. Factor k + n + 1/5*k**3 + 4/5*k**2.
(k + 1)**2*(k + 2)/5
Let o(w) be the second derivative of 2/21*w**7 - 2*w**3 - 2/5*w**6 + 2*w**2 + 2/3*w**4 + 2/5*w**5 + 0 - 15*w. Factor o(d).
4*(d - 1)**4*(d + 1)
Let m(x) be the second derivative of -x**4/42 - 13*x**3/21 - 22*x**2/7 + 105*x. Factor m(c).
-2*(c + 2)*(c + 11)/7
Let v(s) be the third derivative of s**7/5040 - s**6/480 - 5*s**4/24 + 5*s**2. Let a(t) be the second derivative of v(t). Find h, given that a(h) = 0.
0, 3
Let l(t) be the second derivative of t**5/330 + t**4/33 + t**3/11 - 9*t**2 + 4*t. Let f(g) be the first derivative of l(g). Let f(z) = 0. What is z?
-3, -1
Suppose 0 + 45/2*c - 45/2*c**3 + 3/2*c**4 - 3/2*c**2 = 0. What is c?
-1, 0, 1, 15
Let c(j) be the third derivative of 0*j**4 + 0 + 0*j - 3/50*j**5 - 1/75*j**6 + 9/10*j**3 + 12*j**2 - 1/1050*j**7. Solve c(d) = 0 for d.
-3, 1
Let z(p) be the third derivative of -p**5/180 + 49*p**4/24 + 74*p**3/9 - 267*p**2 + 1. Solve z(w) = 0 for w.
-1, 148
Let z(t) be the second derivative of -t**6/10 + 9*t**5/4 + 71*t**4/4 + 93*t**3/2 + 57*t**2 - 102*t. Suppose z(w) = 0. Calculate w.
-2, -1, 19
Let i = 793/3 - 264. Let w(m) be the first derivative of 1/2*m**2 - 2 + 0*m + i*m**3. Factor w(c).
c*(c + 1)
Let v(q) be the third derivative of q**8/1344 + q**7/420 - q**6/32 + q**5/60 + 5*q**4/24 - 111*q**2. Factor v(o).
o*(o - 2)**2*(o + 1)*(o + 5)/4
Factor -1/4*c**5 + 0 + 0*c**2 + 9/4*c**3 + 0*c + 0*c**4.
-c**3*(c - 3)*(c + 3)/4
Let o(l) be the first derivative of -13/3*l**3 + 20 + 15/2*l**2 - 2*l. Factor o(t).
-(t - 1)*(13*t - 2)
Let r(b) be the first derivative of b**6/1980 + 2*b**5/165 + 4*b**4/33 - 7*b**3/3 + 15. Let z(m) be the third derivative of r(m). What is x in z(x) = 0?
-4
Suppose 4*t = a + 20, 2*t - 24 + 8 = 2*a. Let s be 1/(-5) + 3/12*t. Factor 2/5*i**2 + 2/5 + s*i.
2*(i + 1)**2/5
Let a = 729/70 - 7/10. Let i = a + -87/14. Solve -3/2*l**3 - 2*l + 8*l**2 - 8*l**4 + i*l**5 + 0 = 0.
-1, 0, 2/7, 1, 2
Factor 3 + u**3 + 11 + 4 - u - 18*u**2.
(u - 18)*(u - 1)*(u + 1)
Let x be 1326/48 + 6/16. Let f be 3 + x/12 - (3 - -2). Factor f + 1/6*u**2 + 1/2*u.
(u + 1)*(u + 2)/6
Factor 2/15*k**3 - 2/3 - 2/15*k + 2/3*k**2.
2*(k - 1)*(k + 1)*(k + 5)/15
Suppose 135*w - 540 = -45*w. Factor 0 - 10/3*u**2 + 2/3*u**w + 4*u.
2*u*(u - 3)*(u - 2)/3
Let f(p) = 2*p**3 + 122*p**2 + 120*p + 3. Let y be f(-60). Solve 6/5*k**2 - 8/5*k - 1/5*k**4 + 3/5 + 0*k**y = 0.
-3, 1
Let i = 162 - 164. Let m be 1/9 - (i - (-114)/54). Factor m*v - 1/5*v**4 - 1/5*v**3 + 0*v**2 + 0.
-v**3*(v + 1)/5
Suppose 4*z - 3*g - 27 = 0, 25 = 5*z - g - g. Factor z*m**5 - 4*m**4 + 10*m**4 - 5*m**4.
m**4*(3*m + 1)
Let a(c) = -c**4 - 1 + c**2 - 2*c + c + 0*c. Let f(z) = -7*z**4 - z**3 + 8*z**2 - 6*z - 6. Let i = 642 - 641. Let y(j) = i*f(j) - 6*a(j). Solve y(h) = 0.
