he second derivative of n(k). Factor q(l).
l*(l - 1)*(l + 1)**2
Let z(p) be the first derivative of 3*p**7/112 - 7*p**6/240 - p**5/80 + 127*p - 115. Let j(i) be the first derivative of z(i). Determine y so that j(y) = 0.
-2/9, 0, 1
Let s = -311 + 914/3. Let y = -83/15 - s. Factor 1/5*o**2 - y*o + 4/5.
(o - 2)**2/5
Let b(n) be the first derivative of -n**4/12 + 484*n**3/9 + n**2/6 - 484*n/3 + 6469. Suppose b(o) = 0. What is o?
-1, 1, 484
Let m = -18068/689 - -1398/53. Let h be 6/2 - 2 - -1. Factor -4/13 - 6/13*j - m*j**h.
-2*(j + 1)*(j + 2)/13
Factor 15409470*k - 1410648*k + 4*k**3 + 14967*k**2 - 3198885 - 301756.
(k + 1871)**2*(4*k - 1)
Factor 1201157047/4 + 2398924187/4*s + 3187/4*s**4 - 1691765/2*s**3 + 597190211/2*s**2 - 1/4*s**5.
-(s - 1063)**3*(s + 1)**2/4
Suppose -211 - 2183 = 42*t. Let s be 440/570 + -3 + (-165)/t. Suppose 2/3 - s*l**2 - 2/3*l**3 + 2/3*l = 0. What is l?
-1, 1
Suppose -4*s = -4*z, 2 = -3*s - 0*z + 4*z. Let p be 14/(-189)*-3*s. What is j in 0 + 0*j + 2/9*j**5 - 4/9*j**4 + p*j**2 - 2/9*j**3 = 0?
-1, 0, 1, 2
Let 14*u**2 - 49/3*u - 32 - 5/3*u**3 = 0. What is u?
-1, 3, 32/5
Let y(j) be the third derivative of -5*j**6/72 - 9*j**5/4 + 14*j**4/3 - 34*j**3/9 + 4*j**2 - 1262. Suppose y(l) = 0. What is l?
-17, 2/5
Let k(s) be the third derivative of -s**6/160 - 3*s**5/20 - 35*s**4/32 + 662*s**2. Let k(t) = 0. What is t?
-7, -5, 0
Determine n so that -6750 - 60*n - 2/15*n**2 = 0.
-225
Factor -254/11 + 2/11*d**2 - 252/11*d.
2*(d - 127)*(d + 1)/11
Let h(f) be the first derivative of 2/3*f**2 - 4*f + 53 + 1/3*f**3 - 1/12*f**4. Let h(k) = 0. Calculate k.
-2, 2, 3
Factor 3808/3*o + 32258/3*o**4 - 60452/3*o**3 + 8086*o**2 + 128/3.
2*(o - 1)**2*(127*o + 8)**2/3
Suppose -331 = -2*k + 3*b, -1103 = -5*k - 4*b - 310. Factor -8*m - 94*m**4 - 98*m**5 - 158*m**4 - 57*m**3 - 72*m**2 - k*m**3.
-2*m*(m + 1)**2*(7*m + 2)**2
Suppose -3*m = 4*i - 118, 0*i = 4*i + m - 122. Suppose i*y - 48 = 7*y. Let -6/11*f**y + 18/11*f - 10/11 - 2/11*f**3 = 0. What is f?
-5, 1
Let s(w) be the third derivative of -1/32*w**4 + 0*w + 1/160*w**5 + 0 - 1/2*w**3 - 73*w**2. Factor s(f).
3*(f - 4)*(f + 2)/8
Let w(m) be the first derivative of -m**3/4 - 225*m**2/8 + 57*m - 1483. Factor w(n).
-3*(n - 1)*(n + 76)/4
Let f(y) be the third derivative of 8/135*y**5 + 19*y**2 - 1/6*y**4 + 0 + 1/270*y**6 - 2*y + 0*y**3. Factor f(k).
4*k*(k - 1)*(k + 9)/9
Factor 196/9*m**4 + 0*m - 2/9*m**5 + 0 - 6050/9*m**3 + 20000/3*m**2.
-2*m**2*(m - 48)*(m - 25)**2/9
Let l(s) = 41*s + 186. Let p be l(-6). Let a be 10/(-135)*-21*p/(-70). Suppose -2/3*i**2 - 2*i - a = 0. What is i?
-2, -1
Solve 607*i**2 + 168 + 292*i - 461*i**2 + 0*i**3 + i**4 + 23*i**3 = 0 for i.
-14, -6, -2, -1
Let q be 6/9 + (-16)/(-12). Suppose -8 = q*j - 12. Factor -i**2 - 3*i**2 + 15 + 18*i + 6*i**j + i**2.
