) be the third derivative of w**6/20 - w**5/15 - w**4/4 + 2*w**3/3 + 28*w**2 - 2. Suppose j(o) = 0. Calculate o.
-1, 2/3, 1
Determine v, given that 8/13 + 6/13*v - 2/13*v**2 = 0.
-1, 4
Let r be (9 - 1)/(-2)*-5. Factor 8*z**2 + 0 - 10 + 15*z + 5*z**5 + 2*z**2 - r*z**3.
5*(z - 1)**3*(z + 1)*(z + 2)
Let x(v) be the first derivative of -v**6/6 - 11*v**5/5 - 21*v**4/2 - 64*v**3/3 - 16*v**2 + 119. Factor x(y).
-y*(y + 1)*(y + 2)*(y + 4)**2
Factor 9/4 - 19/4*f - 1/4*f**3 + 11/4*f**2.
-(f - 9)*(f - 1)**2/4
Let g be (-57)/(-15) + (-29)/(-145). Factor 0*i - 4/5*i**2 + 0 - 1/5*i**g + 4/5*i**3.
-i**2*(i - 2)**2/5
Let c(o) be the second derivative of -1/6*o**4 - 2/3*o**3 + 3*o - o**2 + 0. Suppose c(b) = 0. What is b?
-1
Let i(o) = -o**2 + 17*o - 28. Let t be i(15). Suppose 0*f - f - 4 = 3*r, -4*r + 4*f + 16 = 0. Solve -1/2 + 1/2*n**t + r*n = 0 for n.
-1, 1
Let j(f) be the second derivative of -f**8/10080 - f**7/5040 + f**6/2160 + f**5/720 - 10*f**3/3 - 5*f. Let l(q) be the second derivative of j(q). Factor l(c).
-c*(c - 1)*(c + 1)**2/6
Factor -3*j**4 - 6413 + 108*j**3 + 1613 - 4320*j - 40049*j**2 + 39317*j**2.
-3*(j - 20)**2*(j + 2)**2
Let o(w) be the first derivative of -2*w**3/15 + 44*w**2/5 - 968*w/5 - 2. What is k in o(k) = 0?
22
Let a(z) = z**3 + 7*z**2 - 2*z - 10. Let x be a(-7). Suppose -u + x = -0*u. Factor 13*r + 9*r + 16*r**2 - 44*r**3 - 24*r**u + 36*r**5 - 6*r.
4*r*(r - 1)**2*(3*r + 2)**2
Let q(n) = -n**2 - n - 1. Let j(p) = 5*p**2 + 7*p + 6. Let w(y) = -j(y) - 6*q(y). Let a be w(3). Let 8*u - 4*u + 3*u**2 - a + 0*u - u = 0. Calculate u.
-2, 1
Suppose -4*f + 3 + 5 = 0. Solve p - 3*p + 2*p**2 - 2*p - f*p = 0 for p.
0, 3
Factor -7*z**2 - 5*z + 2*z**2 + 5*z**3 - 5*z**2 + 0*z**3 + 10.
5*(z - 2)*(z - 1)*(z + 1)
Let b = 719/3 + -718/3. Let g(j) be the first derivative of -b*j**3 - 7 + 0*j - j**2. Factor g(f).
-f*(f + 2)
Let p = -120/11 - -8651/792. Let k(x) be the third derivative of 0*x**6 + 0 - x**2 + 0*x + 1/90*x**5 + 0*x**3 - 1/315*x**7 + 1/1008*x**8 - p*x**4. Factor k(t).
t*(t - 1)**3*(t + 1)/3
Suppose -6*k - 12*k + 36 = 0. Let b be ((-6)/(-18))/(k/4). Factor -2/3*a**2 - b*a**4 + 14/9*a**3 - 2/3*a + 4/9.
-2*(a - 1)**3*(3*a + 2)/9
Let v(c) be the second derivative of -c**6/75 + 9*c**5/50 - 13*c**4/30 - 3*c**3/5 + 14*c**2/5 - 56*c. Determine y so that v(y) = 0.
-1, 1, 2, 7
Let m = 239 + -237. Let s(b) be the first derivative of -5 - 5/16*b**4 - 3/4*b**3 - 1/2*b - 7/8*b**m - 1/20*b**5. Let s(i) = 0. Calculate i.
-2, -1
Factor -152/5*b**2 - b + 15 - 16*b**3.
-(4*b + 5)**2*(5*b - 3)/5
Let y(g) be the first derivative of -2*g**3/39 - 8*g**2/13 + 18*g/13 - 110. Determine i so that y(i) = 0.
-9, 1
Suppose 12 = -a + 8. Let z be (a*2/4 - -2)/(-1). Factor 2/3*d**3 + z*d - 1/6*d**4 + 0 - 2/3*d**2.
