- 387. Let n(f) = 0. Calculate f.
-76, -1
Let g be (6 - 7)*(-218)/(-6). Let n = 37 + g. Factor -4/3 + 2*z - n*z**3 + 0*z**2.
-2*(z - 1)**2*(z + 2)/3
Let x = -12 - -14. Let z = -10 - -31/3. Factor 1 - z*i**x - 2/3*i.
-(i - 1)*(i + 3)/3
Suppose q - 3*v = -5*v - 3, 3*q + 2*v - 7 = 0. Let f(o) = -o**2 - 2*o + 2. Let r be f(0). Factor r*c - 6 - 22*c + 12*c**2 + 9*c**2 + q*c.
3*(c - 1)*(7*c + 2)
Let d = 17683/1080 + -442/27. Let m(i) be the third derivative of 0*i**3 + 0*i - 4*i**2 + d*i**5 + 0 + 1/72*i**4. Let m(w) = 0. What is w?
-2, 0
Factor 48/5 + 2/5*s**2 - 10*s.
2*(s - 24)*(s - 1)/5
Let m(g) be the first derivative of g**3/3 + 5*g**2/2 - g + 1. Let o(p) = -3*p. Let v(k) = 4*k + 53. Let x be v(-14). Let s(q) = x*m(q) - 5*o(q). Factor s(w).
-3*(w - 1)*(w + 1)
Let r(t) = 3*t**3 + 5*t**2 - 9*t + 11. Let l be 0 + (-3 + 51)/8. Let u(s) = 9*s - 3*s**3 + 0*s**2 - s**2 - 5*s**2 - 12. Let q(o) = l*r(o) + 5*u(o). Factor q(d).
3*(d - 1)**2*(d + 2)
Solve 66724352 - 1102*m**3 + 102*m**3 + 69312*m**2 + 2*m**4 + 229*m**3 - 3511808*m + 163*m**3 = 0.
76
Suppose 87*p + 16*p - 407 = -98. Determine k so that -16/5*k - 2/5 - 38/5*k**2 - 24/5*k**p = 0.
-1, -1/3, -1/4
Let s(y) be the second derivative of -y**5/10 - 8*y**4/21 - 11*y**3/21 - 2*y**2/7 - 3*y + 8. Factor s(m).
-2*(m + 1)**2*(7*m + 2)/7
Let n(i) be the third derivative of -i**6/120 - 3*i**5/40 - 4*i**3/3 + 25*i**2. Let y(s) be the first derivative of n(s). Suppose y(x) = 0. Calculate x.
-3, 0
Suppose 3*v = -6, -2*m + 5*v - 5 = -3*m. Let n be (-20)/(-15) - 4/(-6). Determine c, given that 12*c**2 - 9*c**3 + 2 + 12*c**3 + n + 2 + m*c = 0.
-2, -1
Let i be 16/(-96) - 125/6. Let l = i - -26. Solve -a**3 + 4*a + 5*a**3 - 3*a**3 - l*a = 0 for a.
-1, 0, 1
Let a(i) be the second derivative of 0 + 0*i**2 - 5/12*i**4 - 1/5*i**5 - 1/6*i**3 + 4*i. Find f such that a(f) = 0.
-1, -1/4, 0
Let g(w) be the second derivative of -w**5/90 - 7*w**4/54 - 8*w**3/27 + 16*w**2/9 + 2*w + 4. Factor g(h).
-2*(h - 1)*(h + 4)**2/9
Let i = -3 - -14. Let k = i - 9. Factor -4*h**2 - 5*h**2 + 1 + 8*h**k.
-(h - 1)*(h + 1)
Let a(j) be the second derivative of j**6/1620 - j**5/180 + j**4/54 + 3*j**3/2 - 9*j. Let p(v) be the second derivative of a(v). What is k in p(k) = 0?
1, 2
Suppose -24*k**2 + 54 - 39*k**3 + 107*k**3 - 33*k - 30*k**3 - 35*k**3 = 0. Calculate k.
-2, 1, 9
Let q(l) = 3*l**3 - 20*l**2 + 49*l - 28. Let n(o) = 3*o**3 - 18*o**2 + 48*o - 27. Let k(d) = 2*n(d) - 3*q(d). Factor k(g).
-3*(g - 5)*(g - 2)*(g - 1)
Let k = 23 + -21. Let v = 0 - -3. Factor 3*h**k - v - h**2 + 0*h**2 + 7 + 6*h.
2*(h + 1)*(h + 2)
Let n(a) = 36*a**3 + 67*a**2 - 8*a - 53. Let w(g) = -11*g**3 - 22*g**2 + 3*g + 18. Let j(s) = -2*n(s) - 7*w(s). Find x, given that j(x) = 0.
