en that b(w) = 0.
-1, -2/3
Let p(x) be the third derivative of -x**8/60480 + x**7/15120 - x**5/15 + 5*x**2. Let w(c) be the third derivative of p(c). Determine n so that w(n) = 0.
0, 1
Let v(u) be the second derivative of u**4/30 - 2*u**3/15 + u**2/5 + 2*u. Factor v(y).
2*(y - 1)**2/5
Suppose 7*j - 2*j - 25 = 0. Factor 1/3*b**j - 1/3*b**2 + b**3 + 0 - b**4 + 0*b.
b**2*(b - 1)**3/3
Suppose -6*u = 14*u. Factor u - 1/4*q - 1/4*q**2.
-q*(q + 1)/4
Suppose -3*r = -5 - 4. Let d = r - 0. Factor 7*a + 4 - 2*a**3 + 0*a**d - a.
-2*(a - 2)*(a + 1)**2
Factor 0 + j**5 - 8*j**2 - 3*j + 2*j**3 + 3*j**4 + 6*j**2 - 1.
(j - 1)*(j + 1)**4
Factor 5*i**4 - 3*i**4 + i**4 + 0*i**4 - 6*i**3.
3*i**3*(i - 2)
Let f(x) be the third derivative of -x**5/80 + x**3/8 + 9*x**2. Factor f(m).
-3*(m - 1)*(m + 1)/4
Let c(z) be the first derivative of -z**4 + 6 - 2/3*z**2 - 16/9*z**3 + 0*z. Factor c(n).
-4*n*(n + 1)*(3*n + 1)/3
Let b(f) be the third derivative of -f**7/945 + f**6/108 - 4*f**5/135 + f**4/27 - 6*f**2. Find r, given that b(r) = 0.
0, 1, 2
Let o(s) be the second derivative of -1/8*s**2 - 5*s - 1/48*s**4 + 0 - 1/12*s**3. Factor o(u).
-(u + 1)**2/4
Let m be 20/(-45) - (-646)/765. Factor 0*j + m*j**2 + 0.
2*j**2/5
Factor -12/7*y**4 + 8/7*y**2 + 4/7 + 12/7*y - 8/7*y**3 - 4/7*y**5.
-4*(y - 1)*(y + 1)**4/7
Let r(g) = g**2. Let s(d) = -5*d**2 + 9*d + 6. Suppose 0 = -5*a + f + 10, -2*a = 3*a - 3*f - 20. Let z(n) = a*r(n) - s(n). Factor z(k).
3*(k - 2)*(2*k + 1)
Solve 1/4*j**2 + 1/4*j + 0 = 0.
-1, 0
Let j(x) be the second derivative of -x**6/21 + 4*x**5/35 - x**4/42 - 2*x**3/21 + 19*x. Factor j(c).
-2*c*(c - 1)**2*(5*c + 2)/7
Suppose 2*y + 3*c - 12 = 0, -3*c = -y - 4*y + 9. Determine i, given that 2/9*i**2 + 2/9*i - 2/9 - 2/9*i**y = 0.
-1, 1
Let s(v) = -6*v + 29. Let y(c) = c - 6. Let o(u) = -2*s(u) - 11*y(u). Let g be o(-6). Suppose -1 - 1/4*n**g + n = 0. What is n?
2
Factor 192/7*t + 24/7*t**2 + 512/7 + 1/7*t**3.
(t + 8)**3/7
Suppose -16 = -5*a - y, 0*a - a - 12 = 4*y. Let u(d) = -a - d - 1 + 6. Let q(o) = -o**2 - 3. Let m(s) = -q(s) - 2*u(s). Factor m(c).
(c + 1)**2
Let b(k) = -6*k**3 - 2*k**2 - k. Let x(v) = -5*v**3 - v**2. Let t(g) = g**3 - 2. Let w be t(0). Let j(h) = w*b(h) + 3*x(h). Factor j(i).
-i*(i - 1)*(3*i + 2)
Factor 4*d**3 - 12*d**4 - 7*d**4 + 17*d**4.
-2*d**3*(d - 2)
Solve -65*p**3 + 69*p - 10 - 4*p + 654*p**2 - 569*p**2 - 75*p**4 = 0.
-1, 2/15, 1
Let o(d) = 36*d**2 + 21*d + 15. Suppose -2*u - 51 - 17 = 4*i, 0 = 5*i + u + 79. Let m(p) = -5*p**2 - 3*p - 2. Let n(t) = i*m(t) - 2*o(t). Factor n(y).
3*y*(y + 1)
Let t(d) be the second derivative of -d**4/60 - d**3/30 + d**2/5 + 32*d. Factor t(v).
-(v - 1)*(v + 2)/5
Let f(m) = 2*m**3 - 2*m**2 + 3*m - 1. Let i be f(1). Let z be (-2)/(-6)*12/10. Factor -8/5*x + z*x**i + 8/5.
