ppose 2*p**2 + 5*p**3 + 0*p**3 - 8*p**c - 9*p**2 = 0. Calculate p.
0, 3
Let k(w) be the first derivative of w**4/32 - 25*w**3/24 + 47*w**2/16 - 23*w/8 - 104. Factor k(x).
(x - 23)*(x - 1)**2/8
Let k(o) = -14*o**2 - 20*o - 12. Let u(v) = 39*v**2 + 58*v + 36. Let d(a) = -17*k(a) - 6*u(a). Factor d(g).
4*(g - 3)*(g + 1)
Let r be 7 + -9*(-3)/(-9). Let g(v) be the first derivative of -5 + 8/11*v**2 + 0*v + 56/33*v**3 + 18/55*v**5 + 15/11*v**r. Factor g(j).
2*j*(j + 2)*(3*j + 2)**2/11
Let o = -170 - -2041/12. Let s(t) be the third derivative of -1/3*t**3 + 4*t**2 + 0*t + 0 + o*t**4 + 1/15*t**5. Let s(q) = 0. What is q?
-1, 1/2
Factor 65*q**2 + 6*q - 3*q - 63*q**2 + 2 + q.
2*(q + 1)**2
Let u(x) be the first derivative of x**6/18 + x**5 + 9*x**4/4 - 239*x**3/9 + 12*x**2 + 108*x + 136. Let u(n) = 0. What is n?
-9, -1, 2
Let t(f) be the third derivative of f**8/1008 + f**7/35 + 4*f**6/45 - f**5/90 - 11*f**4/24 - 8*f**3/9 + 6*f**2 - 12*f. Determine x, given that t(x) = 0.
-16, -1, 1
Let w be 7/14 + 323/266. Factor -8/7*v**2 - w*v**3 - 2/7*v**5 - 8/7*v**4 + 0 - 2/7*v.
-2*v*(v + 1)**4/7
Let i(r) be the second derivative of -1/18*r**3 - 1/20*r**5 + 5*r - 1/9*r**4 + 0*r**2 + 0. Factor i(q).
-q*(q + 1)*(3*q + 1)/3
Let x(k) = 20*k**4 - 100*k**3 - 216*k**2 - 240*k - 96. Let h(r) = -6*r**4 + 33*r**3 + 72*r**2 + 80*r + 32. Let t(m) = -16*h(m) - 5*x(m). Factor t(d).
-4*(d + 1)*(d + 2)**3
Suppose 1995*a + 684 = 2032*a - 500. Factor 19*c**2 - 16 + 5/2*c**3 + a*c.
(c + 4)**2*(5*c - 2)/2
Let j(v) = 75*v**4 - 660*v**3 + 1008*v**2 + 1986*v + 663. Let a(u) = -u**2 - u + 2. Let o(s) = -6*a(s) - j(s). Factor o(i).
-3*(i - 5)**2*(5*i + 3)**2
Let o(h) be the first derivative of 2*h**5/55 - 18*h**4/11 + 70*h**3/33 - 120. Solve o(m) = 0 for m.
0, 1, 35
Solve 48 - 22/3*n**3 - 44/3*n**2 - 2/3*n**4 + 40*n = 0 for n.
-6, -1, 2
Let n = 109 - 69. Let l = n - 23. Factor l*m**4 - 5*m**3 - 80*m**5 + 23*m**4 + m - m.
-5*m**3*(4*m - 1)**2
Let p(w) be the second derivative of 8*w + 0*w**2 + 1/6*w**4 - 1/3*w**3 - 2. Factor p(m).
2*m*(m - 1)
Determine x, given that -3/2*x**3 - 7/2*x**2 + 27/2*x + 1/2*x**4 - 9 = 0.
-3, 1, 2, 3
Let a(s) be the second derivative of 31*s**6/10 + 69*s**5/5 + 59*s**4/4 - s**3 + 84*s. Factor a(g).
3*g*(g + 1)*(g + 2)*(31*g - 1)
Let h = 25/61 + -1729/5856. Let f(x) be the third derivative of 0 + 3/80*x**5 + 1/12*x**3 + 0*x + x**2 + h*x**4. Suppose f(l) = 0. Calculate l.
-1, -2/9
Let v(a) be the third derivative of a**8/560 - a**7/175 - a**6/100 + 2*a**5/25 - 7*a**4/40 + a**3/5 - a**2 + 48. Factor v(i).
3*(i - 1)**4*(i + 2)/5
Let v(y) be the first derivative of -y**4/2 + 14*y**3/3 - 11*y**2 + 10*y - 73. Factor v(r).
-2*(r - 5)*(r - 1)**2
Let q(s) be the first derivative of -7*s**3 - 144*s**2/7 + 12*s/7 - 130. Factor q(r).