-d**2*(d - 2)**2/6
Let u(g) be the second derivative of g**4/15 + 8*g**3 + 118*g**2/5 + 59*g - 4. Factor u(v).
4*(v + 1)*(v + 59)/5
Let p(a) = 2*a + 10. Let r be p(-3). Let z(w) be the second derivative of 0 - 6*w - 1/4*w**r + 3/2*w**2 + 1/2*w**3 - 3/20*w**5. Suppose z(c) = 0. Calculate c.
-1, 1
Let v(q) be the second derivative of -q**6/480 - q**5/80 + q**3 + 9*q. Let a(n) be the second derivative of v(n). Suppose a(k) = 0. Calculate k.
-2, 0
Let h = 153/7 + -3053/140. Let t(q) be the first derivative of 1/5*q + h*q**4 + 1/5*q**3 + 3/10*q**2 - 7. Let t(w) = 0. Calculate w.
-1
Let u(f) = -4*f**3 + 46*f**2 - 25*f - 6. Let w(a) = -a**3 + 9*a**2 - 5*a - 1. Let v(k) = 2*u(k) - 11*w(k). Solve v(y) = 0.
1/3, 1
Let g(b) be the first derivative of b**3/4 + 39*b**2/8 + 45*b/2 - 266. Factor g(u).
3*(u + 3)*(u + 10)/4
Let l(y) = -23*y**5 + 4*y**4 + 24*y**3 - 5*y**2 - 5*y + 5. Let d(c) = 12*c**5 - 3*c**4 - 12*c**3 + 3*c**2 + 3*c - 3. Let j(s) = 5*d(s) + 3*l(s). Factor j(q).
-3*q**3*(q - 1)*(3*q + 4)
Let i = -6139/4 - -1535. Solve i*y**2 + 0*y + 0 = 0 for y.
0
Find g such that -162/5*g**2 - 372/5*g - 3*g**3 + 3/5*g**4 - 264/5 = 0.
-2, 11
Let f(q) be the third derivative of -2/3*q**4 + 0 - 50*q**2 + 0*q + 0*q**3 + 1/15*q**5. Solve f(p) = 0.
0, 4
Suppose -259 = -4*y - 5*x, -3*x + 4*x = 3. Factor -y*z**3 + 12*z**4 + 2*z + 76*z**3 - 55*z**3 - 10*z + 36*z**2.
4*z*(z - 2)*(z - 1)*(3*z - 1)
Determine k so that -414*k**2 + 1134/5*k - 216/5 + 290*k**3 - 50*k**4 = 0.
3/5, 4
Let v(r) = r**3 + 7*r**2 - 7*r + 11. Let n be v(-8). Suppose 2*a = -10, 3*w - 4*a = -9 + 47. Factor -n*x - w + 1 + x**2 + 2*x + 3.
(x - 2)*(x + 1)
Let c be ((-10)/(-2))/(5 + 4/(-1)). What is n in 12*n**2 + 175*n**c + 17*n**2 + 14*n - 45*n**3 + 51*n**2 + 6*n - 230*n**4 = 0?
-2/5, -2/7, 0, 1
Let a(s) = -2*s**2 + 258*s + 18228. Let c(x) = x**2 + 4*x - 1. Let f(u) = -a(u) - 3*c(u). Determine t, given that f(t) = 0.
-135
Let s(j) be the second derivative of -11*j**6/10 - 21*j**5/20 + j**4 + 38*j + 2. Factor s(a).
-3*a**2*(a + 1)*(11*a - 4)
Find d such that 250/21*d**5 + 104/21*d**2 - 60/7*d**3 - 50/21*d**4 + 0 - 16/21*d = 0.
-1, 0, 2/5
Solve -648/25*j**2 + 1416/25*j + 14/25*j**3 - 352/25 = 0.
2/7, 2, 44
Let h(w) be the first derivative of -5*w**6/24 + 7*w**5/4 - 15*w**4/4 - 259. Factor h(x).
-5*x**3*(x - 4)*(x - 3)/4
Let u(k) be the third derivative of 1/525*k**7 + 0*k**4 + 0 + 0*k + 0*k**3 + k**2 + 1/300*k**6 - 1/75*k**5. Factor u(m).
2*m**2*(m - 1)*(m + 2)/5
Let n(m) = 8*m**5 - 4*m**3 + 4*m**2 - 4*m. Let p(l) = 126 - 9*l**3 - 126 + 17*l**5 - 9*l + 9*l**2 + l**4. Let u(s) = 9*n(s) - 4*p(s). Factor u(h).
4*h**4*(h - 1)
Let q(b) be the third derivative of -b**9/90720 + b**8/10080 - b**7/3780 + b**5/4 - 22*b**2. Let d(l) be the third derivative of q(l). Factor d(i).
