Factor l(x).
-2*(x - 2)*(x + 35)/5
Let x(q) = q**2 + 23*q - 140. Let p be x(5). Let r(g) be the second derivative of p*g**2 + 1/9*g**3 - 1/54*g**4 + 0 + 7*g. Find i, given that r(i) = 0.
0, 3
Let z(a) be the third derivative of a**9/22680 + a**8/1800 + a**7/420 + a**6/300 - 5*a**3/2 + 15*a**2. Let n(j) be the first derivative of z(j). Factor n(m).
2*m**2*(m + 1)*(m + 3)**2/15
Let b(u) = -u**2 - 3*u + 12. Let h be b(2). Suppose s + 5*n + 4 = 7*n, -2*s - h = -n. Factor s*z**2 + 2/5*z**3 + 0*z**4 - 1/5*z + 0 - 1/5*z**5.
-z*(z - 1)**2*(z + 1)**2/5
Suppose -3*a = -23*l + 28*l - 18, 0 = l. Let r(k) be the third derivative of 0*k - 1/15*k**3 + 1/150*k**5 + 2*k**2 + 1/60*k**4 + 0 - 1/300*k**a. Factor r(c).
-2*(c - 1)**2*(c + 1)/5
Let r(s) be the third derivative of s**7/70 + 3*s**6/40 - 3*s**5/10 - s**4 - 328*s**2. Solve r(b) = 0 for b.
-4, -1, 0, 2
Let z(w) = -4*w**3 + 7*w**2 - 3*w. Let q be ((-1)/(-2))/((-6)/(-4) + -2). Let u(f) = f**2 - f. Let x(g) = q*z(g) - 5*u(g). Factor x(c).
4*c*(c - 2)*(c - 1)
Factor 8/11 - 28/11*t**3 - 120/11*t + 114/11*t**2.
-2*(t - 2)**2*(14*t - 1)/11
Let m(i) be the third derivative of 1/160*i**6 + 0*i + 13*i**2 - 1/24*i**5 + 0 + 1/24*i**4 + 1/3*i**3. Factor m(o).
(o - 2)**2*(3*o + 2)/4
Suppose 0*y - y + 4*g + 6 = 0, -y + g = -3. Suppose 4*r - 3*r = -3*u + 8, y*u - 10 = 4*r. Factor 3*k**2 - 3*k**2 + k**2 - k + 4*k**u - 3*k**3 - 1.
(k - 1)*(k + 1)**2
Suppose -24 = -2*g - 8. Let b be (g/2)/1 - 2. Factor -v**b - v + 0*v - 5 + 5*v + 1.
-(v - 2)**2
Let j(h) = 5*h**3 - 4*h**2. Suppose 77 = -7*v - 0*v. Let i(s) = -3*s**3 + 2*s**2. Let z(o) = v*i(o) - 6*j(o). Determine d, given that z(d) = 0.
-2/3, 0
Suppose -82*o = -266*o - 76 + 444. Solve 4/11*i + 0 + 2/11*i**o = 0.
-2, 0
Let f(t) be the first derivative of -3*t**5/25 + 3*t**4/10 - 3*t**2/5 + 3*t/5 + 97. Factor f(g).
-3*(g - 1)**3*(g + 1)/5
Suppose 37*w - 44 - w**3 - 47*w - 46*w**2 - 88*w + 9*w = 0. Calculate w.
-44, -1
Let h(k) be the first derivative of 1/6*k + 1/18*k**3 - 1/6*k**2 - 15. Determine f so that h(f) = 0.
1
Let w be 172*(-18)/(-24)*(-1 - 0). Let f = w - -391/3. Factor f*o**3 - 4/3*o + 0 + 0*o**2.
4*o*(o - 1)*(o + 1)/3
Let x be 3/(-2)*(-16)/6 - 2. Let i(n) be the first derivative of -3/2*n**x + n**3 + 0*n + 3. Determine q, given that i(q) = 0.
0, 1
Let s(u) be the third derivative of -u**8/84 + 2*u**7/21 + u**6 + 10*u**5/3 + 35*u**4/6 + 6*u**3 + 2*u**2 - 60. Determine o, given that s(o) = 0.
-1, 9
Let r = 51795577/152997141 + -96/110627. Let l = r - 2/461. Factor -l*p**2 + 0 - 2/3*p.
-p*(p + 2)/3
Let z(x) = x**2 - 69. Let k be z(-8). Let m be (-15 + 11 - k)/(13/4). Factor -6/13*y - m - 2/13*y**2.
-2*(y + 1)*(y + 2)/13
Let h be (-175)/(-105) + ((-8)/(-6) - 1). Factor -8*f - f**h - f + 4*f.