-4, -1, 1
Let v(h) be the third derivative of -h**5/180 - h**4/8 - h**3 - 136*h**2. Find a, given that v(a) = 0.
-6, -3
Let p(u) = 5*u**3 + 3*u**2. Let n(d) = 4*d**3 + 2*d**2. Let q(h) = 4*n(h) - 3*p(h). Let i(l) = 4*l**3 - 6*l**2. Let j(m) = 2*i(m) - 4*q(m). Factor j(a).
4*a**2*(a - 2)
Let f = 17 + -9. Find n such that 57*n - 90 + f*n**3 + 48*n - 6*n**3 + 3*n**3 - 40*n**2 = 0.
2, 3
Let s(y) = -6*y**2 - 4. Let g(h) = 5*h**2 + 3. Let v(k) = 4*g(k) + 3*s(k). Let c be v(-4). Determine o so that -6*o**3 - c*o + 6 + 18*o**2 + 2 + 8*o**2 = 0.
1/3, 2
Let p(z) = -3*z + 32. Let d be p(10). Let h be ((-4)/7)/(d - (-32)/(-14)). Factor 8/5*l + 2/5*l**h + 8/5.
2*(l + 2)**2/5
Suppose -2*r = 3*a - 6, 3*r + 8 = 2*a + 2*a. Let t = 4 + r. Factor -8*l**3 - t*l**4 + 2*l - 3*l**2 - 1 + 1 + l**4.
-l*(l + 1)*(l + 2)*(3*l - 1)
Let y be (49 - 52) + (15 - -3)/3. Let b(v) be the first derivative of 6*v + 15/2*v**2 - 5 + 3/4*v**4 + 4*v**y. Let b(d) = 0. Calculate d.
-2, -1
Let k(w) be the third derivative of w**5/210 + 5*w**4/84 - 2*w**3/3 - 2*w**2 + 7. Factor k(n).
2*(n - 2)*(n + 7)/7
Let y(h) be the second derivative of -50*h**7/63 - 82*h**6/9 - 199*h**5/15 + 889*h**4/9 - 1120*h**3/9 + 200*h**2/3 - 120*h. Suppose y(x) = 0. Calculate x.
-5, 2/5, 1
Factor -14580 - 5*i**2 - 42*i - 293*i - 205*i.
-5*(i + 54)**2
Let d(v) be the third derivative of -1/60*v**5 - 2*v**2 - 1/3*v**3 + 1/8*v**4 + 0 + 0*v. Factor d(u).
-(u - 2)*(u - 1)
Let x(v) = -5*v**2 - 316*v - 4793. Let s(y) = -5*y**2 - 315*y - 4795. Let k(q) = 6*s(q) - 5*x(q). Determine g so that k(g) = 0.
-31
Let h(m) be the third derivative of 96*m**5 - 10*m**4 + 5*m**3/12 + m**2 - 12. Factor h(v).
5*(48*v - 1)**2/2
Let h(r) be the first derivative of r**4/8 + 2*r**3/3 - 7*r**2 + 16*r + 184. Factor h(z).
(z - 2)**2*(z + 8)/2
Let o(g) be the first derivative of -5 - 2*g**2 + 1/3*g**3 + 0*g. Let a(j) = 4*j**2 - 13*j. Let b(l) = 4*a(l) - 14*o(l). Suppose b(d) = 0. Calculate d.
-2, 0
Let s(x) be the first derivative of -3*x**5/5 - 3*x**4 + 6*x**3 + 6*x**2 - 15*x - 296. Find u such that s(u) = 0.
-5, -1, 1
Suppose 5837*c - 5832*c = 10. Factor 3/2*u**4 + 0*u**c + 3*u - 3*u**3 - 3/2.
3*(u - 1)**3*(u + 1)/2
Let i(x) = x**5 - x**4 - 1. Let u(l) = -5 + 6 - 4*l**2 - l - l**4 + 6*l**2. Let g(k) = 3*i(k) + 3*u(k). Factor g(a).
3*a*(a - 1)**3*(a + 1)
Let h(p) be the second derivative of 2/3*p**3 - 3*p - 1/6*p**4 - 2/5*p**5 + 0*p**2 + 1/5*p**6 + 0. Determine s so that h(s) = 0.
-2/3, 0, 1
Let r(s) be the first derivative of -s**8/420 - s**7/42 - s**6/30 + s**5/6 + 2*s**4/3 + 5*s**3 - 4. Let k(l) be the third derivative of r(l). Factor k(g).
-4*(g - 1)*(g + 1)**2*(g + 4)
Let a(y) be the third derivative of -25*y**8/252 - 8*y**7/63 + 221*y**6/90 + 4*y**5 + 2*y**4 + 2*y**2 - 41. Let a(i) = 0. Calculate i.