-3*(r + 2)*(49*r - 2)/7
Let v(n) = -n**3 - 4*n**2 + n - 12. Let c be -1 + -2 + (1 - 3). Let s be v(c). Let -s*j + j**3 + j**2 + 3 + 3*j + 0 = 0. What is j?
-3, 1
Let o be (-470)/15*3/(-2). Factor 10*n - 3*n**2 - o - 1 + 14*n + 0.
-3*(n - 4)**2
Let w(k) be the third derivative of -k**8/56 + k**7/15 + k**6/6 - k**5/3 - 7*k**4/12 + k**3 - k**2 - 10. Solve w(m) = 0.
-1, 1/3, 1, 3
Factor -7/2 - 52*m**3 - 54*m**2 - 23*m - 16*m**4.
-(2*m + 1)**3*(4*m + 7)/2
Find q such that -16/3*q**3 + 0*q + 0 + 8/3*q**2 - 10/3*q**4 = 0.
-2, 0, 2/5
Let n(m) be the first derivative of -5*m**4/4 + 13*m**2/2 - 12*m - 39. Let a(x) = 5*x**3 - 12*x + 13. Let z(v) = 2*a(v) + 3*n(v). Solve z(r) = 0 for r.
-2, 1
Factor 4*m**2 + 1/2*m**3 + 10*m + 8.
(m + 2)**2*(m + 4)/2
Let m = -45 + 49. Factor f**3 + 5*f**4 - f**m - 12*f**2 + 3*f**3 + 4*f**3.
4*f**2*(f - 1)*(f + 3)
Let j be (-2 + (-81)/(-42))/(64/(-512)). Factor -24/7 + 44/7*h - 16/7*h**2 - j*h**3.
-4*(h - 1)**2*(h + 6)/7
Let s(f) = f**3 + 2*f**2 + 2*f + 1411. Let i be s(0). Let w be 0 + (1 - 4) + i/332. What is n in -9/4*n**4 + 0 + 3/4*n**3 + 1/4*n + w*n**2 = 0?
-1/3, 0, 1
Let a = 51 - 48. Suppose 6*p - 15 = a. Factor 0 - 4*b**2 + 2/3*b**p + 6*b.
2*b*(b - 3)**2/3
Let n = 3175/2233 - -15/2233. Let c(p) = 2*p - 1. Let j be c(2). Solve -4/7*o + n*o**5 - 26/7*o**4 + 0 + 18/7*o**j + 2/7*o**2 = 0 for o.
-2/5, 0, 1
Suppose 34 = -2*b + 46. Let s(g) be the third derivative of 0*g**3 + 1/60*g**b + 0*g**4 + 0 + 6*g**2 + 1/30*g**5 + 0*g. Find c, given that s(c) = 0.
-1, 0
Let o(k) = k**3 + 5*k**2 - 3*k. Let v be o(-5). Factor -m**5 + 2*m**4 - 2*m**5 + 6*m**3 - v*m**2 + 4*m**4 + 21*m - 9*m**2 - 6.
-3*(m - 1)**4*(m + 2)
Let h(g) = g**5 - 2*g**3 - g**2 - g - 1. Let l(j) = -3*j**5 - 51*j**4 + 201*j**3 + 249*j**2 + 6*j + 6. Let i(k) = 6*h(k) + l(k). Find b, given that i(b) = 0.
-1, 0, 9
Suppose 5*s - 6 - 4 = 0. Let v(z) = s + 7*z - 8*z - 1. Let w(x) = -2*x**2 + 9*x - 7. Let p(h) = -3*v(h) - w(h). What is o in p(o) = 0?
1, 2
Let x(d) be the first derivative of -8*d**7/105 - 22*d**6/25 - 72*d**5/25 - 16*d**4/15 + 12*d - 6. Let y(q) be the first derivative of x(q). Solve y(f) = 0.
-4, -1/4, 0
Let m = 2001 - 1997. Let x(h) be the third derivative of -1/3*h**m - 4*h**2 + 0*h + 0 + 1/30*h**5 + h**3. Factor x(y).
2*(y - 3)*(y - 1)
Factor -6*b**2 - 36*b + 0*b**2 + 10*b**2 - 88.
4*(b - 11)*(b + 2)
Let n = -1 + 19. Suppose -n*b + 22*b = 0. Solve b + 3/2*c - 3/4*c**2 = 0.
0, 2
Let n(w) be the third derivative of w**6/420 + 11*w**5/210 + 5*w**4/42 - 288*w**2. Suppose n(z) = 0. Calculate z.
-10, -1, 0
Let y(k) = 6*k**2 - 6*k - 7. Let u be y(2). Let l(j) be the second derivative of -1/24*j**4 + 1/12*j**3 + 0 - 5*j + 1/4*j**2 - 1/40*j**u. Factor l(i).
-(i - 1)*(i + 1)**2/2
Factor -834/7*j - 57963/7 - 3/7*j**2.