-2, 0, 1
Let n(g) = 12*g**3 - g**2 - g + 1. Let b be n(1). Suppose -c + b = 2*z, -c + 12 = 5*z - 11. Factor -1/4*f**5 + 0*f + 1/4*f**4 - 1/4*f**2 + 0 + 1/4*f**c.
-f**2*(f - 1)**2*(f + 1)/4
Let k(v) be the third derivative of 0*v + 0 + 4/27*v**3 + 1/36*v**4 - 11/270*v**5 - 36*v**2 + 1/135*v**7 - 1/180*v**6. Let k(f) = 0. Calculate f.
-1, -4/7, 1
Let m(u) be the first derivative of -u**4/2 - 8*u**3/3 + 25*u**2 + 56*u + 356. Factor m(o).
-2*(o - 4)*(o + 1)*(o + 7)
Let h(f) be the first derivative of f**5/150 - f**4/150 + 5*f**2/2 - 1. Let n(d) be the second derivative of h(d). Solve n(w) = 0 for w.
0, 2/5
Let l be (-5 - -4)/3 + (-80)/(-15). Let q(v) be the third derivative of -2*v**2 - 1/540*v**6 + 1/27*v**3 + 1/108*v**4 + 0*v - 1/270*v**l + 0. Factor q(p).
-2*(p - 1)*(p + 1)**2/9
Let m(s) be the first derivative of -s**6/60 + s**5/50 + s**4/8 - s**3/30 - 2*s**2/5 - 2*s/5 + 48. Factor m(r).
-(r - 2)**2*(r + 1)**3/10
Suppose -3*i - 6 = -3*r, i + 12*r - 14*r + 6 = 0. Let p(g) be the first derivative of 0*g - 9/4*g**4 - 2*g**3 + i + 0*g**2. Determine n, given that p(n) = 0.
-2/3, 0
Let y(q) be the third derivative of 0*q - 1/270*q**5 + 0 - 54*q**2 + 0*q**3 + 1/108*q**4. Find i, given that y(i) = 0.
0, 1
Let y(w) be the second derivative of 0 - 11/3*w**4 + 8*w**2 - 35*w + 7/15*w**5 + 64/9*w**3. Factor y(b).
4*(b - 3)*(b - 2)*(7*b + 2)/3
Let k(t) be the third derivative of t**10/151200 - t**9/60480 - 7*t**5/60 + 7*t**2. Let r(h) be the third derivative of k(h). Factor r(q).
q**3*(q - 1)
Let q = 27 - 15. Suppose -2*s = -5*s + 5*f + 19, -2*s + 3*f + q = 0. Factor -165/2*g**2 - 121/2*g**s - 24*g - 2.
-(g + 1)*(11*g + 2)**2/2
Let i be (25/(-9) - -3)*(-558)/(-992). Factor -27/8*x**2 - 243/8*x - i*x**3 - 729/8.
-(x + 9)**3/8
Let r(o) be the second derivative of 0 - 1/32*o**4 + 12*o - 1/2*o**3 - 3*o**2. Determine m, given that r(m) = 0.
-4
Let i = 71 + -51. Suppose -5*h - 10 = -i. Let 38*f + 8 - 21*f + 4*f**h - 29*f = 0. What is f?
1, 2
Factor -14*l - 8/3*l**2 + 0 + 2/3*l**3.
2*l*(l - 7)*(l + 3)/3
Let a = 25 - 21. Factor -6*l - 3*l**a + 3*l + 4*l**5 + 11*l**4 - l - 8*l**2.
4*l*(l - 1)*(l + 1)**3
Let k(n) = n - 7. Let f(w) = 2*w - 8. Let m(i) = 5*f(i) - 6*k(i). Let h(q) = -q**2 - 13*q - 5. Let s(g) = 2*h(g) + 7*m(g). Factor s(b).
-2*(b - 2)*(b + 1)
Let b be 2 + -5 - -3 - 0/1. Let v(f) be the third derivative of 2/9*f**3 + b*f - 7/36*f**4 + 1/10*f**5 + 0 - 1/36*f**6 + 4*f**2 + 1/315*f**7. Factor v(c).
2*(c - 2)*(c - 1)**3/3
Let i = -316 + 320. Let r(a) be the first derivative of 4/3*a**3 - i + 0*a**2 + 0*a. Factor r(f).
4*f**2
Let a(y) = -4*y - 23. Let z be a(-7). Let r(o) be the second derivative of -8*o + 0 + 1/120*o**z - 5/72*o**4 - 1/3*o**2 + 2/9*o**3. Factor r(x).