3*(i + 1)*(i + 5)
Let t(m) = m**3 + 72*m**2 + 267*m + 4142. Let f be t(-69). Factor 9/2*x + 9/2*x**3 + 12*x**f - 3.
3*(x + 1)*(x + 2)*(3*x - 1)/2
Factor 144 + 25*h**3 + 427 - 87 - h**3 - 524*h**2 + 77*h + 2739*h.
4*(h - 11)**2*(6*h + 1)
Let s be ((-26)/468)/(5/6 - 1). Let a(y) be the third derivative of -s*y**5 + 1/24*y**6 + 0*y + 2*y**2 + 25/24*y**4 - 5/3*y**3 + 0. Factor a(i).
5*(i - 2)*(i - 1)**2
Let v = 509 - 626. Let q be (-6)/(-35)*(2 + v/81). Let 2/21*m**2 - 4/7 + q*m = 0. What is m?
-3, 2
Let f(h) be the second derivative of h**6/120 + h**5/20 + h**4/16 + 194*h - 3. Let f(j) = 0. Calculate j.
-3, -1, 0
Suppose -1792*q - 98/3*q**2 - 24576 = 0. What is q?
-192/7
Let r(c) be the first derivative of -4/5*c - 39/5*c**2 - 50 + 39/10*c**4 + 4/15*c**3. Solve r(d) = 0 for d.
-1, -2/39, 1
Let u(s) be the third derivative of -2*s + 0 - 31*s**2 + 14/45*s**5 - 2/9*s**3 + 55/36*s**4. Factor u(d).
2*(d + 2)*(28*d - 1)/3
Let d(j) be the first derivative of -7/2*j + 90 + 1/18*j**3 + 5/3*j**2. Find r such that d(r) = 0.
-21, 1
Let j(g) = -g**2 + 21*g + 2. Let l(x) = -5*x**2 + 1867*x + 856. Let s(k) = -18*j(k) + 2*l(k). Factor s(d).
4*(d + 419)*(2*d + 1)
Factor -340*j**2 - 155*j + 976*j**2 - 382*j**2 - 414*j**2.
-5*j*(32*j + 31)
Let y be 6/54*-3 + 74/6. Suppose -y + 2 = -5*u. Let 6 + j**2 + 7*j**u - 4*j**4 - 10 = 0. What is j?
-1, 1
Let h(t) = -2*t**2 + 2*t - 2. Let s(n) = n**3 + 316*n**2 - 317*n - 6. Let q(c) = 15*h(c) - 5*s(c). Factor q(d).
-5*d*(d - 1)*(d + 323)
Let f = -11/768 - -9611/768. Factor 45/2*r - f + 2*r**3 - 12*r**2.
(r - 1)*(2*r - 5)**2/2
Let v(a) = -8*a**2 - 49*a + 3. Let u(y) = y**2 + 6*y. Let o(k) = 9*u(k) + v(k). Let q be o(0). Solve 9/4 - 9/4*z**2 - 3/4*z + 3/4*z**q = 0 for z.
-1, 1, 3
Let x(v) be the first derivative of -1/2*v**4 + 1/3*v**6 - 168 + 2*v**3 + 0*v**2 - 6/5*v**5 + 0*v. Factor x(w).
2*w**2*(w - 3)*(w - 1)*(w + 1)
Let u = -211339/770 + 657/154. Let i = -269 - u. Factor -12/5*m - 1/5*m**3 + 8/5 + i*m**2.
-(m - 2)**3/5
Let r(y) be the first derivative of 35*y**6/6 - 127*y**5/5 + 723*y**4/20 - 193*y**3/15 - 59*y**2/5 + 48*y/5 - 2275. Solve r(n) = 0 for n.
-2/5, 3/7, 1, 8/5
Suppose -26 = 3*c - 35. Factor 4*b**4 - 4*b**c - 33*b**4 + 31*b**4.
2*b**3*(b - 2)
Let a = -978537 + 978539. Factor -2*i**a + 0 + 2/5*i**3 + 12/5*i.
2*i*(i - 3)*(i - 2)/5
Let z(c) be the third derivative of -c**5/30 - 27*c**4/4 + 82*c**3/3 + 1001*c**2. Factor z(j).
-2*(j - 1)*(j + 82)
Let x = -656227/3 - -218743. Suppose -18 + 14/3*t**2 + x*t**3 - 14*t = 0. What is t?
-9, -1, 3
Let s(t) = 39*t**3 + 753*t**2 + 12960*t + 72972. Let g(h) = -16*h**3 - 301*h**2 - 5184*h - 29189. Let p(b) = -12*g(b) - 5*s(b). Factor p(n).
