(m) be the second derivative of -9*m + 0*m**4 + 0 - d*m**3 + 1/20*m**5 - 1/84*m**7 + 0*m**6 + 0*m**2. Factor w(i).
-i*(i - 1)**2*(i + 1)**2/2
Suppose 15*v + 255 = 66*v. Factor 16/3*s**v + 5/3*s**2 - 40/3*s**4 - 5/3*s - 1/3 + 25/3*s**3.
(s - 1)**3*(4*s + 1)**2/3
Let j = 4/461 + 24874/2305. Suppose 11 = 4*w - 61. Find m such that 12/5*m + 0 + 58/5*m**2 + w*m**3 + j*m**4 + 2*m**5 = 0.
-3, -1, -2/5, 0
Find k, given that 13*k**4 + 5*k**2 + 0 + 7/2*k**5 + 0*k - 43/2*k**3 = 0.
-5, 0, 2/7, 1
Let m(q) be the first derivative of -2*q**2 + 38*q**3 - 52 + 6859/10*q**5 + 0*q - 1083/4*q**4. Factor m(s).
s*(19*s - 2)**3/2
Let n be 1/(2/(-84)*-2). Suppose n = 4*z - 39. Factor -2*h**5 - z*h**4 + 11*h**4 - 2*h**3 - 2*h**2 + 2*h**2.
-2*h**3*(h + 1)**2
Let q(b) = -3*b**5 + 5*b**4 + 8*b**3 - 18*b**2 - 2*b + 14. Let m(x) = -x**5 + x**4 + 2*x**3 - x**2 - x - 1. Let i(a) = 4*m(a) - 2*q(a). Factor i(h).
2*(h - 2)**3*(h + 1)*(h + 2)
Let y(h) = 3*h**4 - 3*h**3 - 2*h + 2. Let w(r) = -r**4 + r**3 - r**2 + r - 1. Let l(n) = 2*w(n) + y(n). Factor l(t).
t**2*(t - 2)*(t + 1)
Let g be (-42)/24 + 1/(-4). Let t be 640/30 + g/6. Factor 8*n**5 - n**3 + 0*n**3 + 14*n**5 - t*n**5.
n**3*(n - 1)*(n + 1)
Factor -8*h**2 - 10 + 13*h**2 - 5 - 4*h**2 - 1.
(h - 4)*(h + 4)
Let g(n) be the first derivative of -1/4*n**4 + 1/2*n**2 + 0*n + 2 - 1/10*n**5 + 1/6*n**3. Factor g(d).
-d*(d - 1)*(d + 1)*(d + 2)/2
Let i(v) be the second derivative of -v**5/25 - 2*v**4/15 + 8*v**3/15 + 16*v**2/5 + v - 49. Determine m, given that i(m) = 0.
-2, 2
Let w(l) = 15*l**3 - 675*l**2 + 1120*l + 85. Let y(u) = u**3 - 48*u**2 + 80*u + 6. Let b(z) = -6*w(z) + 85*y(z). Suppose b(n) = 0. Calculate n.
-8, 0, 2
Let i(g) be the third derivative of g**6/72 - g**5/12 - 5*g**4/8 - 2*g**3 - 11*g**2. Let y(w) be the first derivative of i(w). Factor y(a).
5*(a - 3)*(a + 1)
Let o = -3 + 3. Suppose o*c + c = 2. Factor 2 + v - v**2 - c + 0*v.
-v*(v - 1)
Let r(a) be the third derivative of -a**8/784 + 2*a**7/245 - 3*a**6/280 - a**5/35 + a**4/14 - a**2 - 63. Find z, given that r(z) = 0.
-1, 0, 1, 2
Let k = 396 - 393. Let f(b) be the third derivative of 0*b**4 + 8*b**2 + 1/100*b**5 + 0*b - 1/10*b**k + 0. Let f(a) = 0. Calculate a.
-1, 1
Let c(f) be the third derivative of -f**5/20 + 13*f**4/8 - 6*f**3 - 295*f**2. Find a such that c(a) = 0.
1, 12
Let q = 1914 - 5741/3. Factor i - q*i**2 - 2/3.
-(i - 2)*(i - 1)/3
Let r(c) be the first derivative of 3/2*c + 13 - 5/18*c**3 + 1/24*c**4 + 1/4*c**2. Factor r(k).
(k - 3)**2*(k + 1)/6
Let s be -9 + 36/16 - -7. Factor -1 + s*a**2 + 3/4*a.
(a - 1)*(a + 4)/4
Let l be ((-4)/(-10))/((-3)/5)*-3. Suppose l*k - 9*k = -k. Find o such that k - 4/5*o**2 - 2/5*o**3 - 2/5*o = 0.
-1, 0
Let k(s) be the third derivative of s**5/12 - 5*s**4/2 + 30*s**2. Let k(m) = 0. What is m?
