)*(r + 1)
Let u(o) be the third derivative of 3*o**2 - 1/50*o**5 + 1/60*o**4 + 1/180*o**6 + 0 + 1/45*o**3 + 0*o. Suppose u(z) = 0. Calculate z.
-1/5, 1
Let j(z) = -z**2 + 3*z - 1. Let a be j(4). Let k be ((-2)/5)/(1/a). Factor -2 + d**k + 4 - 3.
(d - 1)*(d + 1)
Let k be 1/2 - 7/42. Find p, given that 0 - p**3 + 1/3*p**4 + p**2 - k*p = 0.
0, 1
Let r(w) be the first derivative of w**4/12 - 7*w**2/6 + 2*w + 32. What is a in r(a) = 0?
-3, 1, 2
Factor 0*i + 0*i**2 + 0 - 3*i**3 - 21/2*i**4.
-3*i**3*(7*i + 2)/2
Find l, given that 18 + 38*l + 12*l**2 + 8*l**2 - 93*l - 6*l**4 - 2*l**5 + 13*l + 12*l**3 = 0.
-3, 1
Suppose 4*t + 3*l = 36, -3*t = -5*l - 13 - 43. Suppose -3*d - t = -7*d. Factor d*q + q - 2 + 2*q**2 - 4*q**2.
-2*(q - 1)**2
Let f be (2 - 1) + (-3678)/15. Let y = f - -245. Determine d, given that 4/5*d + 1/5*d**3 + 0 + y*d**2 = 0.
-2, 0
Let j be (-3619)/(-70) - (-1)/(-5). Let f = j - 50. Factor f*m**3 - 3/2*m + 0 + 0*m**2.
3*m*(m - 1)*(m + 1)/2
Determine m, given that -1/2*m**2 - 2*m + 0 = 0.
-4, 0
Let k(a) = -4*a**3 + 12*a**2 + 12*a + 7. Let r(l) = -l**3 + 4*l**2 + 4*l + 2. Let b(t) = 2*k(t) - 7*r(t). Factor b(f).
-f*(f + 2)**2
Let t(a) be the third derivative of -a**9/20160 - a**8/5040 + a**7/5040 + a**6/360 - a**5/15 - 4*a**2. Let w(p) be the third derivative of t(p). Factor w(k).
-(k + 1)**2*(3*k - 2)
Let z(o) be the third derivative of o**8/112 - o**7/35 + o**5/10 - o**4/8 - 2*o**2. Factor z(l).
3*l*(l - 1)**3*(l + 1)
Suppose 2*j = 3*j - 6. Factor -v + 2*v**4 + 3*v**4 + v**3 - j*v**4 - v**2 + 2*v**2.
-v*(v - 1)**2*(v + 1)
Let k(w) be the first derivative of 16*w**3/3 + 2*w**2 + 9. Suppose k(x) = 0. What is x?
-1/4, 0
Let f**2 - f**4 - f**5 - 2*f + 3*f**3 + 0*f + 0*f**4 = 0. What is f?
-2, -1, 0, 1
Suppose k - 40 = -3*k + 5*a, 0 = 5*k + 3*a - 13. Suppose k*n - 15 = -0*i - 2*i, 5*n - 15 = 3*i. What is m in 3/4*m + i - 3/4*m**2 = 0?
0, 1
Let d(t) = -4*t**4 + 4*t**3 + 4*t**2 + 5*t. Let b(p) = -p**2 - p. Let j(c) = -5*b(c) - d(c). Let j(a) = 0. What is a?
0, 1/2
Let l(b) be the first derivative of -2*b**3/9 - 3. Let l(h) = 0. What is h?
0
Factor -4/5*y**2 - 8/5*y - 4/5.
-4*(y + 1)**2/5
Suppose -3*m = -2*z - 39 - 10, 2*m - 3*z - 31 = 0. Suppose m = q + 3*s, -5*q = -3*s - 3 + 8. Factor -2 - q*f - 1/2*f**2.
-(f + 2)**2/2
Factor 2/3*c**3 + 0*c + 28/9*c**4 - 4/9*c**2 + 0.
2*c**2*(2*c + 1)*(7*c - 2)/9
Let n(a) = -2*a**2 + 5*a. Let k(g) = 5*g**2 - 14*g. Let z(x) = 3*k(x) + 8*n(x). Factor z(h).
-h*(h + 2)
Let j(k) be the first derivative of -k**8/560 - 11*k**7/2520 - k**6/540 - 5*k**3/3 - 2. Let z(o) be the third derivative of j(o). Find b, given that z(b) = 0.
-1, -2/9, 0
Let y(f) be the third derivative of f**6/720 - f**5/60 + f**4/12 + 2*f**3/3 + 3*f**2. Let a(m) be the first derivative of y(m). Factor a(d).
