 1)**3/7
Factor -4585/3*d**4 - 143875/3*d**3 - 119164/3 - 1540855/3*d**2 - 845680/3*d - 49/3*d**5.
-(d + 31)**3*(7*d + 2)**2/3
Factor 5/2 + 7/4*s + 1/4*s**2.
(s + 2)*(s + 5)/4
Let i(k) be the second derivative of -2*k**6/3 + 7*k**5/15 + 11*k**4/6 + 4*k**3/3 + 3*k**2/2 - 6*k. Let d(y) be the first derivative of i(y). Factor d(x).
-4*(x - 1)*(4*x + 1)*(5*x + 2)
Let q be (5/(-20))/(44*(-8)/256). Factor -4/11*b**3 + 4/11*b + 2/11*b**4 - q + 0*b**2.
2*(b - 1)**3*(b + 1)/11
Let i be (2/15)/((-24)/(-100)*105/84). Factor -i*d**3 + 0*d**2 + 0 + 4/9*d.
-4*d*(d - 1)*(d + 1)/9
Let v(c) = 5*c**4 - 7*c**3 - 40*c**2 - 30*c - 12. Let k(i) = 9*i**4 - 15*i**3 - 80*i**2 - 61*i - 22. Let o(m) = -6*k(m) + 11*v(m). Factor o(u).
u*(u + 2)**2*(u + 9)
Suppose 2/11*y**3 + 20/11*y**2 + 14/11*y - 36/11 = 0. Calculate y.
-9, -2, 1
Factor 88*l - 70*l + 3*l**3 - 12*l**2 - 3*l**2.
3*l*(l - 3)*(l - 2)
Let h(o) be the first derivative of -6*o**5/25 + 17*o**4/10 - 4*o**3/3 - 368. Suppose h(b) = 0. Calculate b.
0, 2/3, 5
Let s be (5/10)/(3/18). Factor 0*z**s - 1/2*z**5 + 1/2*z + 0 - z**4 + z**2.
-z*(z - 1)*(z + 1)**3/2
Let i(r) be the third derivative of -r**6/40 + 3*r**5/10 + 34*r**2 + 1. Suppose i(k) = 0. What is k?
0, 6
Let d be 1 + ((-2)/5)/(126/180). Determine k, given that 18/7*k**2 - 12/7*k**3 + 3/7*k**4 - 12/7*k + d = 0.
1
Suppose 2*l = -20 + 28. Let s(b) be the third derivative of 0 - 1/48*b**l - 1/12*b**3 - 1/480*b**5 + 0*b + 11*b**2. Factor s(q).
-(q + 2)**2/8
Let l = -14/201 - -176/603. Factor l*x**2 + 0 + 0*x + 2/9*x**3.
2*x**2*(x + 1)/9
Let h(u) be the first derivative of -7*u**2 - 10*u**3 - 8/5*u**5 - 2*u - 13/2*u**4 + 11. Find v such that h(v) = 0.
-1, -1/4
Suppose -4*p - 10 = -18. Suppose 3*f - d + 2 = d, -d + p = -f. Factor -6 + 4*s - 2/3*s**f.
-2*(s - 3)**2/3
Let b(f) be the first derivative of -f**4 - 64*f**3/9 + 22*f**2 - 56*f/3 + 74. Suppose b(n) = 0. Calculate n.
-7, 2/3, 1
Let p(j) be the third derivative of 13/12*j**4 + 0*j + 13*j**2 + 4/21*j**7 + 1/42*j**8 + 0 + 37/60*j**6 + 16/15*j**5 + 2/3*j**3. Determine c so that p(c) = 0.
-2, -1, -1/2
Let z(d) = -3*d**5 + 22*d**4 - 16*d**3 - 27*d**2 + 7. Let p(j) = -j**5 + 7*j**4 - 5*j**3 - 9*j**2 + 2. Let q(x) = -14*p(x) + 4*z(x). Factor q(n).
2*n**2*(n - 3)**2*(n + 1)
Let w(i) = -i**2 + 1. Let d(q) = -q + 2*q**2 + 5*q**2 - 3*q**2 + 4*q**2 - 7. Let r(k) = -5*d(k) - 35*w(k). Factor r(z).
-5*z*(z - 1)
Let u(g) be the second derivative of 3*g**5/10 - 26*g**4/3 + 69*g**3 + 162*g**2 + 3*g + 45. Factor u(z).
2*(z - 9)**2*(3*z + 2)
Let u(x) be the third derivative of 6*x**2 + 1/12*x**3 + 0 + 1/120*x**5 + 0*x + 1/24*x**4. Let u(c) = 0. What is c?