0, 12
Suppose 4*y + 42 = 11*y. Let w(s) be the second derivative of 0 - 1/6*s**3 + 0*s**2 + y*s + 3/40*s**5 - 1/24*s**4. Find u, given that w(u) = 0.
-2/3, 0, 1
Let l(s) be the first derivative of -2*s**3/27 + 38*s**2/9 - 16*s - 198. Let l(i) = 0. What is i?
2, 36
Let u(f) be the third derivative of f**8/28 + 26*f**7/105 - f**6/30 - 7*f**5/5 - f**4/3 + 16*f**3/3 - 243*f**2. Solve u(s) = 0.
-4, -1, 2/3, 1
Suppose -3*l = -9*l. Suppose h - 13 + 10 = l. Factor 0 + 1/5*j + 1/5*j**h + 2/5*j**2.
j*(j + 1)**2/5
Suppose 3*g - 12 = 0, 2*i - 50 - 392 = 5*g. Let y = -2077/9 + i. Factor 2/9*f**3 - 4/9*f**2 - y*f + 4/9.
2*(f - 2)*(f - 1)*(f + 1)/9
Let t(g) be the third derivative of g**6/300 - 2*g**5/25 + 3*g**4/5 + 176*g**2. Find h such that t(h) = 0.
0, 6
Suppose 26*u + 3*u + 37 = 153. Find j such that -20/3 + u*j**3 - 76/3*j**2 + 28*j = 0.
1/3, 1, 5
Let p(q) be the first derivative of q**4/3 - 2*q**3/3 + q**2/2 + 17*q + 7. Let h(i) be the first derivative of p(i). Factor h(f).
(2*f - 1)**2
Let z(v) = -3*v**3 - 9*v**2 + 6*v - 30. Let r(c) = -c**2 - c + 5. Let f(q) = 6*r(q) + z(q). Suppose f(b) = 0. Calculate b.
-5, 0
Let u(h) = h**3 + 79*h**2 - 160*h + 162. Let m be u(-81). Determine l so that -1/3*l**5 + 0*l + m*l**4 - 2/3*l**2 + l**3 + 0 = 0.
-2, 0, 1
Let f(x) = 8*x + 1. Let g = 19 + -18. Let n be f(g). Factor 1 - 14*b**2 - 13*b**2 + n*b**4 + 1 - 8 - 27*b + 3*b**3.
3*(b - 2)*(b + 1)**2*(3*b + 1)
Let z be 1/(-1 + (-4)/(-3)). Suppose -260*w + 760 - 240 = 0. Determine k so that 1/5*k**z + 0 - 1/5*k + 1/5*k**4 - 1/5*k**w = 0.
-1, 0, 1
Let l(d) be the third derivative of d**5/60 + 11*d**4/24 + 2*d**3 + 2*d**2. Let z be l(-10). Factor 3*n**2 - 3*n + 0*n + 3 + 0*n**z - 3*n.
3*(n - 1)**2
Let k be ((-20)/15)/(-2)*123. Let y = k - 80. Find g, given that 0*g - g**y + 1/2*g**4 + 0*g**3 + 1/2 = 0.
-1, 1
Let c be (1 + -11)/5 - -2. Suppose c = 5*p - 3*p + r - 17, -4*p = -5*r + 1. Factor 2*g + 9*g + 4*g**3 - p*g**2 - g**3 - 8*g.
3*g*(g - 1)**2
Let k(n) be the second derivative of 3/5*n**6 + 0 - 6*n + 6/5*n**5 - 1/2*n**4 + 1/14*n**7 - 9/2*n**3 - 6*n**2. Solve k(t) = 0 for t.
-4, -1, 1
Factor -6*a**2 + 3*a**2 + 0*a**2 - a**2 + 4*a**4.
4*a**2*(a - 1)*(a + 1)
Let t = 1309/696 + -1/174. Factor -21/8*r + 3/4 - t*r**3 + 3/8*r**4 + 27/8*r**2.
3*(r - 2)*(r - 1)**3/8
Solve 0 + 186/5*m - 99/5*m**2 + 3/5*m**3 = 0.
0, 2, 31
Let b(j) = -j + 8. Let o be b(10). Let k be (-5)/o + (-6)/12. Factor 6*f**4 + 2*f**2 - 4*f**4 + 2*f**2 - 4*f**4 - k*f**3.
-2*f**2*(f - 1)*(f + 2)
Factor -5 - 6*d**3 + 7*d**2 + 5*d**2 + 3*d - 7*d**2 + 3*d**5 + 2 - 3*d**4 + d**2.
3*(d - 1)**3*(d + 1)**2
Find w such that 6/5*w**5 + 0 + 726/5*w - 24*w**4 + 264*w**2 + 468/5*w**3 = 0.
