n).
-2*n*(n - 1)/15
Let w(k) be the first derivative of -2/33*k**3 - 162/11*k - 28 - 18/11*k**2. What is q in w(q) = 0?
-9
Suppose 5 = -3*c - 19. Let y(w) = -7*w**2 - 23*w + 24. Let z(d) = 20*d**2 + 68*d - 72. Let b(f) = c*y(f) - 3*z(f). Find r, given that b(r) = 0.
-6, 1
Let u(w) be the second derivative of w**7/63 - 4*w**6/15 + 22*w**5/15 - 35*w**4/9 + 17*w**3/3 - 14*w**2/3 + 20*w. Suppose u(q) = 0. Calculate q.
1, 2, 7
Let l = -17 - -31. Let f = l + -12. Factor 19*q - 8*q - q**f + 1 - 11*q.
-(q - 1)*(q + 1)
Let c = 16060 + -48179/3. Let 0*z**2 - c*z**4 + 0*z + 0 + 2/3*z**3 = 0. What is z?
0, 2
Let p be (4 - -2) + ((-48)/3)/4. Factor 3*k**2 - 3*k**2 - 1 + k**p.
(k - 1)*(k + 1)
Let n = -1849 - -1849. Let j(a) be the third derivative of 0*a**3 - a**2 - 1/60*a**4 + 0 + 1/300*a**5 + n*a. Factor j(o).
o*(o - 2)/5
Let i(o) be the third derivative of -o**6/40 - 11*o**5/20 + 3*o**4/2 - 375*o**2. Solve i(x) = 0.
-12, 0, 1
Let t(z) = -7*z**2 + 27*z**3 - 7*z**4 - 18*z**4 + 5*z**4. Let w(s) = -40*s**4 + 55*s**3 - 15*s**2. Let a(h) = 5*t(h) - 2*w(h). Find x, given that a(x) = 0.
0, 1/4, 1
Let r be (-356)/28 + 220/22 - (-5)/1. Factor 8/7 + 0*v**4 - 8/7*v**2 + 12/7*v + 4/7*v**5 - r*v**3.
4*(v - 2)*(v - 1)*(v + 1)**3/7
Determine g, given that 108/7 + 39/7*g + 3/7*g**2 = 0.
-9, -4
Let w = 21 - 62/3. Let v be (4 + -4)/((-4)/(-120)*-6*10). Factor -1/3*p**2 + 2/3*p + v - w*p**3.
-p*(p - 1)*(p + 2)/3
Let a = -2727/8 - -341. Let r(h) be the third derivative of 0*h + h**2 - 3/70*h**7 + 0 + 0*h**3 - a*h**4 + 3/20*h**5 + 1/40*h**6. Factor r(u).
-3*u*(u - 1)*(u + 1)*(3*u - 1)
Let q(h) = 30*h**2 + 300*h + 455. Let r(x) = 7*x**2 + 74*x + 114. Let t(a) = -6*q(a) + 25*r(a). What is d in t(d) = 0?
-2, 12
Let h(x) be the first derivative of -5/2*x**2 - x**3 + 1/5*x**5 + 13 - 2*x + 1/4*x**4. Factor h(p).
(p - 2)*(p + 1)**3
Let l = -52 - -59. Factor 7*s - l - 26*s**2 - s + 3 + 24*s.
-2*(s - 1)*(13*s - 2)
Factor 0 - 2/5*v**3 - 722/5*v - 76/5*v**2.
-2*v*(v + 19)**2/5
Let x(f) be the third derivative of f**5/100 - 3*f**4/40 + f**3/5 + 255*f**2. Solve x(d) = 0 for d.
1, 2
Let v = 21 - 20. Suppose o = 2 + v. Find p such that 3*p**4 + 16*p**o + 61*p**4 + 26*p**5 + 2*p**5 = 0.
-2, -2/7, 0
Suppose 3*m + 0*i - 9 = i, 2*i = -4*m + 12. Factor -4/5*b**2 + 4/5*b + 1/5*b**m + 0.
b*(b - 2)**2/5
Suppose -4*s = 5*m + 29 - 7, 4 = 2*s - 5*m. Let k(y) = 17*y**2 + 4*y. Let q(z) = 52*z**2 + 12*z. Let w(d) = s*q(d) + 10*k(d). Factor w(p).
2*p*(7*p + 2)
Let w be 3/((2 - 0)*2/4). Let h(c) be the first derivative of 0*c**w + 1/39*c**6 + 0*c + 4/65*c**5 + 4 + 0*c**2 + 1/26*c**4. Factor h(q).
2*q**3*(q + 1)**2/13
Let i(b) be the first derivative of 2*b**5/5 + 2*b**4 - 17. Factor i(w).
