.
-1, 2
Let o(a) be the first derivative of a**3/15 + 19*a**2/5 + 361*a/5 - 50. Factor o(c).
(c + 19)**2/5
Let f(c) be the second derivative of -c**7/840 + 17*c**6/360 - 2*c**5/3 + 8*c**4/3 + 4*c**3 - 27*c. Let y(x) be the second derivative of f(x). Factor y(a).
-(a - 8)**2*(a - 1)
Let o(n) be the third derivative of n**6/20 - 17*n**5/15 + 101*n**4/12 - 10*n**3 - 366*n**2. Factor o(v).
2*(v - 6)*(v - 5)*(3*v - 1)
Suppose 0 = -2*a + 16*a - 644. Suppose a*v = 49*v. Factor v + 0*x + 4/7*x**3 + 8/7*x**2.
4*x**2*(x + 2)/7
Let p(x) be the third derivative of -x**8/10080 + x**6/90 - x**5/5 + 13*x**2. Let a(n) be the third derivative of p(n). Factor a(v).
-2*(v - 2)*(v + 2)
Suppose 2*g - 9 + 1 = -c, 4*c - g - 23 = 0. Let -8*x**2 + x**4 + 6*x + 3*x**2 + 5*x**2 - c*x**3 + 4*x**2 - 5 = 0. Calculate x.
-1, 1, 5
Factor -184/5*p**2 - 36/5 - 24*p**3 - 36/5*p**4 - 4/5*p**5 - 132/5*p.
-4*(p + 1)**3*(p + 3)**2/5
Let v(z) be the first derivative of z**7/210 + z**6/30 + z**5/15 - 5*z**3 - 2*z - 22. Let d(y) be the third derivative of v(y). Determine f so that d(f) = 0.
-2, -1, 0
Let z(b) be the third derivative of -b**6/150 + 2*b**5/25 - 4*b**4/15 - 50*b**2. Factor z(u).
-4*u*(u - 4)*(u - 2)/5
Let m(k) be the second derivative of -k**6/40 - k**5/10 - k**4/8 - 6*k**2 - 32*k. Let r(u) be the first derivative of m(u). Let r(c) = 0. What is c?
-1, 0
Let c = -194 - -214. Suppose 27*l = 32*l - c. What is o in -10/3*o**3 + 8/3*o - 16/9 + 28/9*o**2 - 2*o**l = 0?
-2, -1, 2/3
Factor 27/2 + 3/2*g**2 + 15*g.
3*(g + 1)*(g + 9)/2
Let y(l) be the third derivative of l**9/12096 - l**8/1344 + l**7/504 - 23*l**4/24 - 11*l**2. Let j(q) be the second derivative of y(q). Factor j(c).
5*c**2*(c - 2)**2/4
Let t(s) = 12*s**5 - 30*s**4 + 32*s**3 - 6*s**2 + 4*s - 4. Let v(a) = a**5 + a**4 + a - 1. Let o(z) = t(z) - 4*v(z). Determine c so that o(c) = 0.
0, 1/4, 1, 3
Suppose 2*t = 4, -5*w + t + 54 = 36. Let f(p) be the first derivative of -5 + 5/2*p**2 + 4/3*p**3 + 2*p + 1/4*p**w. Solve f(g) = 0 for g.
-2, -1
Let i(s) be the third derivative of s**8/672 + s**7/420 - s**6/120 - s**5/60 + s**4/48 + s**3/12 + 39*s**2. Determine v, given that i(v) = 0.
-1, 1
Let h be 65/10*(-52)/(-845). Factor 4/5*a + 0 - h*a**2.
-2*a*(a - 2)/5
Let b = 2738/4125 - -4/1375. Solve -8/3*o - b*o**2 - 8/3 = 0.
-2
Let t(a) be the third derivative of 9*a**2 - 1/2*a**4 - 4 + 0*a + 1/30*a**5 + 5/3*a**3. Determine i so that t(i) = 0.
1, 5
Let m(x) = 7*x**3 + 26*x**2 + 7*x. Let r = 8 - 3. Let l(q) = 7*q**3 + 26*q**2 + 8*q - 1. Let z(f) = r*m(f) - 6*l(f). Find i, given that z(i) = 0.
-3, -1, 2/7
Let r(m) be the first derivative of 5*m**3/3 - 175*m**2/2 + 114. Factor r(n).
5*n*(n - 35)
Let g(y) = 2*y**2 - y. Let c be g(-1). Suppose -n + 3 = 2*b - b, 0 = -4*b - c*n + 14. Factor 10*a**b - 4*a**3 - 6*a**4 - 42 + 42.
