2
Find u such that -81*u**2 + 39*u - 39*u**3 + 3/5*u**4 + 402/5 = 0.
-2, -1, 1, 67
Suppose -2*m + 1 = -3*v, 7*v = -3*m + 12*v. Factor 3*n - 30*n - 19*n**3 + 18*n**3 + 12*n**2 - m*n - 4*n.
-n*(n - 6)**2
Let u(n) = -4*n**2 - 9294*n + 20994719. Let f(k) = -k**2 - 26*k - 1. Let o(r) = -20*f(r) + 4*u(r). Suppose o(v) = 0. Calculate v.
4582
Let j(o) = -o**2 - o + 1. Let w(a) = 2*a**2 - 88*a + 3. Let h = -26 - -27. Let x(k) = h*w(k) - 3*j(k). Factor x(s).
5*s*(s - 17)
Let d = 227/3 - 75. Let r be ((-54)/144)/(18/(-208)). Factor 0*z - d*z**2 - 7*z**4 + r*z**3 + 0.
-z**2*(3*z - 1)*(7*z - 2)/3
Let b = -1814/19 + 9089/95. Factor -9/5 - 6/5*h - b*h**2.
-(h + 3)**2/5
Let m be -19 + ((-2)/10)/(151/(-16610)). Suppose -8/7*b**m + 0*b + 10/7*b**2 + 0 - 2/7*b**4 = 0. Calculate b.
-5, 0, 1
Solve 2/5*p**5 - 26/5*p**4 + 0 - 114/5*p**3 - 32*p + 298/5*p**2 = 0 for p.
-5, 0, 1, 16
Suppose -2*t + 4023 - 365 = -d, 3*t = d + 5486. Suppose h - 3*a = 2*h - 474, 0 = -4*h + 5*a + t. Factor y**4 + 2*y**3 + 462*y - h*y.
y**3*(y + 2)
Let m = 314275/404091 - -2/44899. Let a(o) be the first derivative of -2/3*o**2 - m*o**6 + 10/9*o**3 - 7 + 3/2*o**4 + 0*o - 2/3*o**5. What is v in a(v) = 0?
-1, 0, 2/7, 1
Let o(d) = 3*d**2 + 20*d - 19. Let h(g) = 20*g - 20. Let n(x) = 5*h(x) - 4*o(x). Let q(v) = v**2 + v. Let r(m) = -n(m) - 8*q(m). Factor r(z).
4*(z - 6)*(z - 1)
Let w = -364 + 374. Determine m so that -w*m**2 - 14*m + 2 - 2*m**3 - 12 + 4 = 0.
-3, -1
Let y(k) be the third derivative of 0*k - 5/3*k**3 - 109*k**2 + 1/8*k**4 + 1/60*k**5 + 0. Factor y(v).
(v - 2)*(v + 5)
Let a = -3424 - -3424. Determine k, given that 0 + 1/5*k**4 + 4/5*k**2 + a*k - 4/5*k**3 = 0.
0, 2
Let t = 6527 - 6524. Let h(l) be the first derivative of 0*l**2 + 2 + 1/6*l**t - 2*l. Factor h(p).
(p - 2)*(p + 2)/2
Let d(c) = c**3 + 15*c**2. Let g be d(-15). Factor 49*o**5 + 0*o**4 + g*o - 6*o**3 - 50*o**5 + 0*o - o - 4*o**2 - 4*o**4.
-o*(o + 1)**4
Let q be (-8)/(-72) + (-181)/9. Let k = 21 + q. Determine z, given that 18*z**3 - 2*z + 3 + k - 17*z + 24*z**2 - 3*z = 0.
-2, 1/3
Let n(b) be the third derivative of 0 + 0*b + 1/30*b**5 + 8/3*b**3 + 196*b**2 - 7/12*b**4 + 1/240*b**6. Factor n(z).
(z - 2)**2*(z + 8)/2
Suppose -f - 5 = -z - 3*z, -f - 5 = 4*z. Suppose -3*q + 23 - 17 = z. Factor 10*u**q - 5*u**4 + 8*u**2 - 5 - 8*u**2 - 5*u**5 - 5*u + 10*u**3.
-5*(u - 1)**2*(u + 1)**3
Suppose -l = 5*n + 11, 0 = -l - 2*n - 2. Suppose 3*q - 8 = m, 3*q = -3*m + 20 + l. Factor -p**q + 2*p + 2*p**4 - 5*p**2 + 2*p**2.
p*(p - 1)**2*(p + 2)
Let y(m) be the third derivative of -m**5/90 + 55*m**4/36 - 106*m**3/9 + 1370*m**2. Factor y(q).
-2*(q - 53)*(q - 2)/3
Let l = 108 + -105. What is j in -9*j**2 - j**l - j**3 - 15 - j**3 + 14*j + 13*j = 0?