(d - 2)**2/2
Let i = -285 + 1996/7. Determine s, given that -3/7*s**4 - i*s**5 - 1/7*s**2 + 0*s + 0 - 3/7*s**3 = 0.
-1, 0
Let s(k) be the first derivative of -5*k**3 - 5*k**2 + 5*k + 14. Factor s(l).
-5*(l + 1)*(3*l - 1)
Let x(r) be the second derivative of r**4/12 + 2*r**3 - 9*r**2/2 + 10*r. Let v be x(-13). Factor 2/5*f - 2/5*f**3 + 2/5*f**2 - 2/5*f**v + 0.
-2*f*(f - 1)*(f + 1)**2/5
Let t(m) be the third derivative of -m**5/4 + m**4/2 - 2*m**3/5 - 4*m**2. Factor t(z).
-3*(5*z - 2)**2/5
Suppose -3*p - p - 4 = 4*g, 0 = -5*p - 5. Let o = -1860/7 + 266. Factor -2/7*s**2 + g*s + o.
-2*(s - 1)*(s + 1)/7
Let a(d) be the third derivative of -d**11/332640 + d**9/30240 - d**7/5040 + d**5/20 + 3*d**2. Let x(m) be the third derivative of a(m). Factor x(t).
-t*(t - 1)**2*(t + 1)**2
Let r(t) be the third derivative of 0*t - t**2 + 0*t**4 - 1/60*t**5 + 1/420*t**7 + 0 + 0*t**6 + 1/12*t**3. Factor r(w).
(w - 1)**2*(w + 1)**2/2
Let c = 2507/28 + -357/4. Let v be 0 + 1 - (-3)/(-7). Factor -v*a + c + 2/7*a**2.
2*(a - 1)**2/7
Let d(a) be the third derivative of -5*a**8/2016 - a**7/252 + a**6/144 + a**5/72 - 7*a**2. Suppose d(v) = 0. What is v?
-1, 0, 1
Let i(m) be the third derivative of m**5/150 + m**4/30 + m**3/15 + m**2. Factor i(r).
2*(r + 1)**2/5
Let c = 177 + -177. Let -16*f**4 + 10*f**3 + 0*f + c - 32/3*f**5 - 4/3*f**2 = 0. Calculate f.
-2, 0, 1/4
Let o = -84 + 87. Factor 2/5*s**2 + 0 + 4/5*s**o + 0*s.
2*s**2*(2*s + 1)/5
Let s(u) = u - 7. Let t be s(10). Solve -m - m**t - 4 + 6*m + m**2 + 7 = 0 for m.
-1, 3
Factor 0*l**2 + 1/4*l - 1/4*l**3 + 0.
-l*(l - 1)*(l + 1)/4
Let w(j) be the second derivative of j**7/294 + j**6/105 + j**5/140 + 5*j. Factor w(p).
p**3*(p + 1)**2/7
Let l(d) be the first derivative of d**6/27 + 4*d**5/45 + d**4/18 - 8. Factor l(v).
2*v**3*(v + 1)**2/9
Let h(x) be the first derivative of x**3/9 - 2*x**2/3 + 4*x/3 - 5. Solve h(m) = 0.
2
Let u(d) be the second derivative of d**4/16 - d**3/12 - d**2/8 - 6*d. Determine i, given that u(i) = 0.
-1/3, 1
Let z be (-4 - -5)/((-2)/(-6)). Solve 1/4*d**z + 0 + 0*d + 1/4*d**2 = 0.
-1, 0
Let i = 79 + -75. Let f(z) be the third derivative of 0*z**3 + z**2 + 1/27*z**i + 0 + 0*z - 1/180*z**6 - 1/945*z**7 + 0*z**5. Suppose f(g) = 0. What is g?
-2, 0, 1
Suppose -36*l + 105 = -3. Factor 0 - 4/3*f**l + 4/3*f + 2/3*f**2 - 2/3*f**4.
-2*f*(f - 1)*(f + 1)*(f + 2)/3
Let a be ((-20)/(-5) + -5)/(-5). Let k(p) be the first derivative of -2/15*p**3 + 4 + 0*p - a*p**2. Determine u so that k(u) = 0.
-1, 0
Let i(t) be the second derivative of 0 + 2/9*t**2 - 1/18*t**4 - t + 1/135*t**6 - 1/90*t**5 + 1/27*t**3. Suppose i(n) = 0. What is n?
-1, 1, 2
Suppose 0 = -3*w + 15, -4*w + 32 = y + 2*y. Suppose -4*r**4 - 2*r + 4 + 3*r**4 - 2*r**3 - 12*r**2 + 5*r**y = 0. What is r?
