- 285*z**4 + 68*z**3 + 398*z**2 + 58*z**2 = 0?
-19/6, -3, 0, 2
Let d be 20 - -2 - (4/(-2) - -5). Suppose d*m = -23*m. Factor 0*p**2 - 2/5*p**5 + m*p**3 + 0*p**4 + 0 + 0*p.
-2*p**5/5
Let o(n) = -26*n + 172. Let s be o(5). Solve 6*h**5 - s*h**3 - 4*h**5 - 8*h**4 + 0*h**5 = 0 for h.
-3, 0, 7
Let g(u) = 3*u**4 - 15*u**3 + 60*u**2 - 60*u + 18. Suppose 28*x = 31*x + 18. Let r(d) = d**3 + d**2 - 1. Let j(l) = x*r(l) + g(l). Factor j(a).
3*(a - 2)**3*(a - 1)
Factor 39167*m - 2452*m**2 + 151136*m - 374544 - 22383*m + 209072*m + 4*m**3.
4*(m - 306)**2*(m - 1)
Let y(u) = -u**2 + 129*u + 810. Let h be y(-6). Let 9/4*b**5 + h - 9*b**2 + 6*b**4 - 9/4*b**3 + 3*b = 0. What is b?
-2, 0, 1/3, 1
Let r(b) = b**3 - 3*b**2 - 10*b + 64. Let f(g) = -g**2 - g - 2. Let p(s) = 5*f(s) + r(s). Suppose p(k) = 0. Calculate k.
-3, 2, 9
Let f = -21769 - -21772. Let q(x) be the third derivative of -x**f - 1/6*x**4 + 21*x**2 + 0 + 1/30*x**5 + 0*x. Factor q(p).
2*(p - 3)*(p + 1)
Let c = -4 - 4. Let k(l) = l**2 + 10*l + 19. Let g be k(c). Determine w, given that 14*w**g + 6*w + 12*w**3 - 28*w**3 - 4*w**2 = 0.
-3, 0, 1
Let s(u) be the second derivative of u**6/60 - 7*u**5/8 - 19*u**4/3 - 13*u**3 + 6*u + 73. Factor s(f).
f*(f - 39)*(f + 2)**2/2
Let y(m) = -m - 38. Let s(k) = -k - 75. Let j(r) = -2*s(r) + 5*y(r). Let w be j(-14). Determine c, given that 3/4*c + 0 - 1/4*c**w = 0.
0, 3
Let j(x) = x**2 + 28*x - 20. Let t(a) = 4*a**2 + 113*a - 84. Suppose -41*g + 22*g = -114. Let n(b) = g*t(b) - 22*j(b). Factor n(k).
2*(k - 1)*(k + 32)
Suppose -g + 2 = 0, 0 = -3*k - 2*k - 4*g + 48. Suppose 5*x - 3*x - k = 0. Find u, given that 5*u**4 - u**4 - u**x - 3*u**3 + 3*u + u**2 - 4*u**2 = 0.
-1, 0, 1
Let d(l) = 3*l**2 + 25. Let q(w) = -4*w**2 - 70*w + 298. Let m(t) = -2*d(t) - q(t). Find c such that m(c) = 0.
6, 29
Factor 1/7*g**2 + 235225/7 - 970/7*g.
(g - 485)**2/7
Factor -5*y**2 + 120*y + 96 - 127 + 32 + 899.
-5*(y - 30)*(y + 6)
Let x(n) be the first derivative of 0*n**2 - 3/5*n + 1/5*n**3 + 54. Let x(u) = 0. What is u?
-1, 1
Suppose 59 = -2*i + 17. Let w = 28 + i. Factor -10*b**3 + 6*b + w*b**5 - 2*b**5 - b.
5*b*(b - 1)**2*(b + 1)**2
Find f, given that -3270 - 24*f**2 + 407*f + 70*f**2 + 698*f - 25*f**2 - 26*f**2 = 0.
3, 218
Let 15/2*n**2 - 15/2 + 1/2*n - 1/2*n**3 = 0. What is n?
-1, 1, 15
Let f(x) be the second derivative of -8*x**7/7 - 28*x**6 - 2451*x**5/20 - 217*x**4/2 + 194*x**3 - 84*x**2 + 2*x - 856. Solve f(d) = 0 for d.
-14, -2, 1/4
Let m(k) be the third derivative of 1/240*k**6 + 0 - 5/24*k**4 + 4*k - 3*k**2 + 2/3*k**3 + 1/120*k**5. Determine y so that m(y) = 0.
-4, 1, 2
Let t(c) be the second derivative of 3*c**5 - 305*c**4/12 - 790*c**3/3 - 375*c**2/2 + 3657*c. What is f in t(f) = 0?