-2*i*(i - 2)*(i - 1)/3
Factor 40*h - 46*h**3 - 67*h**3 + 111*h**3 + 96 - 8*h**2.
-2*(h - 4)*(h + 2)*(h + 6)
Suppose 0 = -6*x + 10*x - 4*q + 20, 2*x + q - 5 = 0. Factor x - 2/5*a + 1/5*a**2.
a*(a - 2)/5
Let g(t) = -9*t**2 - 9*t - 6. Suppose 7*o = 3*o + 12. Let u(w) = -14*w**2 - 18*w - 4 - o*w**2 - 8. Let l(k) = -11*g(k) + 6*u(k). Factor l(i).
-3*(i + 1)*(i + 2)
Let x(b) be the third derivative of -b**6/540 + 29*b**5/270 + 25*b**4/27 - 128*b**3/27 + 632*b**2. Find c such that x(c) = 0.
-4, 1, 32
Suppose -2*h + 5*w + 26 = 0, -114*h + 110*h = 3*w. Factor -24/11*y**h + 0*y - 24/11*y**2 + 0 - 6/11*y**4.
-6*y**2*(y + 2)**2/11
Suppose 21*y - 20*y + 4*u - 60 = 0, 0 = -2*y - 5*u + 114. Suppose -67*f**4 + 21*f**2 + 98*f**4 - 6*f + 18*f**3 - y*f**4 - 12*f**5 = 0. Calculate f.
-2, -1, 0, 1/4, 1
Find w, given that -20/7*w - 2/7*w**2 - 6 = 0.
-7, -3
Let g(i) be the first derivative of i**6/180 - i**5/15 + 7*i**3 - 7. Let b(h) be the third derivative of g(h). Factor b(q).
2*q*(q - 4)
Let z(x) be the first derivative of x**5/10 + 21*x**4/8 + 9*x**3 + 709. Factor z(m).
m**2*(m + 3)*(m + 18)/2
Let t(d) = -3*d**3 + 2*d**2 + 5. Let k(p) = p**3 + 6*p**3 - 4*p**3 - 4 - p**2. Let j = -50 + 55. Let g(v) = j*k(v) + 4*t(v). Factor g(l).
3*l**2*(l + 1)
Factor -71*h**2 + 2016*h + 335*h**2 + 2352 - 2285*h**4 - 72*h**3 + 2288*h**4.
3*(h - 14)**2*(h + 2)**2
Let b(m) be the third derivative of m**7/10710 + m**6/6120 - m**5/1020 + m**4/4 + 18*m**2. Let i(a) be the second derivative of b(a). Factor i(k).
2*(k + 1)*(2*k - 1)/17
Let 0 - 1/2*c**2 + 1/6*c**4 + 1/3*c + 0*c**3 = 0. Calculate c.
-2, 0, 1
Let t = 10392919/41605 - -2/8321. Let b = t - 247. Factor -4/5*v**3 + 0 + 0*v + 0*v**2 - b*v**4.
-2*v**3*(7*v + 2)/5
Factor 18/5 + 7/5*i - 1/5*i**2.
-(i - 9)*(i + 2)/5
Let p(y) be the first derivative of -6*y**5/35 - 3*y**4/14 + 40*y**3/7 + 305. Factor p(o).
-6*o**2*(o - 4)*(o + 5)/7
Let u(a) be the first derivative of -3*a**5/5 + 3*a**4/4 + 5*a**3 + 9*a**2/2 + 44. Solve u(p) = 0.
-1, 0, 3
Let w(d) = -1. Let p(l) = -3*l**2. Let r = -32 - -21. Let k = -10 - r. Let t(z) = k*p(z) - 3*w(z). Factor t(h).
-3*(h - 1)*(h + 1)
Let h(o) = -o - 1. Suppose 4*t + 90 = 9*t. Let m = t + -13. Let k(v) = 48*v**2 + 19*v - 2. Let n(w) = m*h(w) - k(w). Determine a, given that n(a) = 0.
-1/4
Let x = -1172 + 18731/16. Let b = -73/80 - x. Determine i so that -8/5 + 1/5*i**3 + b*i**2 - 4/5*i = 0.
-2, 2
Let k(d) be the second derivative of 2*d**6/15 + 3*d**5/5 - 5*d**4/3 - 2*d**3 + 8*d**2 - 15*d + 4. Factor k(r).
4*(r - 1)**2*(r + 1)*(r + 4)
Suppose 32 = 3*b + 11. Suppose -4*u = -a + b, -5*a + u = -8 - 8. Suppose -1 - 3/2*q + 1/2*q**a + 0*q**2 = 0. Calculate q.
-1, 2
Factor 114 + 99 - 231 - g**3 + g + 18*g**2.
-(g - 18)*(g 