- 1)/7
Factor -376/13*n**2 - 7644 - 2/13*n**3 - 1442*n.
-2*(n + 6)*(n + 91)**2/13
Let x(n) = 4*n**2 - n + 2. Let t(g) be the third derivative of 3*g**5/20 + 3*g**4/8 + 7*g**3/6 - 205*g**2. Let o(y) = t(y) - x(y). Find p, given that o(p) = 0.
-1
Factor -237*z - 56169/2 - 1/2*z**2.
-(z + 237)**2/2
Suppose -15 = 160*r - 163*r. Let s(u) be the first derivative of -2/5*u**4 + 0*u - 3 + 0*u**2 - 8/15*u**3 - 2/25*u**r. Suppose s(y) = 0. What is y?
-2, 0
Determine r, given that -111/7*r**2 + 1/7*r**3 - 424/7 + 534/7*r = 0.
1, 4, 106
Let k = -11883 - -11887. Let w = 133/186 + -3/62. Factor w*o**5 + 0 + 0*o**k + 2/3*o + 0*o**2 - 4/3*o**3.
2*o*(o - 1)**2*(o + 1)**2/3
Let p be (-14)/49 + (-632)/(-56). Let f(i) be the first derivative of -1/30*i**4 - 1/45*i**6 + 0*i**3 + 0*i + p + 0*i**2 + 4/75*i**5. Factor f(w).
-2*w**3*(w - 1)**2/15
Let n be 6540/8175 + (-4368)/(-15) + 2. Find m, given that 28*m - 2/3*m**2 - n = 0.
21
Let -1666*k - 2/3*k**3 + 66*k**2 + 4802/3 = 0. Calculate k.
1, 49
Factor -206925*o**2 - 253*o**3 + 1529*o**3 - 103*o**4 + 101*o**4 + 3403*o**2.
-2*o**2*(o - 319)**2
Let p = -64614 - -64618. Factor -4/5*b**4 + 0 - p*b**3 + 0*b - 16/5*b**2.
-4*b**2*(b + 1)*(b + 4)/5
Suppose 4*o + 5*q = 37, 13*q - 17 = -4*o + 12*q. Factor -3/7*k**5 - 27/7*k**3 - 15/7*k**4 - 6/7*k + 0 - o*k**2.
-3*k*(k + 1)**3*(k + 2)/7
Suppose 5/2*h + 0 - h**5 + 23/4*h**2 - 15*h**3 + 31/4*h**4 = 0. What is h?
-1/4, 0, 1, 2, 5
Let d = -3317/4 - -3327/4. Suppose -5/4*j + 5/4*j**3 - 5/2*j**2 + d = 0. Calculate j.
-1, 1, 2
Let f(l) be the first derivative of 1/12*l**4 - 126 - 13/3*l - 1/6*l**2 + 13/9*l**3. Solve f(k) = 0.
-13, -1, 1
Let a = 741 + -751. Let h be (-26)/a - (17 + (-1680)/100). Find m, given that h*m**4 + 0 + 0*m - 9/5*m**3 - 3/5*m**5 + 0*m**2 = 0.
0, 1, 3
Let g(w) = -40*w**2 - 2280*w + 4. Let f be g(-57). Let 0*l**3 - 10/13*l**2 + 8/13 + 0*l + 2/13*l**f = 0. What is l?
-2, -1, 1, 2
Let x = 409/3332 + 106/833. What is p in 0*p + 1/4 - x*p**2 = 0?
-1, 1
Suppose -608 = 4*o - 5*v, 0 = -o - 2*o - 5*v - 491. Let r = 159 + o. Solve -6*c - 18 - 1/2*c**r = 0 for c.
-6
Let h = -193 - -192. Let z(v) = 3*v**2 + 105*v + 1083. Let w(p) = -p. Let j(l) = h*z(l) + 9*w(l). Factor j(t).
-3*(t + 19)**2
Let h(k) be the third derivative of -k**6/180 + 2*k**5/15 - 7*k**4/12 - 19*k**3/3 - 3*k**2 + 14. Let u(i) be the first derivative of h(i). Factor u(l).
-2*(l - 7)*(l - 1)
Let k be 24/15 - ((-416)/80 + 36/20). Solve -13/2*n**3 - n**k + 0 - 13/2*n**4 + 5*n**2 + 0*n = 0.
-5, -2, 0, 1/2
Let f be 374/(-51) - ((-8)/(-3))/(3/(-9)). Let -1/3*a - 4/3*a**2 + 2/3*a**3 + 2/3 - 1/3*a**5 + f*a**4 = 0. Calculate a.