(x - 2)**2*(x - 1)/6
Let l be 43/(-129) + (-19)/3 - -7. Let y(v) = -v**2 - 4*v + 3. Let p be y(-4). Factor 1/3*h - 1/3 - l*h**p + 1/3*h**2.
-(h - 1)**2*(h + 1)/3
Let s(u) = u**5 + 2*u**3 - 2*u**2 + u. Let v(g) = -10*g**5 + 70*g**4 + 236*g**3 + 404*g**2 + 238*g + 62. Let k(m) = 12*s(m) + v(m). Factor k(c).
2*(c + 1)**4*(c + 31)
Let d = 10 - 6. Suppose -v = 5*r - 68, r - d*r = -v + 76. Factor -70*k**2 - 1 + v*k**2 + 1 - 9*k.
3*k*(k - 3)
Let a(h) be the first derivative of h**4/28 - 3*h**2/14 + 2*h/7 - 95. Solve a(g) = 0.
-2, 1
Let a(k) = k**3 + k**2 + k - 1. Let t(b) = 12*b**3 - 10 - 115*b**2 + b**3 + 95*b - 3*b**3 + 0*b**3. Let u(i) = -10*a(i) - t(i). Suppose u(j) = 0. Calculate j.
1/4, 1, 4
Suppose 4*n = 9*n + 5*l - 15, -4*n + 7 = -l. Let z(i) be the second derivative of 1/78*i**4 - n*i - 1/13*i**2 + 0 + 0*i**3. Suppose z(r) = 0. Calculate r.
-1, 1
Let d = -11 + 12. Let n(p) = 13*p - 10. Let s be n(d). Factor 1/3 + s*x**2 + 2*x.
(3*x + 1)**2/3
Let j = -125 + 127. Let q(d) be the third derivative of 0*d**3 + 0*d - 3*d**j + 0*d**4 + 0 + 1/90*d**5. Solve q(k) = 0 for k.
0
Let p(r) be the third derivative of -r**7/70 + r**6/10 + r**5/4 + 37*r**2. Suppose p(n) = 0. Calculate n.
-1, 0, 5
Let j(t) be the third derivative of t**6/360 + 11*t**5/180 - t**4/18 - 22*t**3/9 - 3*t**2 - 84*t. Let j(w) = 0. What is w?
-11, -2, 2
Let g be (-15998)/4000 + 6 + -2. Let b = g - -15987/26000. Let -b + 32/13*j - 14/13*j**2 = 0. Calculate j.
2/7, 2
Let b(o) be the first derivative of -o**5/10 - 7*o**4/2 - 49*o**3 - 343*o**2 - 2401*o/2 + 89. Factor b(m).
-(m + 7)**4/2
Suppose -4*n + 37 = 8*g - 11*g, -5*n + 55 = -5*g. Find x such that n - 20/3*x - 8/3*x**2 = 0.
-3, 1/2
Suppose -58 + 10 = -4*m. Let c = -23/2 + m. Solve 1/4*g**4 + 0 - 3/4*g**3 - 1/4*g**2 + 1/4*g**5 + c*g = 0 for g.
-2, -1, 0, 1
Suppose 5*i - 25 = 0, -5*k + 5 = 53*i - 55*i. Factor 12/5*g + 8/5 + 6/5*g**2 + 1/5*g**k.
(g + 2)**3/5
Let f = -14 - -19. Suppose 5*u = -19 + 4, -f*l + 19 = -3*u. Factor 5*y - 4*y + 0*y**2 + 3*y**l - 8*y**2.
-y*(5*y - 1)
Let s(y) = 76*y**2 + 352*y. Let u(w) = -7*w**2 - 32*w. Let a(g) = 3*s(g) + 32*u(g). Let a(l) = 0. Calculate l.
-8, 0
Let y(o) = 6*o**3 + 5*o**2 + 5*o + 6. Suppose 4*d - 2*t + 64 = -7*t, 15 = -d - t. Let j(n) = -n**3 - n**2 - n - 1. Let m(g) = d*j(g) - 2*y(g). Factor m(b).
-(b - 1)**2*(b + 1)
Let c(x) = 6*x**2 + 6*x. Let r(n) = -n**2 - n. Suppose -m = -2, 5*b + 163 = m - 2*m. Let q(h) = b*r(h) - 6*c(h). Factor q(f).
-3*f*(f + 1)
Let q(a) be the third derivative of 0*a + 0 + 1/20*a**6 + 37*a**2 - 5/2*a**4 + 50/3*a**3 + 1/210*a**7 - 11/60*a**5. What is v in q(v) = 0?
-5, 2
Let c(q) be the second derivative of -q**5/5 + 3*q**4 - 16*q**3 + 32*q**2 + 24*q. Suppose c(h) = 0. Calculate h.
1, 4
Let r(m) be the first