t o(y) be the second derivative of 23*y + 1/42*y**7 + y**2 + 1/5*y**5 + 0 - 2/15*y**6 - 5/6*y**3 + 1/6*y**4. Factor o(m).
(m - 2)*(m - 1)**3*(m + 1)
Suppose 10*f = 5*f + 20. Solve 3 - 15 + 2*d**2 + f*d**3 - 20*d - 6*d**2 = 0 for d.
-1, 3
Let z be (-118)/(-45) - ((-532)/(-378)*3 - 4). Factor -12/5*o + z + 3/5*o**2.
3*(o - 2)**2/5
Let w(y) be the second derivative of y**5/140 - y**4/42 - y**3/42 + y**2/7 + 74*y + 2. Determine h, given that w(h) = 0.
-1, 1, 2
Let q(w) be the second derivative of w**4/28 - 11*w**3/14 + 15*w**2/7 - 15*w - 2. Let q(r) = 0. What is r?
1, 10
Let m(r) be the third derivative of r**9/90720 - r**8/5040 + r**7/840 - r**6/270 + r**5/30 - 9*r**2. Let y(v) be the third derivative of m(v). Factor y(s).
2*(s - 4)*(s - 1)**2/3
Let d(h) be the first derivative of 0*h**2 + 0*h**4 + 2/21*h**6 - 11 + 0*h + 0*h**3 + 0*h**5. Factor d(y).
4*y**5/7
Let f be 6/(-6) + (4 - 2). Let r be (9 - 9)*(f + 0). Factor r*d**2 - 82*d - 3 + 82*d + 3*d**2.
3*(d - 1)*(d + 1)
Suppose -18 = -3*r - 6*r. Let b be 2/4 - (-7)/2. Factor m - m**r - m**b + 5*m - 6*m**3 - 2*m**2 + 4*m**4.
3*m*(m - 2)*(m - 1)*(m + 1)
Let w(g) be the first derivative of -g**4/6 + 34*g**3/9 + 37*g**2/3 + 38*g/3 - 166. Determine k so that w(k) = 0.
-1, 19
Let q(d) be the first derivative of 147/5*d + 189/10*d**2 + 3*d**3 - 41 + 3/20*d**4. Factor q(y).
3*(y + 1)*(y + 7)**2/5
Factor -1570*o - 4*o**3 + 80*o**2 + 1570*o.
-4*o**2*(o - 20)
Let q(j) be the second derivative of 0*j**4 + 1/18*j**3 - 1/60*j**5 + 12*j + 0 - 1/12*j**2 + 1/180*j**6. Find u, given that q(u) = 0.
-1, 1
Let n(f) = 28*f**3 + 4*f**2 - 72*f - 48. Let r(w) = -w**4 + 54*w**3 + 8*w**2 - 143*w - 96. Let l(k) = -7*n(k) + 4*r(k). Let l(c) = 0. Calculate c.
-1, 3, 4
Let j(t) be the second derivative of 1/2*t**3 - 3/20*t**5 + 1/10*t**6 - 1/4*t**4 - 6*t + 0 + 0*t**2. Factor j(k).
3*k*(k - 1)**2*(k + 1)
Factor -277*c**2 - 27*c**3 - 272*c**2 + 28*c**4 + 513*c**2 - 7*c**4 + 12*c.
3*c*(c - 2)*(c + 1)*(7*c - 2)
Let c = 11 + -9. Let o be -9*(-1)/6*c. Factor 26*w**o + 2*w**2 + 2*w - 4*w**2 - 10*w**2 + 8*w**5 - 24*w**4.
2*w*(w - 1)**2*(2*w - 1)**2
Let r be (2 - (4 + 1)) + 7. Let t(h) = -r*h**3 - h**4 + 173*h**2 + 5*h - 173*h**2. Let z(p) = p**4 + 2*p**3 - 3*p. Let f(n) = 3*t(n) + 5*z(n). Factor f(d).
2*d**3*(d - 1)
Suppose 12*m = -m - 4*m. Let o(h) be the first derivative of 0*h**3 - 1/18*h**4 + 5 + 0*h + m*h**2 - 2/45*h**5. Factor o(u).
-2*u**3*(u + 1)/9
Suppose 4*q + 0*r + 4*r = 8, 4*q + 27 = 3*r. Let a be (-6)/35*(0/q + -5). Solve 2/7*l**2 - 6/7*l**3 + a*l + 2/7*l**4 - 4/7 = 0.
-1, 1, 2
Let i = -11/21 - -83/105. Let d(a) be the first derivative of 1/5*a**2 - 1/10*a**4 + 2 - 4/5*a + i*a**3. Factor d(o).