-1, 1, 2
Let o = 102123 + -714837/7. Let a = 916/679 + -20/97. Factor 0 + 26/7*v**3 - 12/7*v**4 + a*v - o*v**2 + 2/7*v**5.
2*v*(v - 2)**2*(v - 1)**2/7
Let s(b) be the second derivative of -b**4/12 - 13*b**3 + 243*b**2/2 - 7*b + 51. Factor s(v).
-(v - 3)*(v + 81)
Let -1/2*i**4 + 92512*i + 169/2*i**3 - 87808 - 4788*i**2 = 0. Calculate i.
1, 56
Let y be 224*(1080/432)/((-86)/(-8) + -2). Factor 768 + 4/3*h**2 + y*h.
4*(h + 24)**2/3
Solve -6368547/7 - 3/7*k**2 - 8742/7*k = 0 for k.
-1457
Let u(n) = -2*n**2 + 294*n - 3722. Let l be u(133). Suppose 4/5*i + 0 - 2/5*i**l = 0. What is i?
0, 2
Let l = 121 + -92. Factor -l*b**4 + 30*b**4 + b**2 + b**3 + 3*b - 6*b**2.
b*(b - 1)**2*(b + 3)
Let m(t) be the first derivative of t**6/15 - 56*t**5/25 - 9*t**4 - 184*t**3/15 - 31*t**2/5 + 944. What is n in m(n) = 0?
-1, 0, 31
Let d(m) be the second derivative of 11/2*m**2 + 0 + 13/12*m**4 - 2/15*m**5 - 17*m - m**3. Let u(q) be the first derivative of d(q). Factor u(t).
-2*(t - 3)*(4*t - 1)
Let l(t) be the first derivative of -5/12*t**4 + 6 - 10*t**2 + 16*t + 25/6*t**3. Let v(b) be the first derivative of l(b). Solve v(q) = 0 for q.
1, 4
Suppose -4*u = 5*j - 41, -2*j + 20 = 4*u - 6. Let a(y) be the second derivative of 1/20*y**j + 0*y**2 - 1/6*y**4 + 1/6*y**3 + 14*y + 0. Factor a(f).
f*(f - 1)**2
Let a be ((1 + -1)/((-120)/(-30)))/(-2). Let t be (-15)/25*1/(-3). Factor 1/5*x + a - t*x**2.
-x*(x - 1)/5
Let s = 23 - 11. Suppose -20*w + s = -18*w. Solve 9*o**4 - 10*o**2 + w*o**4 - 10 - o**4 + 20*o**3 + 5*o**5 + 6*o**4 - 25*o = 0 for o.
-2, -1, 1
Factor 2/9*z**2 - 616/9 + 34/9*z.
2*(z - 11)*(z + 28)/9
Let a(q) = 5281236*q**2 + 19493*q + 102. Let b(j) = 2640617*j**2 + 9746*j + 57. Let v(s) = -4*a(s) + 7*b(s). Let v(c) = 0. What is c?
-3/1625
Let h(d) be the third derivative of d**7/280 + 7*d**6/180 + d**5/6 + d**4/3 - 4*d**3/3 - d**2 + 12. Let j(l) be the first derivative of h(l). Factor j(a).
(a + 2)**2*(3*a + 2)
Determine p, given that -806*p**2 - 137 - 807*p**2 - 64*p + 632 - 808*p**2 + 2422*p**2 = 0.
9, 55
Let r(n) be the first derivative of -n**6/9 + 82*n**5/15 + 7*n**4 + 10203. Determine g so that r(g) = 0.
-1, 0, 42
Suppose -4*x + 147 = -32*b + 239, 0 = 2*b + 3*x - 9. Factor 4/3*i**4 + 24 + 116/3*i**2 - 52*i - 12*i**b.
4*(i - 3)**2*(i - 2)*(i - 1)/3
Let d = 21128/15 - 1408. Suppose -34 - 8 = -n + 4*k, 2*n + 16 = -2*k. Let d + 2/3*i + 2/15*i**n = 0. What is i?
-4, -1
Let h(z) be the second derivative of 0 - 3/2*z**3 + 0*z**2 + 1/4*z**4 - 26*z. Find s, given that h(s) = 0.
0, 3
Let c(j) be the first derivative of 5*j**4/24 + 35*j**3/6 - 485*j**2/12 + 125*j/2 + 904. Solve c(q) = 0 for q.
-25, 1, 3
Let p(t) be the third derivative of 11*t**8/1176 + 6*t**7/245 - 2*t**6/105 - 11*t**5/105 - t**4/28 + 4*t**3/21 + 202*t**2. What is a in p(a) = 0?