-f*(f + 5)
Suppose -162 + 48 - 226 = -170*p. What is f in 0*f + 2/9*f**3 + 0*f**p + 0 = 0?
0
Suppose -2*q = a - 13, -4*q = -3*a - 7 - 4. Factor 13*t**2 + 0 - 18*t**2 - q + 10*t.
-5*(t - 1)**2
Let b(z) be the first derivative of 2*z**3/3 + 34*z**2/3 - 16*z - 138. Factor b(t).
2*(t + 12)*(3*t - 2)/3
Let c = 20761/4 - 5190. Factor c*l + 1/4*l**2 - 1/2.
(l - 1)*(l + 2)/4
Let y(n) = -4*n**3 - n**2. Let d be y(-1). Solve 24*m**d - 1 + 26*m**2 - 1 - 6*m + 6*m = 0.
-1, -1/3, 1/4
Let t(d) be the second derivative of -d**4/6 - 9*d**3 - 72*d**2 + 4*d + 16. Factor t(j).
-2*(j + 3)*(j + 24)
Let s(m) = 3*m**4 + 12*m**3 - 23*m**2 + 16*m - 4. Let o(b) = -2*b**4 - 11*b**3 + 22*b**2 - 15*b + 3. Let l(t) = 4*o(t) + 3*s(t). Factor l(w).
w*(w - 4)*(w - 3)*(w - 1)
Let o = -1129020 - -2010784907/1781. Let t = o - 1/137. Factor -2/13*h**2 + 0*h + t.
-2*(h - 1)*(h + 1)/13
Suppose -4*o + 43 - 31 = 0. Solve -4*n**2 + 11*n - o + 14 + 1 - 3*n = 0 for n.
-1, 3
Let t = -45855/4 - -226111/20. Let c = 159 + t. Factor -2*k - c - 8/5*k**2 - 2/5*k**3.
-2*(k + 1)**2*(k + 2)/5
Suppose -3*f = 1 - 7. Let q(y) be the second derivative of 0 + 1/12*y**4 + 5/18*y**3 + 5*y + 1/3*y**f. Factor q(w).
(w + 1)*(3*w + 2)/3
Let n be (-2)/(36/20 - 2). Suppose -8*k**5 + k**4 + 0*k**2 - 2*k**5 + 3*k**4 + n*k**3 - 4*k**2 = 0. Calculate k.
-1, 0, 2/5, 1
Suppose -3*r + 2*r + 3 = 0. Suppose 4*z = l - 2*l + 8, 5*z + r*l - 10 = 0. Determine v, given that 2/3*v + 4/3*v**z + 2/3*v**3 + 0 = 0.
-1, 0
Let d = 3423 + -3420. Solve 2/13*c**d - 4/13*c**2 + 0 + 2/13*c = 0 for c.
0, 1
Let x(o) = -81*o + 20. Let y be x(1). Let t = -59 - y. Determine v so that 1/7*v + 2/7 - 1/7*v**t = 0.
-1, 2
Let q(l) = 7*l - 8 + 9*l + l**2 + 0*l**2. Let x = 12 - 8. Let t(w) = 15*w - 9. Let o(s) = x*t(s) - 3*q(s). Factor o(y).
-3*(y - 2)**2
Let u(z) = -z**3. Let f(b) = 7*b**3 - 10*b**2 + 9*b. Let x(g) = -g**2 + g. Let d(q) = f(q) - 5*x(q). Let p(m) = -d(m) - 6*u(m). Suppose p(o) = 0. What is o?
0, 1, 4
Let c be ((-19)/(57/12))/(-20). Let i(l) be the first derivative of 10 - 12/5*l - c*l**3 - 6/5*l**2. Factor i(x).
-3*(x + 2)**2/5
Factor -209*i**2 - 169*i + 407*i**2 + 114 + 52*i - 195*i**2.
3*(i - 38)*(i - 1)
Let t(a) be the third derivative of -8*a**2 + a**3 + 3/8*a**4 + 0 - 3/40*a**6 + 0*a - 1/70*a**7 - 1/20*a**5. Determine i so that t(i) = 0.
-2, -1, 1
Let 1/4*p**2 - 41/4*p - 21/2 = 0. What is p?
-1, 42
Let t(j) be the second derivative of j**7/42 - 3*j**6 + 1011*j**5/10 + 67*j**4/3 - 1965*j**3/2 - 2025*j**2 + 85*j. Factor t(u).
(u - 45)**2*(u - 2)*(u + 1)**2
Let x(y) be the first derivative of -52*y**5/5 - 28*y**4 - 16*y**3/3 + 130. Find a such that x(a) = 0.
-2, -2/13, 0
Let m(y) be the first derivative of y**4/7 + 32*y**3/3 + 224*y**2 + 106. Factor m(b).
