he second derivative of l**4/36 - 19*l**3/3 + 220*l**2/3 + 523*l - 4. What is o in f(o) = 0?
4, 110
Let f = -683309/20 + 34181. Let a = -43/4 + f. Factor -4/5*d**2 + a - 4*d.
-4*(d - 1)*(d + 6)/5
Let j(b) be the third derivative of -b**8/28 - 59*b**7/70 + 147*b**6/40 - 101*b**5/20 + 17*b**4/8 - 2*b**2 + 5. Determine d so that j(d) = 0.
-17, 0, 1/4, 1
Suppose -12*o - 4362 + 1242 = 0. Let i be (8/o)/(2 - 82/40). Find r such that -i - 2*r**2 + 24/13*r - 2/13*r**4 + 12/13*r**3 = 0.
1, 2
Let s(k) be the first derivative of -5*k**6/36 + k**5/3 + 25*k**4/12 - 50*k**3/9 - 15*k**2/4 + 15*k + 237. Find h, given that s(h) = 0.
-3, -1, 1, 2, 3
Let x(m) = -2*m**2 - 1. Let l(u) = 5*u**2 - 9*u + 7. Let y(c) = 19*c**2 - 38*c + 27. Let j(h) = -9*l(h) + 2*y(h). Let o(a) = 2*j(a) - 6*x(a). Factor o(d).
-2*(d - 3)*(d - 2)
Suppose -5*g = 15, -r - 2*g = r - 4. Let -r + 13 + 5*h**2 - 8 + 15*h = 0. What is h?
-3, 0
Let i(x) = x**2 + 11*x + 58. Let b(o) = 2*o**2 + 23*o + 109. Let p(s) = 6*b(s) - 11*i(s). Factor p(c).
(c + 1)*(c + 16)
Suppose 4*y = -2*y + 12. Factor 54736*z**3 + 2*z**y - 48*z + 8*z**2 + 32 - 54730*z**3.
2*(z - 1)*(z + 4)*(3*z - 4)
Let a(c) be the second derivative of -c**4/114 - 25*c**3/57 + 26*c**2/19 - 694*c + 1. Determine h, given that a(h) = 0.
-26, 1
Suppose -72*t**2 + 0 - 432/5*t - 3/5*t**4 + 69/5*t**3 = 0. What is t?
-1, 0, 12
Let z = 577547/15 - 38503. Factor z*a**2 + 12/5 + 38/15*a.
2*(a + 1)*(a + 18)/15
Let f be 358/(-3960) - (-6)/(-72)*-3. Let g = f - -4/99. Factor 0*s + 0 + 3*s**3 + 7/5*s**4 + g*s**5 + 9/5*s**2.
s**2*(s + 1)*(s + 3)**2/5
Factor 368*v + 5*v**3 - 640 - 3*v**3 + 0*v**3 + v**3 + 2828*v**2 - 2892*v**2.
(v - 4)**2*(3*v - 40)
Let x(d) be the first derivative of -d**5 + 55*d**4/4 + 20*d**3 - 370*d**2 + 880*d - 875. Factor x(z).
-5*(z - 11)*(z - 2)**2*(z + 4)
Let p(o) be the second derivative of -2*o**3 + 12*o - 3/2*o**2 - 1/180*o**5 + 0 + 1/6*o**4. Let b(r) be the first derivative of p(r). Factor b(l).
-(l - 6)**2/3
Let i(o) be the third derivative of o**5/240 + 7*o**4/8 + 1595*o**3/24 + 8701*o**2. Let i(k) = 0. Calculate k.
-55, -29
Let s(b) = 17*b**2 + 11*b - 6. Let j = -77 - -72. Let i(v) = -15*v**2 - 10*v + 5. Let h(c) = j*s(c) - 6*i(c). Factor h(q).
5*q*(q + 1)
What is u in 132/5*u**2 + 0*u + 98/5*u**3 + 0 - 2/5*u**5 + 12/5*u**4 = 0?
-3, -2, 0, 11
Let y = 2/173675 + 416818/173675. Let 8/5*v**2 - 24/5*v**3 + 4*v + 4/5*v**5 + 4/5*v**4 - y = 0. What is v?
-3, -1, 1
Suppose -5*c + 77 = 2*n, 16*c - 2*n = 11*c + 93. Suppose 5*p - c = h, 9*p + 4 = 10*p. Factor -2/13*m**2 + 0 + 2/13*m**h + 0*m.
2*m**2*(m - 1)/13
Find h, given that 1250/9*h + 622/9*h**2 + 626/9 - 2/9*h**3 = 0.
-1, 313
Let t(z) = -z**3 - z**2 - 16. Let m be t(0). Let n = m + 18. Determine a so that 20 - 11*a + 34*a**2 - 38*a**n - 5*a = 0.