2*w**3*(w + 4)
Suppose -20*a + 79 = 19. Suppose 0 = -a*h + 5*u, -5*h = 2*u + 3*u. Factor -2/3*k**2 + 2/3*k**3 + h*k + 0.
2*k**2*(k - 1)/3
Determine u so that -3/7*u**2 + 0*u - 3/7*u**3 + 0 = 0.
-1, 0
Let m(s) = 20*s**3 + 24*s**2 + 20*s - 16. Suppose -3*p + 6*p = 48. Let l(x) = -4*x**3 - 5*x**2 - 4*x + 3. Let f(n) = p*l(n) + 3*m(n). Solve f(c) = 0.
-1, 0
Let p(y) = -3*y**5 + 7*y**4 + 9*y**3 - 15*y**2 + 6*y. Let f(w) = -6*w**5 + 15*w**4 + 18*w**3 - 30*w**2 + 12*w. Let c(g) = -4*f(g) + 9*p(g). Factor c(r).
-3*r*(r - 1)**3*(r + 2)
Let t(y) be the second derivative of y**4/54 - 4*y**3/9 + 4*y**2 - 9*y + 2. What is q in t(q) = 0?
6
Let n(f) = -7*f - 14. Let q be n(-3). Determine o so that 2*o**2 - 4*o**2 + 9*o**4 - q*o**2 - 20*o + 17*o - 12*o**5 + 15*o**3 = 0.
-1, -1/4, 0, 1
Let s(m) be the first derivative of -4*m**3/3 - 132*m**2 + 544*m + 301. Factor s(l).
-4*(l - 2)*(l + 68)
Let u(d) be the second derivative of -3*d**5/70 + 7*d**4/6 - 208*d**3/21 + 64*d**2/7 - 196*d. Let u(n) = 0. Calculate n.
1/3, 8
Suppose 17 = 2*x - 11. Suppose r**3 + 41*r + 70*r**2 + 44*r + 30 + x*r**3 = 0. What is r?
-3, -1, -2/3
Let r(y) be the third derivative of 13/8*y**4 + 7/40*y**6 + 1/70*y**7 + 0 + 2*y**3 + 3/4*y**5 - 8*y**2 + 0*y. Factor r(w).
3*(w + 1)**3*(w + 4)
Let u(k) be the first derivative of 12*k**5/5 + 8*k**4 - 4*k**3 - 7. Factor u(h).
4*h**2*(h + 3)*(3*h - 1)
Let d(x) be the second derivative of -x**8/4200 - x**7/1050 + x**6/300 - x**3/6 + 14*x. Let p(r) be the second derivative of d(r). Let p(h) = 0. Calculate h.
-3, 0, 1
Let v(a) be the first derivative of 0*a - 4/3*a**3 - a**2 - 31 + 21/4*a**4 + 175/48*a**6 + 11*a**5. What is m in v(m) = 0?
-2, -2/5, 0, 2/7
Let j = 309 + -307. Suppose -2/3*p**j + 0 + 0*p = 0. Calculate p.
0
Let h(l) be the second derivative of -l**6/120 - l**5/15 - l**4/6 - 4*l**3/3 - 18*l. Let x(i) be the second derivative of h(i). Factor x(w).
-(w + 2)*(3*w + 2)
Solve -10/7 + 12/7*s + 22/7*s**2 = 0 for s.
-1, 5/11
Let u(f) be the second derivative of -4*f + 1/165*f**6 - 2 + 0*f**3 - 1/231*f**7 + 0*f**2 + 1/110*f**5 - 1/66*f**4. Factor u(w).
-2*w**2*(w - 1)**2*(w + 1)/11
Let w(h) = -3*h**2 + 50*h - 22. Let c be w(16). Solve c + 18 - 525*t + 549*t - 4*t**2 = 0.
-1, 7
Let n = 60309/74 - 815. Let c = n - -751/814. Determine p, given that -c*p**2 + 0 + 4/11*p = 0.
0, 2/5
Let x(b) = -b**4 - b**3 + b + 1. Let t(c) = -4*c**4 - 29*c**3 - 65*c**2 - 61*c - 21. Suppose 11*p - 7*p = -4. Let n(f) = p*x(f) - t(f). Solve n(j) = 0.
-2, -1
Solve 16/3*q**2 + 14/3*q - 92/9 + 2/9*q**3 = 0.
-23, -2, 1
Let d(p) be the second derivative of -14*p + 0 + 3/4*p**4 + 24*p**2 + 6*p**3 + 3/80*p**5. Factor d(r).
3*(r + 4)**3/4
Let y(u) be the third derivative of -1/28*u**7 + 5/24*u**6 + 5/24*u**4 + 0*u + 0*u**3 - 15*u**2 - 3/8*u**5 + 0. Let y(f) = 0. What is f?
0, 1/3, 1, 2
Let l(q) = -5*q**2 + 16*q - 3. Let d = -26 - -35. Let o(n) = 9*n**2 - 33*n + 6. Let k(b) = d*l(b) + 4*o(b). Factor k(p).