4*b*(b + 28)**2/7
Let i(u) be the first derivative of -2*u**3/15 + 9*u**2/5 - 205. Factor i(s).
-2*s*(s - 9)/5
Let b = 2807/2505 - 9/167. Factor 2/3*f**2 + b*f + 8/15 + 2/15*f**3.
2*(f + 1)*(f + 2)**2/15
Determine w so that -3/11*w**3 - 2/11*w**2 + 12/11*w - 8/11 + 1/11*w**4 = 0.
-2, 1, 2
Let r(v) be the first derivative of -2*v**3/21 + 2*v**2/7 - 2*v/7 - 133. Factor r(n).
-2*(n - 1)**2/7
Suppose 2*b = 3*m - 13, 2*m - 15 = -m + 3*b. Let t(l) be the first derivative of 5/24*l**4 + m - 5/12*l**2 + 1/9*l**3 - 1/3*l. Factor t(o).
(o - 1)*(o + 1)*(5*o + 2)/6
Suppose 4*j + 15*j - 9*j = 0. Let g(b) be the third derivative of -11/270*b**5 + j*b**3 + 6*b**2 + 1/54*b**4 + 0 + 1/60*b**6 + 0*b. Factor g(z).
2*z*(z - 1)*(9*z - 2)/9
Let r be (-5 - -1)*(13 - 14). Factor -r - 10 + 15*t - 5*t**3 - 7 + 31.
-5*(t - 2)*(t + 1)**2
Let o(q) be the third derivative of q**10/30240 + q**9/12096 - q**8/4032 - q**7/1008 + q**5/30 - 12*q**2. Let u(h) be the third derivative of o(h). Factor u(m).
5*m*(m - 1)*(m + 1)**2
Let c be (-13)/(-52) + 3/(-8)*-10. Factor 25*m**2 - 7*m**4 - 5*m**4 + 8*m**3 + c + 4*m**5 - 12*m - 17*m**2.
4*(m - 1)**4*(m + 1)
Let t(c) be the second derivative of -c**7/21 + 8*c**6/15 - 13*c**5/10 + c**4 - 3*c - 23. Find l, given that t(l) = 0.
0, 1, 6
Let s(m) be the second derivative of 1/24*m**4 - 44*m + 0 + 7/6*m**3 + 49/4*m**2. Factor s(x).
(x + 7)**2/2
Let s be (-7 + 2)*(-5)/(50/6). Let l(w) be the first derivative of s*w**2 + 2*w - 7/6*w**3 + 3. Suppose l(m) = 0. What is m?
-2/7, 2
Suppose -3*a = -3*j - 51, 58 = 6*a - a + 4*j. Factor -3*x**2 - 7*x + 5*x + a*x.
-3*x*(x - 4)
Factor 10 + 35*y - 21 - 21 - 43 + 20*y - 10*y**2.
-5*(y - 3)*(2*y - 5)
Let r(x) be the first derivative of x**3/5 + 3*x**2 + 72*x/5 - 276. What is p in r(p) = 0?
-6, -4
Let h be (-564)/(-60) + 4/(-10). Let y be (-28)/(-6) + (-6)/h. Solve 0*o**y + 3*o**4 - 2*o**4 = 0.
0
Let u be (2/7)/((-273)/(-147)). Solve 0*g**2 - 4/13*g**3 + u + 4/13*g - 2/13*g**4 = 0 for g.
-1, 1
Suppose 50*p = 164 + 36. Suppose 0*r - 2/3*r**2 + 0 + 1/3*r**p + 1/3*r**3 = 0. What is r?
-2, 0, 1
Suppose 8*f + 63 = 39. Let w be (f - 3)/(-3) - (4 + -2). Let 0*l**2 + w + 3/2*l**5 + 0*l**4 + 0*l - 3/2*l**3 = 0. Calculate l.
-1, 0, 1
Suppose 6*a - 5*a = 45. Let k = -45 + a. What is f in 1/3*f + 2/3*f**2 - f**3 + k = 0?
-1/3, 0, 1
Let i(p) be the third derivative of -p**7/840 - p**6/240 - 5*p**4/8 - 6*p**2. Let z(b) be the second derivative of i(b). Factor z(u).
-3*u*(u + 1)
Let p(d) be the first derivative of d**8/1344 - d**7/210 + d**6/80 - d**5/60 + d**4/96 - d**2 + 2. Let z(t) be the second derivative of p(t). Factor z(x).
x*(x - 1)**4/4
Let z(k) be the first derivative of 0*k + 0*k**2 - 4/57*k**6 + 34/95*k**5 - 10/19*k**4 + 8/57*k**3 + 44. Suppose z(h) = 0. Calculate h.
0, 1/4,