-5, 1
Let u = 376/1745 + 322/1745. What is b in -4 - u*b**3 - 34/5*b - 16/5*b**2 = 0?
-5, -2, -1
Let u = 50086 - 200343/4. Factor 1/4*r**3 - r**2 - u*r + 1.
(r - 4)*(r - 1)*(r + 1)/4
Let j(r) be the first derivative of r**3/3 + r**2 + 3*r - 1. Let s be j(-2). Find z such that z**2 + z + z + s - 6*z = 0.
1, 3
Let r(d) = 3*d**2 + 19*d - 5. Let w(m) = -28*m - 4*m**2 + 2 + 8 - 2. Let p(z) = -2*z**2 - 9*z + 3. Let c be p(1). Let b(n) = c*r(n) - 5*w(n). Factor b(g).
-4*g*(g + 3)
Let g be 720/20*2*3/(-2). Let d = 112 + g. Let 0*l**2 - 370 + d*l**2 + 1270 - 120*l = 0. What is l?
15
Let t be ((-54)/(-400) + (-171)/456)*10/(-3). Let s = 192/5 - 32. Factor t - s*b**2 - 18/5*b**3 - 2*b.
-2*(b + 1)**2*(9*b - 2)/5
Let s(r) be the third derivative of r**7/42 + 33*r**6/8 + 1297*r**5/6 + 1480*r**4 + 3840*r**3 + 12*r**2 + 27*r. Factor s(b).
5*(b + 1)*(b + 2)*(b + 48)**2
Factor -7098 + 3393/2*a + 387*a**2 + 33/2*a**3.
3*(a + 13)**2*(11*a - 28)/2
Let l be ((-2924)/(-172) + (-50)/3)/((-14)/(-6)). Let l - 2/7*b + 1/7*b**2 = 0. Calculate b.
1
Let p(z) be the second derivative of -z**5/5 + 8*z**4 + 2*z**3/3 - 48*z**2 + 1681*z. Factor p(b).
-4*(b - 24)*(b - 1)*(b + 1)
Let b be ((-144)/(-30))/(-12)*(0 - 40). Solve -16*o**3 - 68*o**4 - 69*o**4 + 133*o**4 - 8*o**2 + 12 + b*o = 0.
-3, -1, 1
Suppose -16*v + 64 = -128. Suppose -v*k + 82 = 29*k. Solve 2/5*g**3 + 0*g + 0*g**k + 0 - 18/5*g**4 = 0 for g.
0, 1/9
Let f(j) be the first derivative of -2*j**3/21 - 46*j**2/7 - 176*j/7 + 2832. Suppose f(z) = 0. What is z?
-44, -2
Let z(g) be the second derivative of 0*g**2 - 1/30*g**6 + 0 - 27436/3*g**3 - 57/10*g**5 + 50*g - 361*g**4. Factor z(j).
-j*(j + 38)**3
Let p = 621192/7 - 88740. Find g, given that 32/7*g**2 + 0 + 12/7*g**3 - p*g = 0.
-3, 0, 1/3
Let g = -9919/3 - -3307. Let b(c) be the first derivative of 0*c + 8/5*c**5 - g*c**6 + 0*c**4 - 8/3*c**3 + 2*c**2 + 7. Solve b(l) = 0 for l.
-1, 0, 1
Let o(y) be the third derivative of -1/30*y**5 - 1/3*y**4 + 0 + 3*y + 63*y**2 + 7*y**3. Factor o(x).
-2*(x - 3)*(x + 7)
Suppose -5*r + 492*r = -679*r + 2332. Factor 180/7*x + 4050/7 + 2/7*x**r.
2*(x + 45)**2/7
Factor 616/5 + 618/5*n**2 + 1/5*n**3 + 1233/5*n.
(n + 1)**2*(n + 616)/5
Let u(a) be the third derivative of a**6/960 + 17*a**5/160 + 93*a**4/64 + 135*a**3/16 - 2*a**2 + 91. Factor u(b).
(b + 3)**2*(b + 45)/8
Suppose 5213*o + 1038 - 11422 = 5255. Factor -14/3*x**2 + 1 + 4/3*x**o + 4/3*x + x**4.
(x - 1)**2*(x + 3)*(3*x + 1)/3
Let r(a) be the second derivative of -a**4/54 + 71*a**3/9 - 836*a**2/9 + 3442*a. Factor r(s).
-2*(s - 209)*(s - 4)/9
Let v(z) be the first derivative of 160/9*z**3 - 6/5*z**5 + 0*z + 45 + 28/3*z**2 + 17/2*z**4. Let v(m) = 0. What is m?
-2/3, 0, 7
Factor -1234*y**4 - 2 + 136*y**3 + 1222*y**4 + 72*y + 8 - 6 - 260*y**2.