2*a**3*(a - 1)*(5*a + 2)
Let r be -1*2 + (8 - 6). Let o = -169 + 174. Determine g so that 5/4*g**2 + r - 1/2*g - 7/4*g**o - 5/4*g**4 + 9/4*g**3 = 0.
-1, 0, 2/7, 1
Let z(d) = -2*d - 5. Let w be z(12). Let f = w + 29. Factor 1/4*m**2 + 1/4*m + f.
m*(m + 1)/4
Suppose -5*n + 0*n = -4*z - 20, z + 16 = 4*n. Suppose z = -q - 2*q + 9. Determine v, given that -5*v - 2*v**q + 12*v + v = 0.
-2, 0, 2
Let r(n) be the second derivative of n**4/6 - 20*n**3/3 - 80*n. Let r(t) = 0. What is t?
0, 20
Let a = 6378/13 - 490. Factor a*c**2 - 10/13*c + 2/13.
2*(c - 1)*(4*c - 1)/13
Let t(k) be the first derivative of k**7/560 - 3*k**5/80 - k**4/8 + 13*k**3/3 + 5. Let g(w) be the third derivative of t(w). Factor g(d).
3*(d - 2)*(d + 1)**2/2
Let z(v) be the second derivative of 3*v**5/10 + 3*v**4/4 - 3*v**3/2 - 3*v**2 + 27*v. Factor z(i).
3*(i - 1)*(i + 2)*(2*i + 1)
Let r = -2/261 + 572/6525. Let d(y) be the first derivative of 5 + 0*y**3 + 0*y**2 + r*y**5 - 1/15*y**6 + 0*y + 0*y**4. What is n in d(n) = 0?
0, 1
Let x = 18/119 - 1/119. Suppose 2*y - 2 = 2*a, 3*y + 2*a - 6*a = 2. Factor 0*v + 1/7 - x*v**y.
-(v - 1)*(v + 1)/7
Let t(u) = 3*u**2. Let d be t(1). Suppose 0 = -5*j + 5*a + 23 - 8, j - 4*a - d = 0. Factor -6*y**3 + 2*y**5 + 3*y**4 + 2*y**2 + y - 5*y**4 + j*y.
2*y*(y - 2)*(y - 1)*(y + 1)**2
Let w be ((-1)/(-30)*15)/(2/12). Factor 3/7*c + 12/7 - 12/7*c**2 - 3/7*c**w.
-3*(c - 1)*(c + 1)*(c + 4)/7
What is q in 8428*q - 81*q**3 + 308*q**2 + 48*q**2 + 22188 + 85*q**3 = 0?
-43, -3
Let r be (-60)/6 - (-2905)/280. Find k such that -3/8 - 9/4*k**2 - r*k**4 - 3/2*k**3 - 3/2*k = 0.
-1
Factor -1/2 + 3/4*b + 5/4*b**2.
(b + 1)*(5*b - 2)/4
Let d(u) = -u**3 - 2*u**2 + 26*u - 12. Let f be d(-7). Suppose f = -4*x + 63. Factor -9/2*q**x + 0 + 5/4*q**4 + 3*q**2 + 2*q.
q*(q - 2)**2*(5*q + 2)/4
Let v(y) be the third derivative of y**7/280 - 29*y**6/480 + 21*y**5/80 - 17*y**4/32 + 7*y**3/12 - 163*y**2. Determine g, given that v(g) = 0.
2/3, 1, 7
Let g(c) be the second derivative of -c**6/40 + 3*c**5/80 + 5*c**4/16 + 3*c**3/8 + 58*c. Factor g(z).
-3*z*(z - 3)*(z + 1)**2/4
Let m be -1 + (-1 - -2) - (-4 - -2). Factor -39 - 8*q + 43 + m*q**2 - q**2 + 3*q**2.
4*(q - 1)**2
Let i be ((-13)/39)/((-2)/126). Let p be i/(-14) + (4 - (-1)/(-1)). Factor 3/2*c + 3 - p*c**3 - 3*c**2.
-3*(c - 1)*(c + 1)*(c + 2)/2
Let f(n) be the third derivative of n**7/350 - n**6/20 + 7*n**5/25 - 3*n**4/5 + 5*n**2 - 24. Factor f(t).
3*t*(t - 6)*(t - 2)**2/5
Let j(g) be the third derivative of -4*g**5/105 + 5*g**4/14 + 8*g**3/21 + 54*g**2. Factor j(i).
-4*(i - 4)*(4*i + 1)/7
Suppose 33*g - 139*g = 365*g - 1413. Determine x, given that 16/9 + 32/9*x + 4/9*x**g + 20/9*x**2 = 0.
-2, -1
Factor -4/7*l**5 + 72/7*l**3 + 0*l**2 - 324/7*l + 0*l**4 + 0.