-1
Let b(a) = -2*a**4 - 17*a**3 + 99*a**2 - 179*a + 112. Let u(w) = -w**4 + w**3 + w**2 - w. Let m(r) = 2*b(r) - 6*u(r). Suppose m(g) = 0. Calculate g.
2, 14
Let s(p) be the second derivative of p**6/15 - p**5/10 - p**4/3 + 170*p. Solve s(i) = 0.
-1, 0, 2
Let d = -2758 - -2760. Let i(t) be the third derivative of 7*t**d - 1/330*t**5 + 0*t + 0 - 1/22*t**4 - 3/11*t**3. Determine r so that i(r) = 0.
-3
Let u(q) be the third derivative of q**4/12 + 13*q**3/3 + 19*q**2. Let z be u(-13). Let -2/9*f**5 + 0*f**2 - 2/9*f + 0 + z*f**4 + 4/9*f**3 = 0. What is f?
-1, 0, 1
Suppose 2*x - 1 = 3. Suppose -r + x*g + 10 = 0, -g + 2 = 4*r - 2. Factor -9*k**3 + k - 2*k**2 - 2*k + 3 - r*k - 13*k**2.
-3*(k + 1)**2*(3*k - 1)
Factor 2/9*b**3 + 8/3*b + 0 + 14/9*b**2.
2*b*(b + 3)*(b + 4)/9
Let j(l) = -2*l**2 + 16*l + 20. Let n be j(9). Factor -2 - n + 6 + o**2 - 3.
(o - 1)*(o + 1)
Let g(k) be the first derivative of -k**6/6 - 2*k**5/15 + 5*k**4/9 - 8*k**3/27 + 68. Factor g(t).
-t**2*(t + 2)*(3*t - 2)**2/9
Let y(r) be the second derivative of -r**4/8 - r**3/4 + 4*r - 29. Factor y(j).
-3*j*(j + 1)/2
Let 216/5*h - 171/5*h**2 - 3/5*h**4 + 0 + 42/5*h**3 = 0. What is h?
0, 3, 8
Let t(y) be the second derivative of -2*y**7/189 - y**6/45 + 7*y**5/90 + 2*y**4/9 + 4*y**3/27 - 380*y. Determine f, given that t(f) = 0.
-2, -1, -1/2, 0, 2
Let o(x) be the first derivative of -2*x**5/25 + 3*x**4/5 - 26*x**3/15 + 12*x**2/5 - 8*x/5 + 212. Factor o(p).
-2*(p - 2)**2*(p - 1)**2/5
Solve 0 + 1/4*b**2 + 25/4*b = 0 for b.
-25, 0
Let r(z) be the second derivative of z**6/180 + z**5/6 + 25*z**4/12 - z**3/3 + 12*z. Let o(w) be the second derivative of r(w). Solve o(l) = 0 for l.
-5
Let t(g) = -21*g**2 + 21*g + 9. Let u = -11 + 13. Let x(f) = -7*f**2 + 5*f + 3 - 1 + 2*f**2. Let q(o) = u*t(o) - 9*x(o). Let q(r) = 0. What is r?
0, 1
Let v(i) be the second derivative of -3*i**7/70 + 14*i**6/25 - 27*i**5/10 + 27*i**4/5 - 27*i**3/10 - 102*i. Suppose v(x) = 0. What is x?
0, 1/3, 3
Let s(o) be the first derivative of -4*o**5/5 + 20*o**4 - 148*o**3/3 + 36*o**2 + 536. Find t, given that s(t) = 0.
0, 1, 18
Let l = 15 + -13. Suppose -c - 4 = -l*c. Factor c*b**3 + 2*b**2 + 3*b**2 - 2*b**2.
b**2*(4*b + 3)
Let v(b) be the third derivative of -1/156*b**4 + 15*b**2 - 1/195*b**6 + 0*b**3 + 0 + 0*b - 1/78*b**5. Factor v(a).
-2*a*(a + 1)*(4*a + 1)/13
Let f(h) = -11*h**2 - 108*h - 422. Let m(a) = -17*a**2 - 162*a - 632. Let i(r) = -8*f(r) + 5*m(r). Factor i(s).
3*(s + 6)*(s + 12)
Let h(b) be the second derivative of -1/8*b**4 - 1/72*b**6 + 1/9*b**3 - 3*b - 3/2*b**2 + 1/15*b**5 + 0. Let a(j) be the first derivative of h(j). Factor a(c).
-(c - 1)**2*(5*c - 2)/3
Let d(p) be the second derivative of -3*p**5/20 + 2*p**4 - 45*p. Determine z so that d(z) = 0.
0, 8
Let u(d) be the third derivative of d**6/120 - 11*d**5/30 - 47*d**4/24 - 4*d**3 + 29*d**2 + 2. Factor u(n).
