*u**4/24 + 2*u**3/3 - 12*u**2. Factor f(g).
(g - 1)*(9*g - 4)
Factor -5*x**2 + 50*x - 26*x + x**2 - 36.
-4*(x - 3)**2
Let x(a) = -5*a**3 - 6*a**2 - 3*a + 2. Let v(h) = -h**3 - h**2 - h. Let w(c) = -4*v(c) + x(c). Find i such that w(i) = 0.
-2, -1, 1
Find d, given that 3/8*d**2 - 15/4 + 27/8*d = 0.
-10, 1
Let b(y) be the second derivative of 0*y**2 + 0 + 2/9*y**4 + 4*y - 1/60*y**5 - 8/9*y**3. Let b(g) = 0. Calculate g.
0, 4
Suppose b + 0*b = -3*r + 14, 0 = 5*b + r - 14. Factor 4*g**2 - 2 + 5 - 3*g**3 - 7*g**b + 3*g.
-3*(g - 1)*(g + 1)**2
Let v be 2/12*(-4 + 20). Factor 2/3 + 0*f**2 - v*f**3 + 2*f.
-2*(f - 1)*(2*f + 1)**2/3
Suppose -3*o = -3*t - 9, -4 = -2*o + 11*t - 7*t. Find u such that -1/7*u**o - 1/7*u**2 + 0 + 0*u - 2/7*u**3 = 0.
-1, 0
Let z(u) be the third derivative of -u**6/120 - u**5/30 - u**4/24 + 29*u**2. Determine i, given that z(i) = 0.
-1, 0
Let l(c) = -3*c**3 - 3*c**2 + 3. Let p(f) = -3*f**3 - 3*f**2 - f + 3. Let j(k) = 4*l(k) - 3*p(k). Find x, given that j(x) = 0.
-1, 1
Let l(s) be the third derivative of s**5/20 + s**4/4 + s**2. Solve l(w) = 0 for w.
-2, 0
Let k = -21 + 25. Let j(r) be the first derivative of 1/4*r**2 + 0*r + 2 - 7/12*r**3 + 5/16*r**k. What is d in j(d) = 0?
0, 2/5, 1
Suppose 10*d = 5*d + 30. Factor 8*a - 4*a - 3*a**2 + a**2 - d*a.
-2*a*(a + 1)
Let z(h) be the first derivative of h**5/25 + h**4/4 + 3*h**3/5 + 7*h**2/10 + 2*h/5 + 9. Factor z(a).
(a + 1)**3*(a + 2)/5
Let j be (8 - 3)*2/5. Solve -4/7 - 2/7*l**j - 6/7*l = 0.
-2, -1
Let j(v) = -v**5 + v**4 + v**3 - v - 1. Let x(b) = -37*b**5 + 85*b**4 - 29*b**3 + 4*b**2 - 5*b - 5. Let z(d) = -5*j(d) + x(d). Suppose z(a) = 0. Calculate a.
0, 1/4, 2
Let c(s) be the third derivative of 2*s**7/75 + 2*s**6/25 + s**5/25 - s**4/15 + 4*s**2 + 4. Determine k, given that c(k) = 0.
-1, 0, 2/7
Suppose -19 = -2*d - 7. Suppose d*g = 4*g + 4. Solve 10/3*b + 8/3*b**g + 2/3 = 0.
-1, -1/4
Let z = -63 - -66. Let v(r) be the second derivative of 0 - 1/18*r**z - 1/18*r**4 - 3*r + 0*r**2. Factor v(q).
-q*(2*q + 1)/3
Let m be ((-8)/(-108))/((-1)/(-9)). Determine f so that -m*f + 0 - 1/3*f**2 + 1/3*f**3 = 0.
-1, 0, 2
Let n(r) be the second derivative of r**6/10 - 9*r**5/10 + 2*r**4 + 3*r**3 - 27*r**2/2 + 13*r. Let n(i) = 0. What is i?
-1, 1, 3
Let b = -95 - -95. Let d(k) be the third derivative of 0*k + 1/75*k**5 - 1/175*k**7 + 0*k**3 + 1/300*k**6 + b - 3*k**2 + 0*k**4. Factor d(u).
-2*u**2*(u - 1)*(3*u + 2)/5
Let r be -5 + 14*(-5)/(-10). Determine y so that -2/7*y**r + 6/7*y + 0 = 0.
0, 3
Let n be (-1 + 3)/(12/18). Let i(m) be the first derivative of -1/2*m**4 + 0*m - n - 1/3*m**3 + 0*m**2. Factor i(f).
-f**2*(2*f + 1)
Let k(r) be the second derivative of -r**5/10 + 6*r. Factor k(q).
-2*q**3
Let f(w) be the first derivative of w**6/30 - w**4/10 + w**2/10 - 6. Factor f(s).
s*