t derivative of 0*b**5 + 0*b**3 + 5/18*b**4 + 0*b - 1/27*b**6 + 6 - p*b**2. Solve d(q) = 0.
-2, -1, 0, 1, 2
Let d be (-64)/256*0/(-2). Factor -1/3*b**2 - 1/3*b**3 + 0*b + 1/3*b**4 + 1/3*b**5 + d.
b**2*(b - 1)*(b + 1)**2/3
Let i(d) = 5*d**2 - 22*d + 4. Let g(r) = 2*r**2 + r. Let h(c) = 2*g(c) + i(c). Factor h(m).
(m - 2)*(9*m - 2)
Solve 15/2*k**4 + 0*k - 3/2*k**3 + 3/2*k**5 - 15/2*k**2 + 0 = 0.
-5, -1, 0, 1
Find s such that -80*s - 225/4*s**2 - 105/4 - 5/2*s**3 = 0.
-21, -1, -1/2
Let d(t) be the third derivative of t**8/3920 + t**7/490 - 2*t**5/35 - 2*t**4/7 + 3*t**3/2 - 44*t**2. Let z(o) be the first derivative of d(o). Factor z(u).
3*(u - 2)*(u + 2)**3/7
Let j = 258 - 258. Let i(z) be the second derivative of 0*z**2 + j*z**3 + 6*z + 0 + 0*z**5 + 1/45*z**6 - 2/9*z**4. Let i(a) = 0. Calculate a.
-2, 0, 2
Suppose 4*j - 65 + 81 = 0. Let x(n) = -6*n**5 + 10*n**4 + 2*n**3 - 10*n**2 + 4*n - 4. Let u(z) = -1. Let p(i) = j*u(i) + x(i). Suppose p(k) = 0. What is k?
-1, 0, 2/3, 1
Let r(d) = d**2 + 8*d + 18. Let j be r(-5). Solve 18*g**4 - 2*g**j - 4*g**5 - 9*g**4 - 8*g**5 + 5*g**3 = 0.
-1/4, 0, 1
Let f = -31 + 34. Determine a, given that -3 - f + 2 + 20*a - 12 - 4*a**2 = 0.
1, 4
Let t(f) be the first derivative of f**5/40 - f**4/16 - f**3/24 + f**2/8 + 209. Let t(n) = 0. Calculate n.
-1, 0, 1, 2
Let c = 7345 + -7345. Find l, given that -4/7*l + 18/7*l**4 + 26/7*l**2 - 40/7*l**3 + c = 0.
0, 2/9, 1
Let x(y) = 52*y**2 - 19*y - 38. Let c(t) = -19*t**2 + 6*t + 13. Let g(w) = 22*c(w) + 8*x(w). Factor g(f).
-2*(f + 1)*(f + 9)
Let n(h) be the second derivative of -h**4/4 + 27*h**3/2 - 39*h**2 + 909*h. Determine m, given that n(m) = 0.
1, 26
Find n such that 200/7 - 40/7*n + 2/7*n**2 = 0.
10
Let z(q) be the third derivative of -q**10/136080 + q**9/68040 + q**8/90720 - q**5/10 + 3*q**2. Let n(j) be the third derivative of z(j). What is p in n(p) = 0?
-1/5, 0, 1
Let h(r) = -r**3 + 12*r**2 + 12*r + 17. Let q be h(13). Suppose 0 = -q*j - j + 10. Factor 4*i**4 - 8*i**j + 12*i**4 - 20*i**4 - 14*i**3 + 2*i**5.
2*i**2*(i - 4)*(i + 1)**2
Factor 32*j**2 + 140*j - 30 - 27 - 8 - 35.
4*(j + 5)*(8*j - 5)
Let s(n) be the second derivative of -n**4/4 - 6*n**3 + 135*n**2/2 + 23*n + 4. Let s(u) = 0. What is u?
-15, 3
Let l(a) = a**2 - 55*a - 236. Let b be l(-4). Suppose b - 1/6*i**4 - 1/3*i - 1/2*i**3 + 1/6*i**5 + 5/6*i**2 = 0. What is i?
-2, 0, 1
Determine b, given that -213867/5 - 3/5*b**2 - 1602/5*b = 0.
-267
Let k = 49/27 - 4/27. Let y(g) be the first derivative of k*g**2 - 8/9*g**3 + 1/6*g**4 - 1 - 4/3*g. Factor y(l).
2*(l - 2)*(l - 1)**2/3
Let a(x) be the second derivative of 25/6*x**3 + 0 + 5/4*x**4 + 5*x**2 - 30*x - 1/6*x**6 - 1/4*x**5. Factor a(k).