-2*(o - 2)*(o - 1)*(o + 1)/5
Let y(q) be the third derivative of 0*q - 1/4*q**4 + 3*q**2 + 0 - 2/3*q**3 - 1/30*q**5. Factor y(i).
-2*(i + 1)*(i + 2)
Let m(u) = 2*u + 1. Let w(a) = 5*a**2 - 261*a + 262. Let i(j) = 2*m(j) - w(j). Factor i(x).
-5*(x - 52)*(x - 1)
Let d(z) be the second derivative of -z**4/2 + 47*z**3/9 - 10*z**2/3 + 2*z - 65. Find g, given that d(g) = 0.
2/9, 5
Let z(b) = -8*b**3 + 7*b**2 - 11*b + 12. Let i(k) be the third derivative of k**6/120 - k**3/6 - 29*k**2. Let a(h) = -35*i(h) - 5*z(h). Factor a(m).
5*(m - 5)*(m - 1)**2
Let j(s) be the first derivative of s**7/210 + s**6/45 + s**5/30 - 7*s**3 - 11. Let a(i) be the third derivative of j(i). Let a(u) = 0. Calculate u.
-1, 0
Let g = 83/24 - 25/8. Let k(f) be the first derivative of 1 + 1/6*f**4 - 1/15*f**5 + g*f - 1/3*f**2 + 0*f**3. Let k(q) = 0. What is q?
-1, 1
Let i(v) be the first derivative of v**4/6 - 2*v**3/3 + 8*v/3 - 128. Suppose i(w) = 0. Calculate w.
-1, 2
Let t be 5/(-10) + (-153)/(-6). Suppose -3*p - t + 82 = 3*j, 2*j - 2*p - 38 = 0. Factor x**4 - j*x + 5*x**4 + 28*x + 5 + 14*x**3 - 3 + 16*x**2 + x**5.
(x + 1)**4*(x + 2)
Let 1/4*s**2 + 4*s + 7 = 0. Calculate s.
-14, -2
Let y(s) be the second derivative of -s**4/4 - 16*s**3 - s + 14. Suppose y(o) = 0. Calculate o.
-32, 0
Let n(u) be the third derivative of -u**5/120 - 17*u**4/48 + u**2 - 19*u. Factor n(h).
-h*(h + 17)/2
Let i(s) be the first derivative of -4/5*s**5 + 20/3*s**3 - 16*s - 8*s**2 + 5*s**4 - 2/3*s**6 + 19. Solve i(f) = 0.
-2, -1, 1, 2
Let b(h) be the third derivative of -h**5/12 - 100*h**4/3 - 16000*h**3/3 - 193*h**2. Factor b(m).
-5*(m + 80)**2
Let g(t) = 7*t**4 - 8*t**3 + 46*t**2 - 72*t + 33. Let o(x) = 2*x**4 + x**3 + x**2 - x - 1. Let w(r) = 2*g(r) - 6*o(r). Solve w(p) = 0 for p.
1, 3, 4
Suppose 4/7*z**2 + 0*z + 2/7*z**4 - z**3 + 0 + 1/7*z**5 = 0. Calculate z.
-4, 0, 1
Let t = 2649 - 2649. Determine k so that 2/3*k**4 + t*k + 2*k**3 + 4/3*k**2 + 0 = 0.
-2, -1, 0
Factor -4*v - 1/3*v**3 - 8/3 - 2*v**2.
-(v + 2)**3/3
Let f(u) = -2*u**2 + 4*u - 7. Let v(w) = -10 + w - 10 + 11*w - 3*w**2 - 3*w**2. Let s(l) = -14*f(l) + 5*v(l). Factor s(t).
-2*(t - 1)**2
Let c(l) = -4*l - 4. Let v(n) = n**3 + n**2 + 11*n + 11. Let o(x) = x**3 - 9*x**2 + 2*x - 7. Let d be o(9). Let y(i) = d*c(i) + 4*v(i). Factor y(p).
4*p**2*(p + 1)
Let v(i) = -i**3 + 60*i**2 + 257*i - 56. Let d be v(64). Find b such that 19/4*b**3 + b**4 + 23/4*b + 3/2 + d*b**2 = 0.
-2, -1, -3/4
Let v(l) be the first derivative of -l**6/2 + 3*l**5 - 6*l**4 + 4*l**3 - 44. Find a, given that v(a) = 0.
0, 1, 2
Let d be ((66/(-16))/11)/((-72)/240). Solve -7/4*t + 1/4 + 11/4*t**2 - d*t**3 = 0 for t.
1/5, 1
Let o(u) be the first derivative of u**6/360 + u**5/120 - u**4/12 - 14*u**3/3 - 12. Let n(q) be the third derivative of o(q). Factor n(l).