(n - 24)*(n + 1)**2
Let w = -42 + 54. What is c in -285*c**2 + 281*c**2 + 13*c**3 + 3*c**3 - w*c**4 = 0?
0, 1/3, 1
Let s(p) be the first derivative of p**7/4620 + p**6/660 + p**5/330 + 4*p**3 + 4. Let m(j) be the third derivative of s(j). Factor m(t).
2*t*(t + 1)*(t + 2)/11
Let a = -240/283 + 3206/3113. Factor 0 + 6/11*z**3 - 10/11*z**2 + 2/11*z**4 - a*z**5 + 4/11*z.
-2*z*(z - 1)**3*(z + 2)/11
Let m(w) be the second derivative of -w**7/21 + 14*w**6/15 - 36*w**5/5 + 88*w**4/3 - 208*w**3/3 + 96*w**2 - 10*w + 6. Factor m(g).
-2*(g - 6)*(g - 2)**4
Let u(j) be the third derivative of j**6/900 - j**5/225 - j**4/36 + 2*j**3/15 + j**2 + 2*j. What is b in u(b) = 0?
-2, 1, 3
Let p = 1542/13 + -9239/78. Factor -1/6*l - 1/6*l**2 + p*l**3 + 1/6.
(l - 1)**2*(l + 1)/6
Let q(h) be the third derivative of h**7/945 - h**6/180 - h**5/45 + 2*h**4/27 + h**2 + 13. Solve q(y) = 0 for y.
-2, 0, 1, 4
Let g(q) be the first derivative of -2*q**5/45 - 5*q**4/18 - 10*q**3/27 + 5*q**2/9 + 4*q/3 - 222. What is a in g(a) = 0?
-3, -2, -1, 1
Let z be (-6)/((-360)/174) + (-5)/2. Factor 0 + z*v**3 - 2/5*v**2 + 2/5*v**4 - 2/5*v.
2*v*(v - 1)*(v + 1)**2/5
Factor 1/2*o**2 - 4 - o.
(o - 4)*(o + 2)/2
Suppose -21 + 39 = 6*j. Factor 1/2*t**2 + 0*t + 1/4*t**5 - 3/4*t**j + 0 + 0*t**4.
t**2*(t - 1)**2*(t + 2)/4
Let w(p) = p**2 + 9*p + 4. Let z(d) = -d**2 - 10*d - 3. Let r(l) = -3*w(l) - 2*z(l). Let j be r(-4). Factor 6*i + i + 2*i + 3*i**2 + j.
3*(i + 1)*(i + 2)
Let p(s) be the first derivative of -s**4/24 - 11*s**3/12 - 9*s**2/2 + 22*s - 13. Let c(d) be the first derivative of p(d). Suppose c(m) = 0. Calculate m.
-9, -2
Let h(s) be the third derivative of -s**7/245 + 31*s**6/420 - s**5/21 + s**2 - 4*s. Determine l so that h(l) = 0.
0, 1/3, 10
Determine t, given that 2/7*t**5 - 64/7 - 104/7*t**2 + 6/7*t**4 - 144/7*t - 20/7*t**3 = 0.
-2, -1, 4
Let g(u) be the first derivative of 2*u**5/15 + u**4/2 - 4*u**2/3 - 19. Factor g(l).
2*l*(l - 1)*(l + 2)**2/3
Let l = -23 - -24. Let o(r) = 1 + l + 3 - 6. Let m(t) = 2*t**3 + 6*t**2 + 6*t + 5. Let d(g) = -2*m(g) - 6*o(g). Factor d(q).
-4*(q + 1)**3
Let w(a) be the second derivative of -a**6/40 + 3*a**4/16 + a**3/4 - 561*a. Suppose w(t) = 0. Calculate t.
-1, 0, 2
Let c(o) be the third derivative of o**9/756 + o**8/210 + o**7/210 + 3*o**3/2 + 6*o**2. Let v(x) be the first derivative of c(x). Solve v(f) = 0.
-1, 0
Let w(q) be the first derivative of 2/27*q**6 - 4/45*q**5 + 4/27*q**3 + 0*q**2 + 1 + 0*q - 1/9*q**4. Determine v, given that w(v) = 0.
-1, 0, 1
Let o(p) be the first derivative of p**4/4 - 4*p**3 - 27*p**2/2 - 14*p - 465. Factor o(s).
(s - 14)*(s + 1)**2
Let y(t) be the first derivative of -4/15*t**3 + 4/25*t**5 - 1/15*t**6 + 0*t**4 + 0*t + 6 + 1/5*t**2. Suppose y(v) = 0. What is v?
-1, 0,