-4*l*(l - 3)**2*(l + 3)**2/7
Let x be 4 - 22/10 - -2. Let o = x + -52/15. What is a in 0 + a - o*a**3 - 2/3*a**2 = 0?
-3, 0, 1
Let -3 + 71*k - 87*k**2 - 17*k**2 + 29*k + 7 = 0. What is k?
-1/26, 1
Solve 8/3*d + 0 + 2/3*d**3 - 10/3*d**2 = 0.
0, 1, 4
Let r(u) be the third derivative of -u**7/42 + u**6/4 - 3*u**5/4 - 322*u**2. What is z in r(z) = 0?
0, 3
Let v be (3/25)/(3/45 + 0). Determine k, given that 3*k**2 + v + 24/5*k = 0.
-1, -3/5
Suppose -2*a + 2*k = 3*k - 59, -5*a + 145 = 3*k. Let f be (-2)/(-4) + 48/a. Factor -2*j - 1/2*j**f - 2.
-(j + 2)**2/2
Factor 87/5*o - 3/5*o**2 + 186/5.
-3*(o - 31)*(o + 2)/5
Let u(j) = j**2 + 6*j - 888. Let s be u(27). Solve -3/5*k**3 + 6/5 - s*k + 12/5*k**2 = 0.
1, 2
Factor 48/5*i + 0 + 4*i**2 - 2/5*i**3.
-2*i*(i - 12)*(i + 2)/5
Let k(i) be the first derivative of 0*i + 0*i**2 + 2/15*i**3 - 6 - 8/25*i**5 + 3/10*i**4. Factor k(b).
-2*b**2*(b - 1)*(4*b + 1)/5
Let l(c) be the second derivative of -2*c**6/15 - 2*c**5 - 8*c**4/3 + 20*c**3/3 + 18*c**2 - c - 4. Let l(a) = 0. Calculate a.
-9, -1, 1
Find u, given that 73*u**2 - 326*u**4 + 47*u**2 + 116*u**3 + 322*u**4 = 0.
-1, 0, 30
Let a = -11043 - -88347/8. Determine g so that 0*g**3 - 3/8 + 0*g - a*g**4 + 3/4*g**2 = 0.
-1, 1
Let n = 1761/4 - 440. Let u(y) be the first derivative of -1/3*y**3 + n*y**4 - 1/2*y**2 + 1/5*y**5 - 6 + 0*y. Let u(x) = 0. What is x?
-1, 0, 1
Let z = -444 - -444. Let y(a) be the third derivative of 1/60*a**6 + 1/12*a**4 + z*a - 1/15*a**5 + 0*a**3 + 0 + 3*a**2. Find p such that y(p) = 0.
0, 1
Let o be 68/168 + (-2)/(-42)*2. Find c, given that 5/2*c**2 - 2*c - o*c**4 + 5/2*c**3 - 1/2*c**5 - 2 = 0.
-2, -1, 1, 2
Let z(n) = -n**2 + 2*n. Let p(j) = 2*j - 4. Let d(a) = 3*p(a) - 3*z(a). Factor d(y).
3*(y - 2)*(y + 2)
Let t(w) be the third derivative of -w**7/1260 - w**6/540 + w**5/90 - 3*w**3 - 18*w**2. Let u(d) be the first derivative of t(d). Factor u(p).
-2*p*(p - 1)*(p + 2)/3
Determine w so that 1/9*w**3 - 4/3 - 23/9*w - 10/9*w**2 = 0.
-1, 12
Let i(y) be the third derivative of y**10/30240 + y**9/2016 + y**8/448 - 13*y**5/60 + 6*y**2. Let z(f) be the third derivative of i(f). Factor z(t).
5*t**2*(t + 3)**2
Let n(o) be the first derivative of 5*o**6/4 - 78*o**5/5 + 105*o**4/2 + o**3 - 435*o**2/4 + 75*o + 75. Solve n(r) = 0 for r.
-1, 2/5, 1, 5
Suppose 2*n + 4 = 0, -3*n = -3*g + 4*g + 8. Let u be (2/14)/(g*(-1)/7). Let 0*z - u*z**2 + 1/2*z**4 + 0 - z**3 + z**5 = 0. What is z?
-1, -1/2, 0, 1
Let -264/7*i**3 - 94/7*i**4 + 0*i + 0 + 72/7*i**2 - 8/7*i**5 = 0. What is i?
-6, 0, 1/4
Let a(l) be the third derivative of 0*l + 3/40*l**6 + 0*l**4 + 0 + 0*l**3 + 0*l**5 - 4*l**2 - 1/70*l**7. What is h in a(h) = 0?
0, 3
Suppose -8*z + 57 = -47. Factor 25*b + z*b**