-5*(k - 2)*(k + 1)**3
Let j = -23/258 + 631/1290. Factor -1/5*m**2 - j*m - 1/5.
-(m + 1)**2/5
Let j(z) = -z**2 - z - 6. Let q(v) = 852*v**2 + 2127*v + 1233. Let a(t) = -15*j(t) + q(t). Let a(y) = 0. Calculate y.
-21/17
Let w(c) = -c**3 + c**2 + 2*c. Let j(y) = -8*y**3 + 42*y**2 - 20*y. Let r(h) = -4*j(h) + 28*w(h). Factor r(k).
4*k*(k - 34)*(k - 1)
Suppose 4*p + 18 - 50 = 0. Let a(n) = n. Let h be a(p). Solve -17*m**2 + 28*m + 5*m**3 - 13*m + 5*m**4 - h*m**2 = 0 for m.
-3, 0, 1
Determine o, given that -20/7*o**2 + 0 + 18/7*o**3 + 0*o + 2/7*o**4 = 0.
-10, 0, 1
Let l(w) = -w**3 + 4*w**2 + 2. Let u be l(4). Let f be 4/(-30) - ((-12464)/1320)/19. Factor -f*n + 0 + 2/11*n**u.
2*n*(n - 2)/11
Let n(c) be the second derivative of c**4/48 + 3*c**3/4 - 115*c**2/8 + 688*c + 1. Factor n(k).
(k - 5)*(k + 23)/4
Let k(o) be the second derivative of -o**4/8 + 15*o**3/4 - 39*o**2/2 + 71*o. Let k(f) = 0. Calculate f.
2, 13
Let v(x) = -534*x**3 + 2148*x**2 - 2157*x + 129. Let j(b) = 41*b**3 - 165*b**2 + 166*b - 10. Let s(i) = 27*j(i) + 2*v(i). Factor s(a).
3*(a - 2)**2*(13*a - 1)
Factor -37*m**2 - 78*m + 75 + 13*m**2 + 14*m**2 + 13*m**2.
3*(m - 25)*(m - 1)
Let s = 7/10034 - -972843/652210. Let q = s + 7/65. Determine j so that 8/5 - q*j + 2/5*j**2 = 0.
2
Let t(z) be the third derivative of -z**7/1680 + z**6/360 - z**5/240 - 23*z**3/3 + 11*z**2 + 2*z. Let i(u) be the first derivative of t(u). Factor i(h).
-h*(h - 1)**2/2
Suppose -4*j = -j - 5*d - 61, -j + 7 = d. Suppose j = 4*s + 2*s. Factor 9/2*m**s + 11/2*m + 1.
(m + 1)*(9*m + 2)/2
Let v = -1830 + 1832. Suppose -2/3*a - 10/9*a**v + 4/9 = 0. What is a?
-1, 2/5
Let -31*y**2 - 40*y**2 + 16*y + 83*y**2 = 0. What is y?
-4/3, 0
Factor 5/7*w**3 + 0 + 3/7*w**5 + 0*w + 1/7*w**2 + w**4.
w**2*(w + 1)**2*(3*w + 1)/7
Let k(z) be the second derivative of -z**7/21 - z**6/15 + 4*z**5/5 + 2*z**4 - 19*z + 1. Suppose k(q) = 0. Calculate q.
-2, 0, 3
Factor -3/2 - 3/4*h**2 + 9/4*h.
-3*(h - 2)*(h - 1)/4
Let s = 391 - 387. Let l(b) be the second derivative of 1/36*b**s + 1/2*b**2 + 1/60*b**5 + 0 + 6*b - 5/18*b**3. Factor l(a).
(a - 1)**2*(a + 3)/3
Let i(x) = -x**2 + 5*x + 2069. Let p be i(-43). Solve p*y + 1/3*y**3 - 7/3 - 3*y**2 = 0 for y.
1, 7
Let i(f) = -9*f**4 - 18*f**3 - 9*f**2 + 3. Let o(n) = n**4 + n**3 - n**2 - n - 1. Let h(a) = -i(a) - 3*o(a). Factor h(z).
3*z*(z + 1)**2*(2*z + 1)
Let c(u) be the second derivative of u**7/21 - u**6/5 - 4*u**5/5 + 2*u**4 + 16*u**3/3 - 292*u + 2. Suppose c(b) = 0. What is b?
-2, -1, 0, 2, 4
Let q = -32923 + 98771/3. Factor 0 + 14/3*w + q*w**2.
2*w*(w + 7)/3
Let i(q) be the first derivative of 7 - 5*q + 20/3*q**3 + 15/2*q**2. Factor i(l).
5*(l + 1)*(4*l - 1)
Let g be (-1 + (-20)/(-15))*(-84)/(-35). Factor -8/5*x**2 + 0 - g*x**3 - 4/5*x.