-3*(n + 16)**2*(n + 19)
Suppose -6*x + 80 = 92. Let w be (124/(-22))/x - 650/(-3575). Solve 10/7*a**4 - 2/7*a + 6/7*a**5 - 4/7*a**w + 2/7 - 12/7*a**2 = 0.
-1, 1/3, 1
Find m such that 0*m**2 + 1/2*m**4 - 170/3*m**3 + 0*m + 0 = 0.
0, 340/3
Let u = -6507 - -6508. Let g(b) be the first derivative of 0*b - 1/5*b**3 + u + 3/10*b**2. Let g(x) = 0. Calculate x.
0, 1
Solve 133 - 1/5*i**2 - 128/5*i = 0.
-133, 5
Let c(f) = -3*f - 20. Let l be c(-6). Let v be 1/4*-10*l - 3. Find q such that -6*q**2 - v - 24*q - 13*q**4 + 10 + 16*q**3 + 6*q**4 + 13*q**4 = 0.
-2, 1/3, 1
Let b = -65 + 69. Let z(n) = -n**2 + 8*n - 6. Let d be z(b). Factor -6*x**4 + 0*x**3 - d*x**4 - 5*x**2 + 5*x**5 + 15*x**3 + x**4.
5*x**2*(x - 1)**3
Let b(t) be the first derivative of -t**4/30 + 52*t**3/15 - 451*t**2/5 - 13448*t/15 + 422. Factor b(g).
-2*(g - 41)**2*(g + 4)/15
Let s(f) = -f**2 - 14*f + 23. Let q be s(-14). Let x be ((-4)/(-10))/(q/115). Suppose 2 - 6/5*u**x + 28/5*u = 0. Calculate u.
-1/3, 5
Solve 103/4*u + 1/4*u**4 + 37/4*u**3 + 105/4*u**2 + 17/2 = 0 for u.
-34, -1
Let x(m) = 2*m**4 - 10*m**3 + m - 1. Let y(w) = -3*w**4 + 44*w**3 + 43*w**2 - 26*w - 42. Let c(r) = -2*x(r) - y(r). Solve c(g) = 0.
-22, -2, -1, 1
Let -3*k - 150 - 3*k - 840*k**3 + 26*k + 152*k**2 + 820*k**3 - 2*k**4 = 0. Calculate k.
-15, -1, 1, 5
Let m be (9 + (-595)/65)*(-156)/36. Determine x so that 16/9*x + 2/3 - m*x**2 = 0.
-1/3, 3
Let p = 3852/2765 - -225/553. Solve p*n**2 + 0 - 21/5*n**3 - 3/5*n**5 + 0*n + 3*n**4 = 0 for n.
0, 1, 3
Let s(y) be the second derivative of 3*y**5/100 + 9*y**4/2 - 462*y - 9. Factor s(l).
3*l**2*(l + 90)/5
Let l(h) be the third derivative of 7/24*h**4 + 1/60*h**5 + 0*h - 129*h**2 - 4/3*h**3 + 0. Factor l(n).
(n - 1)*(n + 8)
Factor -3*u**2 + 22709*u - u**3 - 2*u**3 - 55*u**2 + 13*u**2 - 22817*u + 420.
-3*(u - 2)*(u + 7)*(u + 10)
Let x(z) = 7*z**2 + 8*z. Let f be x(6). Factor f*d**2 - 5*d**3 - 683*d**2 + 333*d**2.
-5*d**2*(d + 10)
Factor 3704/13 + 918/13*i**2 + 2/13*i**3 - 3696/13*i.
2*(i - 2)**2*(i + 463)/13
Suppose -5*o + 10 = -35. Suppose -5*g = 4*j - o, -5*j + 3*g = -0*j - 39. Suppose -9*h**2 + 9*h + j*h**2 - 5 - 1 = 0. Calculate h.
1, 2
Let r(y) be the third derivative of -1/280*y**7 + 1/16*y**5 + 20*y**2 + 0*y**3 + 0 - 1/160*y**6 - 3/32*y**4 + 0*y. Factor r(f).
-3*f*(f - 1)**2*(f + 3)/4
Let s(q) be the first derivative of -q**4/18 + 2*q**3/9 + q**2 + 29*q + 55. Let b(n) be the first derivative of s(n). Factor b(z).
-2*(z - 3)*(z + 1)/3
Let x be (-23714)/(-12)*1 + (-21)/126. Let o be (-1)/((-1*2)/3952). Determine r, given that 12*r - o*r**2 + x*r**2 - 3*r**3 = 0.
-2, 0, 2
Suppose -7*b = -2*b - 970. Let j be (97/b)/((-26)/(-8)). Determine s, given that 8/13*s**2 - j*s**4 - 4/13*s**3 - 6/13 + 4/13*s = 0.
-3, -1, 1
Let t = 53075 - 263601/5. Let x = -353 + t.