-5, 1
Let i(g) = -10945*g**3 + 72325*g**2 + 27635*g + 2520. Let u(n) = -608*n**3 + 4018*n**2 + 1535*n + 140. Let a(c) = -3*i(c) + 55*u(c). Let a(t) = 0. Calculate t.
-2/11, 7
Let s(o) = 8*o**2 + 29*o - 21. Let c be s(12). Suppose 3 = -c*q + 1480*q. Factor 2/5*x**4 + 0*x + 0*x**q + 0 - 2/5*x**2.
2*x**2*(x - 1)*(x + 1)/5
Let j be 5/(-4)*(-6)/(-5)*(-2)/4. Factor -338 - j*f**3 - 79/2*f**2 - 533*f.
-(f + 26)**2*(3*f + 2)/4
Let r(t) be the first derivative of t**5/10 + 29*t**4/36 + 2*t**3/3 + 3*t**2/2 + 16. Let v(s) be the second derivative of r(s). Factor v(f).
2*(f + 3)*(9*f + 2)/3
Solve 25*j**2 - 11*j**3 + j**5 + 4*j**4 - 24 - 76*j**2 - 62*j - 3*j**4 + 2*j**4 = 0.
-3, -2, -1, 4
Let i(x) = -200*x**3 - 370*x**2 - 415*x - 135. Let q = -425 + 419. Let o(m) = -22*m**3 - 41*m**2 - 46*m - 15. Let l(k) = q*i(k) + 55*o(k). Factor l(u).
-5*(u + 1)**2*(2*u + 3)
Suppose 0 = -13*n + 80 + 180. Suppose -15 + 5 - 4*s**4 + n*s**2 - 2*s**4 - 2*s**5 + 4*s**3 - 4*s**4 - 2*s = 0. Calculate s.
-5, -1, 1
Let d = 110 - 105. Suppose -a - d*a = a. Factor -4/7 + 2/7*x**3 + a*x**2 - 6/7*x.
2*(x - 2)*(x + 1)**2/7
Let j(p) be the third derivative of p**8/504 + 13*p**7/315 + 3*p**6/20 - 41*p**5/90 - 29*p**4/9 - 20*p**3/3 + 631*p**2. Solve j(g) = 0 for g.
-10, -3, -1, 2
Let k = 52 + -56. Let l be 2/6*(-36)/k. What is z in z**5 + z**2 + 10*z**l + 0*z**2 - z**4 - 11*z**3 = 0?
-1, 0, 1
Let v(w) be the second derivative of w**7/210 + 11*w**6/50 + 43*w**5/20 - 67*w**4/4 - 36*w**3/5 + 486*w**2/5 - 13571*w. Let v(o) = 0. What is o?
-18, -1, 1, 3
Let d(q) = -q**2 + 7*q - 4. Suppose 0 = 7*w - 26 - 16. Let g be d(w). Factor -21*p + 3*p**g + p**2 - 19*p + 100.
4*(p - 5)**2
Let z(j) = 4*j**2 + 208*j + 192. Let s(g) = -13*g**2 - 627*g - 572. Let x(n) = 4*s(n) + 14*z(n). Suppose x(t) = 0. Calculate t.
-100, -1
Factor 4689*r - 1679*r - 2265025 + 16100*r**2 - 32204*r**2 + 16103*r**2.
-(r - 1505)**2
Let b(f) be the first derivative of 15 - 8/7*f + 4/7*f**2 + 10/21*f**3 - 5/14*f**4 - 2/35*f**5 + 1/21*f**6. Solve b(a) = 0.
-2, -1, 1, 2
Factor 39/2*p - 1/2*p**2 + 20.
-(p - 40)*(p + 1)/2
Let s be (-35 + 31)*(-2)/4. Factor -273*k**2 - 5*k + 317*k**s - 3*k.
4*k*(11*k - 2)
Let g(b) be the third derivative of -b**5/60 - b**4/4 + 55*b**3/6 - 2*b**2 - 100*b. Solve g(c) = 0 for c.
-11, 5
Let w(k) = -k**3 + k**2 + 1. Let s(t) = 22*t**3 - 126*t**2 - 202*t - 23. Let h(f) = -4*s(f) - 92*w(f). Suppose h(n) = 0. What is n?
-101, -2, 0
Let y = -4201/280 + 582/35. Let q(h) be the first derivative of 14 - y*h**2 + 1/12*h**3 + 0*h. Determine u, given that q(u) = 0.
0, 13
Suppose 6*u - 9*u + 6 = 0. Suppose -90*t - 127*t + 651 = 0. Solve 4/7*s**t - 4*s**u + 64/7*s - 48/7 = 0 for s.