-1, 1/2, 2
Let d(k) be the first derivative of k**6/3 + 4*k**5/5 - 4*k**3/3 - k**2 - 35. Suppose d(h) = 0. What is h?
-1, 0, 1
Let l(p) be the second derivative of -p**5/16 + 3*p**4/8 - p**3/2 - 5*p**2/2 + 10*p. Let k(i) be the first derivative of l(i). Factor k(m).
-3*(m - 2)*(5*m - 2)/4
Suppose -10 = 2*a - 6*a - 2*o, -4*a + 4*o + 28 = 0. Factor -3*p - 25*p**4 + 27*p**a - 4*p**3 + 3*p.
2*p**3*(p - 2)
Let i(y) = -y**2 - y + 5. Let f be i(0). Suppose 4*v - f = u, 5*v - 2*v = 2*u. Factor 0*p**2 + 0*p + 0 - 1/2*p**u.
-p**3/2
Let k = 4 - 16/5. Suppose 2*y**2 + k*y + 14/5*y**5 - 2*y**4 - 18/5*y**3 + 0 = 0. Calculate y.
-1, -2/7, 0, 1
Let d(u) be the third derivative of -u**5/60 + u**4/48 + u**3/4 + u**2. Factor d(s).
-(s + 1)*(2*s - 3)/2
What is g in -2*g**2 - 6*g**2 - g + 10*g**2 - 3*g**2 = 0?
-1, 0
Let z be (-1)/(-5 - 63/(-14)). Determine u, given that 8/7 - 4/7*u - 4/7*u**z = 0.
-2, 1
Let x(c) = 2*c**2 + 5*c - 9. Let k be x(-4). Let i(z) be the first derivative of 1/12*z**k + 1/4*z**2 - 1 + 1/4*z. Factor i(u).
(u + 1)**2/4
Suppose 5*i = -3*u - 55, 0 = 4*u - i - i + 30. Let r be ((-12)/u)/(8/20). Factor 2*g - g**3 - g + 0*g**r + 0*g.
-g*(g - 1)*(g + 1)
Let c = -3/52 + 4/13. Factor 1/4*b**2 - 1/4*b**3 - c*b**4 + 0 + 1/4*b.
-b*(b - 1)*(b + 1)**2/4
Suppose j**3 + 0 + 0*j - 1/2*j**4 - 1/2*j**2 = 0. Calculate j.
0, 1
Let m(z) be the second derivative of 5*z**4/12 + 10*z**3 + 90*z**2 - 14*z. Factor m(n).
5*(n + 6)**2
Let x(h) be the first derivative of -5*h**4/4 - 35*h**3/9 - 25*h**2/6 - 5*h/3 - 19. Factor x(t).
-5*(t + 1)**2*(3*t + 1)/3
Let q be (32/10)/(-8) - 11/(-15). Find x, given that q*x**2 + 1/3 + 2/3*x = 0.
-1
Let h(l) be the second derivative of 0*l**3 - 1/40*l**5 + 1/30*l**6 + 0*l**2 - l + 0*l**4 + 0 - 1/84*l**7. Let h(m) = 0. What is m?
0, 1
Let i(b) be the third derivative of -b**8/80640 + b**7/10080 + b**5/20 + 3*b**2. Let n(z) be the third derivative of i(z). Factor n(d).
-d*(d - 2)/4
Let o(t) = -6*t**4 - 8*t**3 + 2*t**2 - 4*t - 4. Let n(h) = 11*h**4 + 15*h**3 - 3*h**2 + 7*h + 7. Let s(p) = -4*n(p) - 7*o(p). Let s(k) = 0. Calculate k.
-1, 0
Determine p, given that 0 + 1/5*p**2 - 1/5*p = 0.
0, 1
Let r(s) = -2*s**2 + s + 2. Let t be r(0). Find p such that -1/4*p - 1/4*p**3 - 1/2*p**t + 0 = 0.
-1, 0
Let j(p) = p**3 - p**2 + p - 1. Let r(t) = 5*t**3 - 4*t**2 + t - 2. Let s(c) = -4*j(c) + r(c). Find g, given that s(g) = 0.
-2, 1
Let n = -27 + 38. Let p = n - 5. Let -6*t**2 - 2*t - p*t**3 - 3*t**4 + t**4 + 0*t**4 = 0. Calculate t.
-1, 0
Let a(r) = 21*r**2 - 60*r - 45. Let y(n) = 6*n**2 - 17*n - 13. Let h(k) = -5*a(k) + 18*y(k). Factor h(c).
3*(c - 3)*(c + 1)
Let j = 309 - 307. What is n in 2/5*n**j - 1/5*n + 1/5*n**3 - 2/5 = 0?
-2, -1, 1
Let i(a) = -a**2