-1, 4/11, 1
Let w(q) be the second derivative of -18/5*q**2 + 0 - 7/20*q**4 + 152*q + 8/5*q**3 + 3/100*q**5. Factor w(g).
3*(g - 3)*(g - 2)**2/5
Suppose h - g - 5 = -1, h + 5*g - 4 = 0. Suppose -116 + 44 = -h*a. Factor 19 - 3*k**2 - 6*k - 14 - 17 + a*k.
-3*(k - 2)**2
Let v(g) be the first derivative of -36 + 2/33*g**3 + 0*g**2 - 2/55*g**5 + 3/11*g**4 - 2/11*g**6 + 0*g. Let v(w) = 0. What is w?
-1, -1/6, 0, 1
Let o(u) be the first derivative of -u**6/960 - 7*u**5/240 + u**4/6 + 53*u**2/2 + 144. Let g(a) be the second derivative of o(a). Factor g(x).
-x*(x - 2)*(x + 16)/8
Let c = 420 - 406. Let x be (-9)/2*c/378*-12. Factor 1/6*d**3 + 1/2*d**x + 1/3*d + 0.
d*(d + 1)*(d + 2)/6
Let t(k) be the first derivative of 2/3*k + 2/15*k**3 - 63 + 1/30*k**4 - 3/5*k**2. Solve t(j) = 0.
-5, 1
Factor -16/17 - 359148/17*b**2 + 4152/17*b + 10355434/17*b**3.
2*(173*b - 2)**3/17
Let b(r) be the first derivative of -r**4/36 + 5*r**3/9 - 25*r**2/6 + 34*r + 7. Let v(o) be the first derivative of b(o). Let v(j) = 0. What is j?
5
Determine k, given that 43/3*k**2 + 79/3*k + 4 + 2*k**3 = 0.
-4, -3, -1/6
Factor 10*p**2 - 85*p - 93 - 11*p**2 - 119 - 23*p.
-(p + 2)*(p + 106)
Let g(m) be the first derivative of 2*m**3/3 - 29*m**2/2 - 15*m - 1587. Factor g(i).
(i - 15)*(2*i + 1)
Let o = -12976 - -12981. Let l(g) be the first derivative of -26 + 0*g - 2/3*g**3 - 3/4*g**4 - 1/5*g**o + 0*g**2. Find h, given that l(h) = 0.
-2, -1, 0
Let y = 12/4583 - -568232/22915. Determine i, given that 2/5*i**2 - y*i + 1922/5 = 0.
31
Let m(d) be the second derivative of 5/6*d**4 - 3*d - 13/24*d**3 - 1/30*d**6 + 0*d**2 + 49/80*d**5 + 8. Determine t, given that m(t) = 0.
-1, 0, 1/4, 13
Let o(l) = -17*l + 3*l + 2*l + 7*l + 41 + 8*l. Let g be o(-13). What is p in 2/7*p - 1/7*p**g - 1/7 = 0?
1
Let d = -18695/2 + 9360. Let m(s) be the second derivative of 29*s + d*s**4 + 60*s**2 + 110/3*s**3 + 1/6*s**6 + 0 + 9/4*s**5. Factor m(q).
5*(q + 2)**3*(q + 3)
Find q such that -48*q**4 + 212 + 255 - 3*q**5 - 645*q - 275 - 72*q**3 + 42 + 534*q**2 = 0.
-13, -6, 1
Let v = 1057/13836 - -8/1153. Let a(w) be the second derivative of 0*w**3 + 0 + 0*w**5 + 0*w**4 + 20*w - 5/84*w**7 + v*w**6 + 0*w**2. Factor a(j).
-5*j**4*(j - 1)/2
Let h = 227602 - 227600. Suppose -18/7*u**4 + 0*u + 0 - 50/7*u**3 + 12/7*u**h = 0. What is u?
-3, 0, 2/9
Suppose -2745 = -163*w + 160*w. Let g = w + -913. Let 2/11*z**g + 2/11*z + 0 = 0. What is z?
-1, 0
Let v(l) be the second derivative of l**6/600 + l**5/150 + l**4/120 + 36*l**2 + 59*l. Let r(z) be the first derivative of v(z). Solve r(d) = 0 for d.
-1, 0
Let d(j) = 7*j**3 + 11*j**2 - 107*j - 117. Let k(i) = -20*i**3 - 32*i**2 + 322*i + 351. Let a(z) = 17*d(z) + 6*k(z). Suppose a(o) = 0. Calculate o.
-13, -1, 9
Find h, given that 289 + 69/4*h**2 - 306*h - 1/4*h**3 = 0.
1, 34
Suppose 4*w + 272 = 7*w + 31*w + 204. Fact