2, 3
Let g(s) be the third derivative of s**5/15 + 74*s**4/3 + 10952*s**3/3 + 8*s**2 + 89*s. Determine r so that g(r) = 0.
-74
Let y(c) be the second derivative of 7/12*c**4 - 3/2*c**3 + 4*c**2 + 0 - 6*c. Let z(x) = 7*x**2 - 9*x + 7. Let d(p) = -5*y(p) + 6*z(p). Factor d(f).
(f - 1)*(7*f - 2)
Let b(l) be the third derivative of -l**5/30 - 51*l**4/2 + 307*l**3/3 - 5594*l**2. Determine u so that b(u) = 0.
-307, 1
Let p(r) be the second derivative of -2*r**6/15 + 199*r**5/5 + 200*r**4/3 - 15*r + 9. Let p(t) = 0. Calculate t.
-1, 0, 200
Let z(i) be the first derivative of 17/3*i**2 + 156 + 20/3*i + 16/9*i**3 + 1/6*i**4. Factor z(s).
2*(s + 1)*(s + 2)*(s + 5)/3
Let f = -64529 - -64532. Factor -16/7*r**4 + 0 - 40/7*r**2 + 44/7*r**f + 12/7*r.
-4*r*(r - 1)**2*(4*r - 3)/7
Let f be (1/(-62))/((-222)/(-210) + -1). Let r = -1/31 - f. Find b such that -b**2 + r*b**3 + 0 + b = 0.
0, 2
Let s be 85*(33/(-22))/((-5)/2). Let 48*g - 76*g**3 + 57*g**4 - 26*g**3 - 36 - 9*g**5 + s*g**2 - 9*g**3 = 0. Calculate g.
-2/3, 1, 2, 3
Let b(w) = -62*w + 120. Let t be b(14). Let m = 8242/11 + t. Let 0*s + m*s**3 - 14/11*s**5 + 0 - 4/11*s**4 + 4/11*s**2 = 0. What is s?
-1, -2/7, 0, 1
Suppose 3*o = -2*o + 15. Let i = -340 + 342. Let 8*v**i + v + 5*v**o - v**3 + 3*v = 0. Calculate v.
-1, 0
Let z(h) be the second derivative of -h**6/135 + 14*h**5/15 - 392*h**4/9 + 21952*h**3/27 - 74*h - 13. What is k in z(k) = 0?
0, 28
Let t(v) be the third derivative of v**9/16632 + v**8/4620 + v**7/4620 + 65*v**3/6 - 69*v**2. Let w(m) be the first derivative of t(m). Factor w(z).
2*z**3*(z + 1)**2/11
Let d be (-111 - -3079)/56 + (-38)/(-2). Determine i, given that d*i**3 + 0*i + 0 + 3/2*i**4 + 864*i**2 = 0.
-24, 0
Let c(x) be the first derivative of x**4/10 + 58*x**3/15 + 11*x**2 + 54*x/5 + 8854. Factor c(s).
2*(s + 1)**2*(s + 27)/5
Let j(l) be the first derivative of l**6/6 - l**5 - 11*l**4/4 + 11*l**3 - 9*l**2 + 3469. Let j(x) = 0. Calculate x.
-3, 0, 1, 6
Factor 3021/4*x - 378*x**2 - 755/2 + 1/4*x**3.
(x - 1510)*(x - 1)**2/4
Let x(o) = -o**2 - 3*o + 4. Let i be x(-3). Suppose 24 = 6*q + 12. Find p such that -7 - q + 4*p**3 - i*p**2 + 0 - 3 - 20*p = 0.
-1, 3
Let g(j) be the first derivative of -23 - 36*j - 39*j**3 - 60*j**2 - 27/4*j**4. Factor g(c).
-3*(c + 3)*(3*c + 2)**2
Let q = 2152/90765 + -3/2017. Let y(b) be the second derivative of 21*b + 1/6*b**4 + 0 - 2/15*b**5 + q*b**6 + 4/9*b**3 - 4/3*b**2. Find k, given that y(k) = 0.
-1, 1, 2
Let s = 12583 - 12583. Let q(t) be the third derivative of -1/2*t**4 - 2*t**3 + 1/20*t**5 + s + 0*t + 1/40*t**6 + 21*t**2. Let q(l) = 0. What is l?
-2, -1, 2
Suppose 8*v - 4*v - 88 = 0. Suppose 0 = 5*j - 42 + v. Find t such that -6*t**3 + 13*t**3 - j*t**2 - 8*t - 3*t**3 = 0.
-1, 0, 2
Let c(b) be the first derivative of b**4/14 - 8*b**3/7 + 36*b**2/7 + 480. Let c(x) = 0. What is x?
0, 6
Suppose -289*y = -3