-3, -2/5, 0, 3
Find n such that 0*n**3 - 1/8*n**4 + 1/4*n + 0 + 3/8*n**2 = 0.
-1, 0, 2
Let o = 604 + -3017/5. Let n(y) be the second derivative of o*y**2 + 1/20*y**4 + 6*y - 3/10*y**3 + 0. Let n(b) = 0. What is b?
1, 2
Let m(w) = -8*w**3 + 5*w. Let l be (1/1)/(21/(-63)). Let f(z) = 55*z**3 - 35*z. Let b(j) = l*f(j) - 20*m(j). Determine c, given that b(c) = 0.
-1, 0, 1
Let d(s) be the second derivative of 16*s**2 + 8/3*s**3 + 0 + 2/15*s**6 - 1/5*s**5 - 10*s - 2*s**4. Solve d(o) = 0 for o.
-2, -1, 2
Find o, given that 2/3*o**3 - 2/15*o**2 + 2/15*o**4 - 2/15*o**5 - 8/15 - 16/15*o = 0.
-1, 2
Solve 0 + 13*p**3 - 1/2*p**4 - 96*p**2 + 144*p = 0 for p.
0, 2, 12
Let h(u) be the second derivative of -5*u**4/12 + 90*u**3 - 7290*u**2 - 3*u + 18. Factor h(y).
-5*(y - 54)**2
Let u(g) be the third derivative of 1/280*g**6 + 0*g - 1/2352*g**8 + 0 - 1/84*g**5 + 0*g**3 + 1/1470*g**7 + 1/84*g**4 - 13*g**2. Find m, given that u(m) = 0.
-2, 0, 1
Let n(w) be the third derivative of -w**6/120 + 9*w**4/8 + 9*w**3 - 5*w**2 + 9. Factor n(q).
-(q - 6)*(q + 3)**2
Let t(p) be the third derivative of p**7/42 + 29*p**6/24 + 56*p**5/3 + 245*p**4/6 - 34*p**2 + 2. Factor t(m).
5*m*(m + 1)*(m + 14)**2
Let a(o) = -3*o**2 - 15. Let c(q) = -q + 3 - 1 - 1 + 0. Let b(h) = a(h) + 9*c(h). Determine d so that b(d) = 0.
-2, -1
Determine u so that 32*u + 216 - 138*u**2 - u - 3*u**4 + 5*u + 39*u**3 = 0.
-1, 2, 6
Suppose -11*q**2 - 52 + 50*q - 1/2*q**3 = 0. What is q?
-26, 2
Let b(h) = -h**2 - 78*h + 1851. Let l(g) = 3*g**2 + 152*g - 3703. Let f(c) = -5*b(c) - 2*l(c). Determine a, given that f(a) = 0.
43
Let f(z) be the second derivative of 5*z**4/4 + z**3 + 123*z. Factor f(u).
3*u*(5*u + 2)
Let d(l) = -2*l + 8. Let b be d(3). Let r(v) be the second derivative of 0*v**b + 0 - 2/25*v**5 + 1/6*v**4 - 2/15*v**3 + 3*v + 1/75*v**6. Factor r(q).
2*q*(q - 2)*(q - 1)**2/5
Let u be (19/(-152))/(12/(-32)). Suppose 1/3*y**5 - 4/3*y**2 + 2*y**3 + u*y - 4/3*y**4 + 0 = 0. Calculate y.
0, 1
Suppose j + 2*u = -17 + 6, -5*u = -2*j - 4. Let g be (720/200)/(0 + j/(-5)). Factor -27/7 - 3/7*o**2 - g*o.
-3*(o + 3)**2/7
Let q = -17499 + 17502. Factor -8/7 - 6/7*n**q + 8/7*n + 10/7*n**2.
-2*(n - 2)*(n + 1)*(3*n - 2)/7
Let u = -10 - -10. Suppose 5*y = -5*a + 25, u = -a + 3. Solve 2 + 4*l**y - 3*l**2 + 2*l**3 - 2*l - 3*l**2 = 0.
-1, 1
Let u = -83 + 14. Let y = 346/5 + u. Factor -y*m**2 - 2/5*m - 1/5.
-(m + 1)**2/5
Suppose 0*o = 2*o + 12. Let k be (-24)/(-8)*(-8)/o. What is d in -7*d + 2*d**3 - 8*d + 13*d - k - 4*d = 0?
-1, 2
Let m(d) = -4*d - 17. Let c be m(-5). Let i(a) = 35*a**2 - 25*a - 13. Let o(l) = 105*l**2 - 75*l - 40. Let n(p) = c*o(p) - 10*i(p). Solve n(x) = 0 for x.
-2/7, 1
Let q(d) be the first derivative of -d - 8 + 7/10*d**6 - 6*d**2 - 12/5*d**5 