(l - 1)*(l + 2)
Let v(c) be the third derivative of -c**7/270 + c**6/36 - c**5/36 - 5*c**4/27 + 2*c**3/9 + 104*c**2. Find w such that v(w) = 0.
-1, 2/7, 2, 3
Let v = 3 - -3. Let n(i) = i - v*i**3 + 5*i**3 + 2*i**3 - 2*i**3. Let p(c) = -4*c**3 + c**2 + 3*c. Let x(r) = -10*n(r) + 2*p(r). Solve x(j) = 0 for j.
-2, 0, 1
Let f(d) be the third derivative of d**8/112 - 4*d**7/35 + 3*d**6/20 + 2*d**5/5 - 7*d**4/8 - 26*d**2 + d. Factor f(q).
3*q*(q - 7)*(q - 1)**2*(q + 1)
Let h(x) be the first derivative of -4*x**3/3 - 42*x**2 + 126. Factor h(q).
-4*q*(q + 21)
Let w(j) be the third derivative of -81/16*j**4 - 9/40*j**5 + 31*j**2 - 243/4*j**3 + 0 + 0*j - 1/240*j**6. Find k, given that w(k) = 0.
-9
Let h(l) be the third derivative of 0 + 7/300*l**6 - 1/30*l**5 - 4/15*l**4 - 4/15*l**3 - 16*l**2 + 0*l. Suppose h(w) = 0. What is w?
-1, -2/7, 2
Determine q, given that 2/5*q**2 - 2/5*q - 2/5 + 2/5*q**3 = 0.
-1, 1
Let d(i) = -14*i**3 - 44*i**2 - 60*i - 20. Let r(h) = 15*h**3 + 44*h**2 + 61*h + 21. Let m(z) = 5*d(z) + 4*r(z). Factor m(n).
-2*(n + 2)**2*(5*n + 2)
Suppose 590*a - 572*a = 0. Factor 3*j - 3/2*j**2 + a.
-3*j*(j - 2)/2
Let t(b) be the second derivative of b**5/60 + 7*b**4/18 + 35*b**3/18 + 11*b**2/3 + b - 54. Factor t(x).
(x + 1)*(x + 2)*(x + 11)/3
Let o be (8/(-16))/(2/(-8)). Factor -5*v**2 + 6*v**2 - v**4 + v + 0*v**o - v**3 + 0*v.
-v*(v - 1)*(v + 1)**2
Suppose -11*a + 7*a = -12. Determine t, given that 2*t**2 - 1467*t**5 + 1471*t**5 - 4*t**a + 4*t**4 - 6*t**2 = 0.
-1, 0, 1
Let k(g) be the third derivative of g**8/30240 - g**7/1512 + g**6/270 - g**5/4 - 5*g**2. Let u(z) be the third derivative of k(z). Determine q so that u(q) = 0.
1, 4
Let g(o) be the first derivative of 0*o**3 + 0*o - 33 + 0*o**2 - 1/4*o**4. Solve g(d) = 0.
0
Let v(z) be the second derivative of 1/15*z**3 - 1/15*z**4 + 1/75*z**6 + 1/105*z**7 + 0 + 1/5*z**2 - 36*z - 1/25*z**5. Solve v(y) = 0 for y.
-1, 1
Solve -6*x - 12 - 2/3*x**2 = 0 for x.
-6, -3
Suppose -2*s + 3*s - 12 = -5*l, -3*s + 10 = 2*l. Let -3 + 24*f - 3*f**s - 2 - 16 = 0. Calculate f.
1, 7
Let w(o) be the first derivative of 5*o**3/3 - 60*o**2 + 104. Factor w(s).
5*s*(s - 24)
Let g(w) be the second derivative of w**4/30 + 8*w**3/15 - 4*w**2 - 86*w. Solve g(j) = 0 for j.
-10, 2
Let l be 6*((-4 - 28/(-6)) + (-77)/210). Factor -l*r**2 + 3/5 - 6/5*r.
-3*(r + 1)*(3*r - 1)/5
Factor 5*u**2 + 3*u**2 + 4*u - 30*u**3 + 28*u**3 - 8 - 2*u**3.
-4*(u - 2)*(u - 1)*(u + 1)
Let x(n) be the first derivative of n**5 + 15*n**4 + 75*n**3 + 125*n**2 - 42. Solve x(s) = 0.
-5, -2, 0
Suppose -13*d + 18*d = -45. Let y = -7 - d. Factor 5*p - y*p**2 - p**2 - 5*p - 6*p.
-3*p*(p + 2)
Let u(c) be the first derivative of -20*c**3/3 - 5*c**2/2 + 25*c - 394. Factor u(q).
-5*(q - 1)*(4*q + 5)
Let o = 216 + -161. Le