-3*(j + 139)**2/7
Let o(g) = -28*g - 44. Let x(f) = -f**2 - 1. Let k(c) = o(c) + 4*x(c). Factor k(s).
-4*(s + 3)*(s + 4)
Let 297/5*s**2 + 29/5*s**3 + 243*s + 1458/5 + 1/5*s**4 = 0. What is s?
-9, -2
Let a = 13736/3 - 4578. Suppose -2/9*y**5 - 2/3*y**3 + 0*y + 2/9*y**2 + 0 + a*y**4 = 0. Calculate y.
0, 1
Let g = -2/247 - -1994/2223. Let b(p) be the first derivative of -1/6*p**4 + g*p**3 - 5 - 5/3*p**2 + 4/3*p. Factor b(v).
-2*(v - 2)*(v - 1)**2/3
Let i be ((-4)/(-3))/((8/(-12))/(-2)). Suppose -i = y - 5, s + 4 = 4*y. Factor 1/4*b**2 + s*b - 1/4.
(b - 1)*(b + 1)/4
Let l = 79 - -82. Let b = 807/5 - l. Factor -2/5*f**4 - b*f**2 - 4/5*f**3 + 0 + 0*f.
-2*f**2*(f + 1)**2/5
Let g(s) be the first derivative of -s**6/33 - 2*s**5/11 - 7*s**4/22 + 2*s**3/33 + 8*s**2/11 + 8*s/11 + 75. Solve g(n) = 0 for n.
-2, -1, 1
Let l(r) = -4*r**4 + 2*r**3 + 14*r**2 - 2. Let g(c) = -5*c**4 + 5*c**3 + 13*c**2 - 3. Let b(m) = 2*g(m) - 3*l(m). Let b(n) = 0. Calculate n.
-4, 0, 2
Let m(g) = 3*g**3 - 3*g**2 - 2*g - 2. Let n(o) = -4*o**3 + 5*o**2 + 3*o + 3. Let c(y) = -3*m(y) - 2*n(y). Solve c(j) = 0.
-1, 0
Let o(w) be the first derivative of 5*w**4/4 + 10*w**3/3 - 55*w**2/2 - 60*w - 197. Factor o(d).
5*(d - 3)*(d + 1)*(d + 4)
Let p be 78/9*1314/2847. What is h in 3/4*h**p + 33/4*h**3 + 81/2 + 243/4*h + 135/4*h**2 = 0?
-3, -2
Let c(b) be the first derivative of -2*b**3/3 + 17*b**2 - 32*b + 59. Find o such that c(o) = 0.
1, 16
Let j(m) = -10*m**5 + 8*m**4 - 40*m**3 + 4*m**2 + 50*m - 20. Let d(z) = z**5 + z**4 + z**3 - 2*z. Let p(n) = -8*d(n) - j(n). Solve p(q) = 0.
-1, 1, 2, 5
Suppose 252 = -4*q + 40*q. Let m(h) be the third derivative of 0*h**3 - 1/60*h**6 + 9*h**2 - 1/48*h**4 - 7/240*h**5 - 1/280*h**q + 0 + 0*h. Factor m(x).
-x*(x + 1)**2*(3*x + 2)/4
Let a(u) be the third derivative of -19*u**2 + 0*u - 1/90*u**5 - 1/9*u**4 - 4/9*u**3 + 0. Find m such that a(m) = 0.
-2
Let d be (-624)/(-325)*(-10 + 20). Factor -d + 3*h**3 + 288/5*h - 126/5*h**2.
3*(h - 4)**2*(5*h - 2)/5
Factor 0*w + 0 + 2/7*w**4 - 4/7*w**2 + 2/7*w**3.
2*w**2*(w - 1)*(w + 2)/7
Determine k, given that 1/3 - 2/3*k**2 + 1/3*k**4 + 2/3*k**3 - 1/3*k**5 - 1/3*k = 0.
-1, 1
Let p = 21913/187800 + -36/313. Let r(h) be the third derivative of 0 + 0*h + 1/15*h**3 + 1/75*h**5 - 8*h**2 - p*h**6 - 1/24*h**4. Find q, given that r(q) = 0.
1, 2
Suppose v = g - v, -4*v = 4*g. Let k(r) be the first derivative of 0*r**3 + 0*r**4 - 2/35*r**5 + 0*r + g*r**2 - 5 - 1/21*r**6. Factor k(c).
-2*c**4*(c + 1)/7
Let d(z) be the first derivative of -3*z**6/7 + 18*z**5/35 + 26*z**4/7 - 64*z**3/21 - 64*z**2/7 - 32*z/7 + 209. Determine s, given that d(s) = 0.
-2, -2/3, -1/3, 2
Let d(p) be the second derivative of p**7/6300 + p**6/900 - 3*p**4/4 + 1