-3, -1/4, 25/3
Let y(a) be the second derivative of -a**7/252 + a**6/9 + 9*a**5/40 - 61*a**4/36 - 23*a**3/9 + 14*a**2 - 25*a - 24. What is j in y(j) = 0?
-2, 1, 2, 21
Let f be (1728/1512 - 2/14)/2. Factor -3/2 - 2*s - f*s**2.
-(s + 1)*(s + 3)/2
Let v be (30/(-4))/(18/(-756)). Let u be (-32)/36*v/(-336). Factor 35/6*d**2 + u*d**3 + 15/2 + 25/2*d.
5*(d + 1)*(d + 3)**2/6
Suppose 4*z = 2*z - 120. Let p be ((-146)/30)/(-1) - 8/z. Factor -j**2 - p*j**4 + 3*j**3 + 3*j**4 - 3 + j**2 + j + 9*j**2.
-(j - 3)*(j + 1)**2*(2*j - 1)
Let q(i) = 10*i**4 + 6*i**2 + 6. Let y(f) = 10*f**4 - f**3 + 5*f**2 + 5. Let p be 3 + 7 + 5/(-1). Let g(l) = p*q(l) - 6*y(l). Factor g(c).
-2*c**3*(5*c - 3)
Let p be ((-3 - (-7 - -3)) + -1)/4. Let -324/5*n**2 - 72/5*n**3 + 0 - 4/5*n**4 + p*n = 0. What is n?
-9, 0
Let p = 479/92 + -65/92. Factor 4*m + p - 1/2*m**2.
-(m - 9)*(m + 1)/2
Let r(j) = j**2 - 4*j - 20. Let g be r(7). Factor -g - 19 - 2*l**3 + 5*l**2 + 24 - 8*l + l**3.
-(l - 2)**2*(l - 1)
Let y(p) be the first derivative of -5*p**6/2 - 11*p**5/3 - 5*p**4/6 + 1201. Suppose y(h) = 0. What is h?
-1, -2/9, 0
Let s(v) be the third derivative of v**5/180 + 55*v**4/72 + 323*v**3/9 - 17*v**2 + 3*v - 5. Factor s(a).
(a + 17)*(a + 38)/3
Let a = 2645 - 2600. Suppose -5*u + 6 = -2*u. Find b, given that -3 + 9*b**2 - 22 - 3*b**2 + 4*b**u - a*b = 0.
-1/2, 5
Let i(d) be the first derivative of -2*d**3/27 + 8*d**2/9 - 32*d/9 + 2613. Factor i(u).
-2*(u - 4)**2/9
Let w = -78 + 114. Let l be 617/w - (-65)/(-260). Factor 32/9 - 112/9*v - 100/9*v**3 + 32/9*v**4 - 4/9*v**5 + l*v**2.
-4*(v - 2)**3*(v - 1)**2/9
Let u = 48 - 57. Let r be (-1)/((-15)/u - 2). Factor 2*l**3 - l**4 - l**2 + 8*l**4 + 13*l**5 + 0*l**r - 9*l**5.
l**2*(l + 1)**2*(4*l - 1)
Determine u, given that -43 - 4*u**2 - 176*u + 195 - 52 + 231 + 437 = 0.
-48, 4
Determine y, given that 382268650 + 1182*y**2 + 1164270*y + 2/5*y**3 = 0.
-985
Suppose -2*j + u + 3*u + 26 = 0, u = -j + 1. Suppose -s = -2*s + j. Find n such that -5*n**5 + 3*n**s - 5*n**4 - 3*n**5 = 0.
-1, 0
Suppose 17*n + 7*n = -11*n. Let w = 402 - 400. Factor -4/3*h**3 + 16/3*h**w + 20/3*h + n.
-4*h*(h - 5)*(h + 1)/3
Let u(d) be the third derivative of -d**6/30 + 13*d**5/15 - 7*d**4/3 - 176*d**3/3 - 26*d**2 + 5*d + 4. Factor u(n).
-4*(n - 11)*(n - 4)*(n + 2)
Let s(o) be the first derivative of o**7/168 + o**6/15 + 19*o**5/80 + o**4/4 - 14*o + 38. Let i(z) be the first derivative of s(z). Factor i(y).
y**2*(y + 1)*(y + 3)*(y + 4)/4
Let d(v) = -8*v - 44*v**3 - 1 + 6*v + 0 - v**2. Let j be d(-1). Solve j*r**3 - 3*r**2 - r**2 + r**2 + 15*r - 9 - 47*r**3 = 0 for r.
-3, 1
Let m(a) = a**3 + 8*a**2 - 5*a - 4. Let x be m(-8). Factor -4*t**4 + 8*t**3 + 16 - 5*t**3 - 7*t**3 + x*t**2 - 44*t.