2*(x - 2)**2/5
Factor 10*f + 14*f - 6*f + 27 + 3*f**2.
3*(f + 3)**2
Let t(u) = -u**2 + 2*u + 3. Let s be t(3). Let w(q) be the second derivative of 0 + 0*q**2 - 1/12*q**4 + s*q**5 + 2*q + 0*q**3 + 1/30*q**6. Factor w(x).
x**2*(x - 1)*(x + 1)
Let u(s) = -25*s**5 + 15*s**4 - 35*s**3 - 15*s**2 + 20. Let k(n) = -n**5 - n**3 - n**2 + 1. Let h(v) = -20*k(v) + u(v). Solve h(b) = 0 for b.
0, 1
Let y be (-14)/40 - (-5 + 136/32). Factor 0 - y*a - 4/5*a**3 + a**2 + 1/5*a**4.
a*(a - 2)*(a - 1)**2/5
Let m be 2/(-6) + 12/36. Solve -2/3*t + m - 2/3*t**3 + 4/3*t**2 = 0 for t.
0, 1
Let f(u) = -5*u**4 - u**3 - u**2 + 7*u + 6. Let q = -34 + 17. Let z(j) = 14*j**4 + 3*j**3 + 3*j**2 - 20*j - 17. Let y(o) = q*f(o) - 6*z(o). Factor y(n).
n*(n - 1)**2*(n + 1)
Let s(v) = v**4 + 18*v**3 - 39*v**2 + 36*v - 12. Let k(j) = -j**4. Let n(c) = 4*k(c) + s(c). Let n(b) = 0. Calculate b.
1, 2
Suppose -5*y = 4*a - 27, -12 = -a - 0*a + 4*y. Suppose -4*g = 4*v + 4, -v - 2*g = -4*g - a. Factor 0*i - 1/2*i**3 + 3/4*i**v - 1/4.
-(i - 1)**2*(2*i + 1)/4
Let p(j) be the second derivative of j**6/10 + 3*j**5/5 + 5*j**4/4 + j**3 + 10*j. Factor p(b).
3*b*(b + 1)**2*(b + 2)
Let x(i) be the third derivative of i**7/105 + i**6/15 + i**5/10 - 47*i**2. Determine z, given that x(z) = 0.
-3, -1, 0
Let s(l) = 10*l**3 + 10*l**2 - 27*l - 40. Let t(p) = -5*p**3 - 5*p**2 + 14*p + 20. Let r(x) = 6*s(x) + 13*t(x). Factor r(m).
-5*(m - 2)*(m + 1)*(m + 2)
Let f(h) = h**3 - h**2 + 12*h - 7. Let n(r) = -r**3 + r**2 - 6*r + 4. Let w(b) = 4*f(b) + 7*n(b). Determine g, given that w(g) = 0.
-1, 0, 2
Let g be 0/1*(3 - 7 - -5). Let b(j) be the third derivative of 1/180*j**5 - 2*j**2 + 0*j - 1/630*j**7 - 1/360*j**6 + 0 + g*j**3 + 1/72*j**4. Factor b(l).
-l*(l - 1)*(l + 1)**2/3
Let v(d) = 2*d**2 + 1. Let b be v(1). Find r, given that -r**2 - 7*r**b + 5*r**3 + 3*r**2 = 0.
0, 1
Let k = -7189/2799 + 4/311. Let t = -20/9 - k. Factor t*m**2 - 2/3*m + 1/3.
(m - 1)**2/3
Let c(i) be the third derivative of -1/90*i**5 + 0 - 3*i**2 + 0*i**4 + 0*i + 1/9*i**3. Factor c(k).
-2*(k - 1)*(k + 1)/3
Factor 3/5*s**4 - 6/5*s**2 + 3/5*s**5 - 6/5*s**3 + 3/5*s + 3/5.
3*(s - 1)**2*(s + 1)**3/5
Let c(h) = -h - 7. Let b be c(-9). Suppose -3*u - 2*r = -11, 3*u + 2*u - 20 = -5*r. Find k such that 0*k + 2/3*k**b + 2/3*k**u + 0 = 0.
-1, 0
Let w be (8/66)/(((-8)/60)/(-1)). Suppose 20/11*t**2 + 10/11*t**4 + 2/11 - 2/11*t**5 - w*t - 20/11*t**3 = 0. Calculate t.
1
Let m(y) be the third derivative of y**5/75 + y**4/30 - 2*y**2. Find h, given that m(h) = 0.
-1, 0
Let f(q) be the first derivative of -q**8/1344 - q**7/420 + q**5/120 + q**4/96 + 3*q**2/2 - 3. Let m(c) be the second derivative of f(c). Factor m(u).