-4*x*(x + 1)**2/5
Let o be (312/(-1456))/((-6)/40). Suppose o + 2/7*a**2 + 12/7*a = 0. Calculate a.
-5, -1
Let r(m) be the third derivative of -m**10/75600 + m**8/5600 - m**7/3150 + 11*m**4/24 + 11*m**2. Let n(s) be the second derivative of r(s). Factor n(j).
-2*j**2*(j - 1)**2*(j + 2)/5
Find n, given that 6*n**3 + 21*n**2 - 1/2*n**4 + 22*n + 15/2 = 0.
-1, 15
Let w(u) be the first derivative of 4*u**2 - 4*u - 4/3*u**3 - 25. Solve w(x) = 0.
1
Let w = 2706 + -29762/11. Suppose -10/11*l**3 + w*l**2 - 14/11*l**4 + 0 + 0*l = 0. Calculate l.
-1, 0, 2/7
Suppose -2*g = -2*j - 4*g + 2, -5*g + 1 = 4*j. Let c = 122/33 + 18/11. Factor -2/9*h**2 - c*h**3 + 4/3*h - 32/9*h**j - 2/9.
-2*(h + 1)**2*(4*h - 1)**2/9
Let o(z) be the first derivative of -2*z**6/51 + 6*z**5/85 + z**4/17 - 8*z**3/51 + 2*z/17 - 80. Suppose o(u) = 0. Calculate u.
-1, -1/2, 1
Let l(s) be the third derivative of -5*s**8/336 + s**7/21 + s**6/24 - s**5/6 + 674*s**2. Suppose l(m) = 0. Calculate m.
-1, 0, 1, 2
Let n = 599 + -599. Let p(z) be the third derivative of -1/36*z**4 + 0*z + 0*z**3 + 1/180*z**5 + n - 3*z**2. Find u, given that p(u) = 0.
0, 2
Let h(y) be the first derivative of -4*y**5/15 + 11*y**4/3 - 47*y**3/3 + 55*y**2/3 - 25*y/3 - 48. Factor h(g).
-(g - 5)**2*(2*g - 1)**2/3
Let d(u) = -u**4 - 10*u**3 + 7*u**2 - 2*u + 2. Let v(q) = -5*q**4 - 20*q**3 + 15*q**2 - 5*q + 5. Let g(l) = -5*d(l) + 2*v(l). Let g(x) = 0. Calculate x.
0, 1
Let b(z) be the first derivative of -z**3 + 15/2*z**2 + 25 + 0*z. Find j such that b(j) = 0.
0, 5
Let h(a) = 2*a**2 + 100*a + 72. Let b(n) = 2*n**2 + n. Let f(v) = -5*b(v) - h(v). Factor f(l).
-3*(l + 8)*(4*l + 3)
Let q(p) = -p**3 - 2 + 18 + 814*p**2 - 828*p**2 + p. Let j be q(-14). Factor -2/3*w**5 + 2/3*w**3 + 0*w + 0*w**4 + 0 + 0*w**j.
-2*w**3*(w - 1)*(w + 1)/3
Let b(t) be the first derivative of -t**7/735 - t**6/105 + t**5/210 + t**4/21 - 3*t**2 - 2. Let x(h) be the second derivative of b(h). Factor x(o).
-2*o*(o - 1)*(o + 1)*(o + 4)/7
Let l(c) be the third derivative of 13*c**5/60 - c**4/12 + c**2 + 13. Suppose l(b) = 0. What is b?
0, 2/13
Let o(s) be the first derivative of -5*s**3/3 + 595*s**2 - 70805*s + 297. Determine c, given that o(c) = 0.
119
Let w(h) be the third derivative of -h**9/161280 - h**8/26880 + h**7/13440 + h**6/960 + h**5/6 + 8*h**2. Let q(k) be the third derivative of w(k). Factor q(d).
-3*(d - 1)*(d + 1)*(d + 2)/8
Let p(q) be the second derivative of -3*q**5/20 - 13*q**4/4 - 8*q**3 + 288*q**2 - 548*q - 1. Factor p(o).
-3*(o - 3)*(o + 8)**2
Determine b, given that -8/3 + 2*b**2 + 0*b + 2/3*b**3 = 0.
-2, 1
Let c(r) = r**5 + r**3 + r**2 + r + 1. Let v(u) = -6*u**5 - 8*u**4 + 5*u**3 - 7*u**2 - 7*u - 7. Let p(x) = -21*c(x) - 3*v(x). Factor p(z).
-3*z**3*(z - 6)*(z - 2)
Solve 2 - 2/9*q**2 - 16/9*q = 0 for q.
-9, 1
Let k be (40/(-24)