-4*y*(y - 9)*(y - 2)*(3*y - 1)
Let c(p) = 2*p**2 + 493*p + 980. Let s be c(-2). Factor s*n**4 + 850/3*n + 500/9 + 470/3*n**2 + 274/9*n**3.
2*(n + 5)**3*(9*n + 2)/9
Suppose 5*p + 2*j = 71, -2*p + 13 = j - 15. Let o be ((-2)/(-4))/((p/(-18))/(-5)). Solve -4*w**2 + 3*w + 6*w**3 - w + 4 - 8*w**o = 0.
-2, -1, 1
Let i(v) be the first derivative of 2*v**5/25 + 4*v**4/5 - 4*v**3/15 - 72*v**2/5 - 126*v/5 + 7760. Solve i(x) = 0 for x.
-7, -3, -1, 3
Let z(n) = -n - 27. Let j be z(-59). Let p be 23/((-1771)/22) + j/14. Factor 2/7*t - 2/7*t**p + 0.
-2*t*(t - 1)/7
Let j(v) be the second derivative of -v**5/150 + 3*v**4/10 + 23*v**3/3 + 185*v**2/3 + 1422*v. Find g, given that j(g) = 0.
-5, 37
Determine p, given that 0*p**2 + 129/7*p**4 + 0*p + 3/7*p**5 + 0 - 132/7*p**3 = 0.
-44, 0, 1
Let y = -7172 - -573761/80. Let r(o) be the third derivative of 0 - 1/1200*o**6 + 6*o**2 + 0*o - 1/120*o**5 + 3/20*o**3 - y*o**4. Let r(x) = 0. What is x?
-3, 1
Let c(v) be the first derivative of v**4/2 - 48*v**3 + 405*v**2 - 1188*v + 8598. Factor c(n).
2*(n - 66)*(n - 3)**2
Find s such that 52*s**2 + 0*s**4 + 22*s**3 + 0*s**3 - 13*s**4 - s**5 + 3*s**5 - 15*s**4 = 0.
-1, 0, 2, 13
Let u(y) = -16*y + 131. Let g be u(8). Suppose -4*b = -z + 8, g*z = 5*b - 5 + 15. Factor 0*h**2 - 2/9*h**3 + 0 + z*h.
-2*h**3/9
Let y(x) be the third derivative of 0*x**3 + 1/60*x**5 - 6*x**2 + 0*x - 13/8*x**4 - 2. Factor y(s).
s*(s - 39)
Let c(o) be the third derivative of -o**8/1008 - o**7/630 + o**6/8 + 17*o**5/36 - 11*o**4/18 - 14*o**3/3 - 134*o**2 + 4. Find l such that c(l) = 0.
-6, -2, -1, 1, 7
Let v be (-480)/(-45)*(0 - 9/(-4)). Suppose -3*d = 3*a - 3, 3*d - a = 3*a + v. Factor -8 + d*x**2 + 6*x - 9*x + 2*x + 5*x.
4*(x - 1)*(x + 2)
Let -40*a**4 - 693*a**2 - 4*a**5 + 108*a**2 + 1600*a + 780*a**3 + 5376 - 2375*a**2 = 0. Calculate a.
-21, -1, 4
Let q(k) be the second derivative of -5*k**7/42 - 24*k**6 - 283*k**5/2 - 1055*k**4/3 - 935*k**3/2 - 350*k**2 - 1553*k. Factor q(w).
-5*(w + 1)**4*(w + 140)
Let y(o) be the second derivative of o**6/10 + 3*o**5/5 - 7*o**4/4 - 5*o**3 + 374*o. Factor y(t).
3*t*(t - 2)*(t + 1)*(t + 5)
Let l = 403 + -396. Suppose -l = -20*h + 53. Factor 8/5 + 36/5*v**h - 44/5*v + 48/5*v**2.
4*(v + 2)*(3*v - 1)**2/5
Factor 16642*c - 210*c**2 - 49298/3 + 2/3*c**3.
2*(c - 157)**2*(c - 1)/3
Factor -2/9*r**2 + 0 + 48*r.
-2*r*(r - 216)/9
Suppose -4*u + 0*u = -16. Suppose -3*x - 5*j = -10*j + 13, u*x = 4*j - 4. Factor -258 + 262 - 14*d**2 + 10*d**x - 3*d - 3*d + 6*d**3.
2*(d - 1)*(d + 1)**2*(5*d - 2)
Let u(q) be the third derivative of -q**8/5040 - q**7/420 + q**6/45 - 34*q**5/15 - 2*q**2 + 3*q. Let o(s) be the third derivative of u(s). Solve o(v) = 0.
-4, 1
Let b be (-684)/(-15) 