-3*(p - 1)*(3*p - 1)
Suppose -11/8 + 1/4*o**4 + 23/8*o**3 - 23/8*o + 9/8*o**2 = 0. What is o?
-11, -1, -1/2, 1
Suppose 5 = -5*s - 5*y, 3*y = 2*s - 2*y - 19. Let f be (-6)/(-24) - (-3)/(-24)*s. Factor -8/3*j**2 + 0*j**3 + f*j + 4/3*j**4 + 4/3.
4*(j - 1)**2*(j + 1)**2/3
Determine p, given that -2/11*p**4 + 32/11*p**2 - 8/11*p**3 - 96/11 + 32/11*p = 0.
-6, -2, 2
Suppose 0 = -4*o, 5*r + 9*o + 535 = 8*o. Let g = 215/2 + r. Factor -g*z**2 + z + 3/2.
-(z - 3)*(z + 1)/2
What is s in -2/19*s**4 - 168/19*s - 12/19*s**3 + 88/19 + 94/19*s**2 = 0?
-11, 1, 2
Let v(q) = q**3 - q**2 + q + 1. Let n(i) = -2*i**3 - 14*i**2 + 2*i + 2. Let h(j) = -n(j) + 2*v(j). Factor h(c).
4*c**2*(c + 3)
Factor -116/3*f**2 - 14/3*f**3 + 12 + 94/3*f.
-2*(f - 1)*(f + 9)*(7*f + 2)/3
Let b(j) = 15*j**2 - 218*j - 540. Let f(t) = 5*t**2 - 72*t - 180. Let i(z) = -4*b(z) + 11*f(z). Solve i(g) = 0 for g.
-2, 18
Solve 0 - 24/5*v**4 + 18*v**3 + 33/5*v - 3/5*v**5 - 96/5*v**2 = 0.
-11, 0, 1
Let c(n) be the second derivative of n**5/4 + 215*n**4/12 + 415*n**3/6 + 205*n**2/2 - 335*n. Factor c(l).
5*(l + 1)**2*(l + 41)
Let w = -199 + 205. Suppose -48*r + 45*r = -w. Factor -3/2*d**r - 1/2 - 2*d.
-(d + 1)*(3*d + 1)/2
Let h(j) be the third derivative of j**5/30 + 17*j**4/6 + 289*j**3/3 + 42*j**2. Factor h(k).
2*(k + 17)**2
Find q such that 5*q - 13*q + q**2 - 7*q**2 - 43*q = 0.
-17/2, 0
Suppose -1/8*g**2 - 2*g + 1/8*g**3 + 2 = 0. What is g?
-4, 1, 4
Let k(o) be the second derivative of -o**7/168 + o**6/12 + 9*o**5/20 + 19*o**4/24 + 13*o**3/24 - 120*o + 2. Factor k(t).
-t*(t - 13)*(t + 1)**3/4
Let u(b) = 14*b**3 + 12*b**2 - 29*b - 42. Let p(a) = -12*a**3 - 12*a**2 + 28*a + 40. Let c(q) = 5*p(q) + 4*u(q). Find t such that c(t) = 0.
-4, -1, 2
Let o(w) be the first derivative of w**4 + 8*w**3/3 - 8*w**2 - 32*w + 108. Determine k so that o(k) = 0.
-2, 2
Suppose -2*b**4 + 8/5*b**3 + 0 + 2/5*b**5 + 0*b**2 + 0*b = 0. What is b?
0, 1, 4
Let q = -3 - -3. Let s be ((-21)/7)/((-9)/6). Factor -s*x**3 + 0 + 2/3*x**4 + q*x + 4/3*x**2.
2*x**2*(x - 2)*(x - 1)/3
Let a = -8101/2 - -4052. Suppose -a*f**2 + 3/4*f + 0 + 3/4*f**3 = 0. What is f?
0, 1
Let o be (-160)/(-14) + (-16)/(-28). Suppose 8*m = 4*m + o. Suppose -6*d**2 - 4*d + 1 + m*d**2 - 8*d**3 + 8*d + 4*d**5 + d**4 + d**2 = 0. Calculate d.
-1, -1/4, 1
Determine o so that -32 + 33*o - 9*o - 21*o**3 + 8*o**3 + 12*o**2 + 9*o**3 = 0.
-2, 1, 4
Let r be 520/(-50) - 4/(-10). Let i be 2/r - 4/(-10). Factor 6/5*q**3 + 4/5*q**4 + 4/5*q**2 + i*q + 0 + 1/5*q**5.
q*(q + 1)**4/5
Let n(m) be the first derivative of m**6/2 + 9*m**5/5 - 33*m**4/4 - 3*m**3 + 15*m**2 - 235. Determine b, gi