-1, 0, 11
Let c(y) = y**2 - 43*y - 240. Let q be c(48). Factor -1/8*n**2 + q*n + 0 + 1/8*n**4 + 0*n**3.
n**2*(n - 1)*(n + 1)/8
Let u(f) = f**2 - 3*f - 18. Let n be 5/75*99 - (-6)/(-10). Let k be u(n). Determine w, given that -44/3*w**2 + 3*w**5 + k - 2*w**4 - 4*w - 47/3*w**3 = 0.
-1, -2/3, 0, 3
Let k(h) be the second derivative of h**7/630 + h**6/45 + 2*h**5/15 + 4*h**4/9 - h**3/3 - 3*h. Let b(t) be the second derivative of k(t). Factor b(f).
4*(f + 2)**3/3
Factor 3*a**3 - 2*a**5 - 60*a**4 - 51*a**3 + 51*a**3 - 3*a**5 - 58*a**3.
-5*a**3*(a + 1)*(a + 11)
Suppose 6*v**4 - 3*v**3 + 8*v**2 - 2*v**2 + 583*v**5 - 6*v**2 - 586*v**5 = 0. Calculate v.
0, 1
Suppose 2*v - 3*a + 54 = 0, -4 = -2*a + 4*a. Let b be (((-8)/v)/2)/((-3)/(-30)). Let -16/3*z - 4 - b*z**2 = 0. Calculate z.
-3, -1
Factor -1/4*x**2 + 0 - 1/4*x**3 + 5*x.
-x*(x - 4)*(x + 5)/4
Let n be -1 - (-14)/10 - (-16116)/(-140). Let g = n + 115. What is f in 0*f + 2/7*f**2 - g = 0?
-1, 1
Suppose -8*i + 12 = -28. Factor 17*v**2 + 7*v**3 - v**3 - 8*v + i*v**2.
2*v*(v + 4)*(3*v - 1)
Factor 2*w - 17 - 2 + 19 + w**2.
w*(w + 2)
Suppose 3*k - 13 = -m, 0*m - 20 = -2*k + 5*m. Suppose -h**4 - 6*h**5 + 0*h**k - h**4 + 2*h**2 + 5*h**5 + h**3 = 0. Calculate h.
-2, -1, 0, 1
Let l(y) be the first derivative of y**6/90 - y**4/18 + y**2/6 - 16*y + 5. Let r(o) be the first derivative of l(o). Factor r(v).
(v - 1)**2*(v + 1)**2/3
Let o(u) = -42*u**2 + 3324*u - 615. Let q(f) = -9*f**2 + 831*f - 154. Let x(g) = -4*o(g) + 15*q(g). Factor x(y).
3*(y - 25)*(11*y - 2)
Let f(r) be the second derivative of 1/7*r**2 + 2/21*r**3 + 1/42*r**4 + 0 + 17*r. Suppose f(k) = 0. What is k?
-1
Let m = -25 + 65. Let n = 47 - m. Determine h, given that -43/3*h**4 + 8/3*h - 7/3*h**3 - n*h**5 + 9*h**2 - 4/3 = 0.
-1, 2/7, 2/3
Let j(t) = t**2 + 61*t + 63. Let f(l) = 8*l**2 + 428*l + 440. Let i(o) = 3*f(o) - 20*j(o). Factor i(v).
4*(v + 1)*(v + 15)
Let t(o) = o**3 - 11*o**2 - o - 10. Let d be t(11). Let w = 23 + d. Factor 2*v**5 - 169*v**2 + 167*v**w + 2*v**4 + v**3 - 3*v**3.
2*v**2*(v - 1)*(v + 1)**2
Solve -3/7*r**4 + 6/7*r**2 + 9/7*r**3 + 24/7 - 36/7*r = 0.
-2, 1, 2
Let 35*q - 60 - 50*q - 24*q - 29*q - 8*q**2 = 0. Calculate q.
-15/2, -1
Let a(w) be the second derivative of 0*w**2 + 0 + 0*w**4 - 2/15*w**6 + 0*w**3 + 15*w - 1/5*w**5. Factor a(c).
-4*c**3*(c + 1)
Suppose -24 = 38*o - 44*o. Let p(r) be the first derivative of -1/20*r**5 - 1/4*r**2 + 1/4*r + 1/8*r**o + 0*r**3 + 2. Factor p(a).
-(a - 1)**3*(a + 1)/4
Let g be (12/(-2880))/(1 + (-2)/1). Let w(a) be the third derivative of 0 + 0*a - 1/48*a**4 + g*a**6 - 1/12*a**3 + 1/120*a**5 + 4*a**2. Factor w(m).
(m - 1)*(m + 1)**2/2
Let w(x) be the first derivative of -4*x**5/35 - 5*x**4/7 - 12*x**3/7 - 2*x**2 - 8*x/7 - 223. Factor w(c).
-4*(c + 1)**3*(c + 2)/7
Let r(f) be th