-4*(t - 1)**3*(t + 4)
Suppose -188*s - 50*s + 476 = 0. Suppose 4*u = 8*u + 2*j - 2, -2*u = 2*j + 2. Suppose -u - 11/5*n - 1/5*n**s = 0. What is n?
-10, -1
Determine q so that -14*q**4 + 96*q**4 + 438*q - 96 - 174*q**3 + 69*q**2 - 264*q**3 - 55*q**4 = 0.
-1, 2/9, 1, 16
Let z = -44 + 50. Suppose -z*f + 4*f = -22. Determine h so that -9*h + 28*h**3 + 6*h**5 - 16 - f*h + 20*h**4 - 2*h**5 - 4*h**2 - 12*h = 0.
-2, -1, 1
Factor -226/5 + 44/3*q + 2/15*q**2.
2*(q - 3)*(q + 113)/15
Let w(g) be the second derivative of g**6/10 + 147*g**5/10 + 2497*g**4/4 + 2352*g**3 + 3456*g**2 - 1840*g. Factor w(f).
3*(f + 1)**2*(f + 48)**2
Let m be (6/40)/((-57)/(-3838)) - 10. Let q(n) be the third derivative of 0 + 0*n - 1/70*n**7 + 0*n**4 + m*n**5 + 23*n**2 + 0*n**3 - 1/40*n**6. Factor q(w).
-3*w**2*(w - 1)*(w + 2)
Let a(y) be the third derivative of -y**5/90 + 127*y**4/36 - 250*y**3/9 - 2235*y**2. Factor a(w).
-2*(w - 125)*(w - 2)/3
Let l(o) be the third derivative of 19 + 1/390*o**5 + 5/39*o**4 - 3*o**2 + 100/39*o**3 + 0*o. Factor l(r).
2*(r + 10)**2/13
Let u = 72 - 80. Let s be u/20 - 36/(-15). Solve 40/3*f + 4/3*f**s + 100/3 = 0.
-5
Let a be (((-69)/690)/(10/75))/(-3). Let -27/4*c + 27/4*c**2 + 0 - 9/4*c**3 + a*c**4 = 0. What is c?
0, 3
Suppose -88 - 352 = -10*c. Let -3*h - c - h + 24*h**2 - 13*h**2 - 4 - 7*h**2 = 0. Calculate h.
-3, 4
Suppose -423*i + 804 = -21*i. Let m(a) be the third derivative of -1/60*a**4 + 4/15*a**3 + 1/300*a**6 - 2/75*a**5 - 27*a**i + 0*a + 0. Factor m(d).
2*(d - 4)*(d - 1)*(d + 1)/5
What is z in -2/13*z**2 + 184/13*z - 360/13 = 0?
2, 90
Suppose -4*h + 2*i + 12 = 0, 5*i = 2*h + h + 5. Suppose 3*v = -h*r + 54, 6*r - 18 = 3*r + 3*v. Find l, given that 2*l**2 + 4 + 5 + r + l**2 - 15*l = 0.
2, 3
Let o = 5636 - 5633. Let t(p) be the first derivative of -27 + 2*p**2 + 8/3*p**o + 5/4*p**4 + 1/5*p**5 + 0*p. Find h such that t(h) = 0.
-2, -1, 0
Let z(k) be the third derivative of 0*k - 35/24*k**4 + 0 + 54*k**2 + 1/12*k**5 + 0*k**3. Factor z(x).
5*x*(x - 7)
Factor -32/3*w**4 + 16/15*w**3 + 38/15*w**2 + 0 + 2/5*w.
-2*w*(4*w + 1)**2*(5*w - 3)/15
Solve 916*a**3 + 449995*a + 126732 + 2995*a**2 + 914*a**3 + 320273 - 1825*a**3 = 0 for a.
-299, -1
Let g(s) = -8*s**4 - 24*s**3 - 44*s**2 - 54*s - 32. Let b(u) = -u**4 - u**3 + u**2 - 2. Let l be 27/(-36) + (-6)/24. Let d(q) = l*g(q) + 6*b(q). Factor d(n).
2*(n + 1)**2*(n + 2)*(n + 5)
Let g = -28/205 - -248/615. Let q(r) be the first derivative of 0*r**2 + 22 + 1/10*r**4 - 2/25*r**5 + g*r**3 + 0*r. Factor q(s).
-2*s**2*(s - 2)*(s + 1)/5
Let w be (-116)/(-6)*3804/18386. Factor -1/3 + 1/6*d**5 - 5/6*d + 2/3*d**w + 2/3*d**3 - 1/3*d**2.
(d - 1)*(d + 1)**3*(d + 2)/6
Let i = 266 + -264. Suppose 0 = p + 3*p - 72. Find m such that 8 - p*m**3 + 6*m**4 + 9*m + i - 4 - 12*m**2 + 9*m**5 = 0.
-1, -2/3, 1
Let k(v) be the second 