-u*(u - 1)*(u + 1)**3/4
Let c(h) = -h**3 + 7*h**2 - 6*h + 5. Let d be c(6). Let m = d + -3. Factor 1 - b + 1/4*b**m.
(b - 2)**2/4
Let h(b) be the third derivative of -b**5/15 - 5*b**4/6 - 27*b**2. Factor h(c).
-4*c*(c + 5)
Let d(w) be the second derivative of -w**4/16 + w**3/8 + 3*w**2/4 + 58*w. Factor d(m).
-3*(m - 2)*(m + 1)/4
Let y(q) = 5*q**2 - q. Let z be y(1). Suppose -2*s = -2*v - 20, 27 = z*s - v + 2. Factor 1/2*u**s - u**2 + 0 - 1/2*u + u**4 + 0*u**3.
u*(u - 1)*(u + 1)**3/2
Let m(k) be the second derivative of 27*k**6/5 + 153*k**5/20 + 11*k**4/3 + 2*k**3/3 - 9*k. Factor m(u).
u*(2*u + 1)*(9*u + 2)**2
Let q(g) be the second derivative of -2*g**6/135 - 2*g**5/9 - 17*g**4/27 - 16*g**3/27 + 13*g - 1. Factor q(x).
-4*x*(x + 1)**2*(x + 8)/9
Let j(l) be the first derivative of l**6/90 + l**5/40 - l**4/24 - l**3 + 3. Let k(g) be the third derivative of j(g). Determine w so that k(w) = 0.
-1, 1/4
Let b(a) be the first derivative of -a**2 - 2*a - 2 - 1/6*a**3. Determine r so that b(r) = 0.
-2
Solve 0 + 0*u**2 + 2/9*u**5 + 0*u**3 - 4/9*u**4 + 0*u = 0 for u.
0, 2
Let n(w) be the first derivative of 2 + 80/3*w**3 + 4*w - 8*w**4 - 17*w**2. Suppose n(g) = 0. Calculate g.
1/4, 2
Let b = 4050 - 36356/9. Let d = b + -452/45. Factor -d*f**4 + 0 + 0*f + 4/5*f**2 + 2/5*f**3.
-2*f**2*(f - 2)*(f + 1)/5
Let z(b) be the third derivative of 1/42*b**4 + 0*b - 1/42*b**5 + 0 + 2*b**2 + 0*b**3. Factor z(i).
-2*i*(5*i - 2)/7
Let q(s) be the third derivative of -s**5/12 + 5*s**4/8 + 7*s**2. Solve q(a) = 0 for a.
0, 3
Suppose -2*j - 3*j = -10. Let k(z) be the second derivative of -1/9*z**3 + 0*z**2 + j*z - 1/30*z**5 + 0 - 1/9*z**4. Factor k(p).
-2*p*(p + 1)**2/3
Let k = 11 + -6. Solve -3*r**5 + r**5 - 5*r**5 - r**4 + 6*r**k = 0 for r.
-1, 0
Let v be 3*(-1)/(519/2). Let u = 1028/865 - v. Suppose -2/5*n**5 + 0 - 6/5*n**3 + 0*n - u*n**4 - 2/5*n**2 = 0. Calculate n.
-1, 0
Let l be (8/28)/(5/(70/6)). Let a be ((-4)/5)/(3/(-5)). Factor a*c**3 + 0 - 2/3*c - l*c**2.
2*c*(c - 1)*(2*c + 1)/3
Let v(o) = -54*o - o**2 + 54*o + o**4 + o**3. Let g(q) = -3*q**5 + 6*q**4 + 9*q**3 - 6*q**2. Let d(c) = -g(c) + 6*v(c). Factor d(u).
3*u**3*(u - 1)*(u + 1)
Let p(w) be the third derivative of w**7/70 + 3*w**6/20 + 9*w**5/20 + 5*w**2 - 1. Factor p(g).
3*g**2*(g + 3)**2
Solve 1/2*k**2 - 1 + 1/2*k = 0 for k.
-2, 1
Let g(a) be the second derivative of -a**5/20 - 7*a**4/12 - a**3/6 - 2*a**2 - 11*a. Let h be g(-7). Suppose 0*u**2 + 0*u + 0 - 1/4*u**h = 0. Calculate u.
0
Let w(b) be the first derivative of -5*b**6/6 + 7*b**5 - 95*b**4/4 + 125*b**3/3 - 40*b**2 + 20*b - 20. Factor w(u).
-5*(u - 2)**2*(u - 1)**3
Let z(t) be the first derivative of -2*t**3/27 + 7*t**2/9 + 16*t/9 - 17. Let z(q) = 0. Calculate q.
-1, 8
Suppose 0 = o - 3*o + 2*t, 2*t = -3*o. Determine p so that o*p + 1/3*p**3 + 0 - 1/6*p