the first derivative of -l**5/240 + 19*l**4/96 + 5*l**3/6 + 2*l**2 + 8*l + 74. Let x(t) be the second derivative of n(t). Let x(w) = 0. Calculate w.
-1, 20
Find t, given that 8/5 - 2/15*t**5 + 14/5*t**3 + 2/15*t**4 + 16/3*t + 94/15*t**2 = 0.
-2, -1, 6
Suppose -g + 45 = 8*g. Let o be (7 - g) + 0 + 3. Factor 48*r**5 + 13*r**3 - 36*r**o + 7*r**3 - 4*r**2 - 28*r**4.
4*r**2*(r - 1)**2*(3*r - 1)
Suppose 69*g - 688 + 214 = -89*g. Factor 2*h + 1/4*h**2 + g.
(h + 2)*(h + 6)/4
Let q(x) be the third derivative of -x**5/12 + 65*x**4/4 + 405*x**3/2 - x**2 - 481*x. Factor q(h).
-5*(h - 81)*(h + 3)
Let j(g) be the third derivative of 0 - 8/9*g**3 - 76*g**2 + 1/18*g**4 + 1/45*g**5 + 0*g - 1/360*g**6. Factor j(b).
-(b - 4)*(b - 2)*(b + 2)/3
Factor -8/17*i - 8/17 - 2/17*i**2.
-2*(i + 2)**2/17
Let f(g) be the third derivative of -g**8/588 + 8*g**7/147 - 31*g**6/70 - 146*g**5/105 + 410*g**4/21 - 400*g**3/7 + 1283*g**2. Suppose f(p) = 0. What is p?
-3, 1, 2, 10
Let z(y) = -y + 22. Let t be z(17). Factor 95*h - 46*h**2 - t*h**5 - 48*h**4 + 87*h**4 + 30*h**3 - 54*h**2 - 30 - 29*h**4.
-5*(h - 2)*(h - 1)**3*(h + 3)
Factor r + 1/3*r**3 + 10/3 - 2*r**2.
(r - 5)*(r - 2)*(r + 1)/3
Let i(n) be the second derivative of -n**7/18 + 229*n**6/90 - 141*n**5/10 + 617*n**4/18 - 811*n**3/18 + 67*n**2/2 + 2309*n. Factor i(v).
-(v - 1)**4*(7*v - 201)/3
Let f(s) be the second derivative of -s**5/30 + 23*s**4/9 + 151*s**3/9 - 196*s**2/3 - 1861*s. Factor f(g).
-2*(g - 49)*(g - 1)*(g + 4)/3
Let r = 268207/12 - 89389/4. Determine p, given that -2/3 + p**3 - r*p**2 + 3*p = 0.
1/3, 1, 2
Let d(g) be the first derivative of 7/45*g**6 + 0*g**2 - 4/45*g**3 + 203 + 8/25*g**5 + 0*g + 1/10*g**4. Factor d(a).
2*a**2*(a + 1)**2*(7*a - 2)/15
Let s = 170 - 168. Determine v so that -3 - 5*v**s + 1 - 15*v - 4 - 4 = 0.
-2, -1
Let j(v) be the second derivative of -v**5/360 - 3*v**4/16 - 13*v**3/18 - 65*v**2 - 122*v. Let w(t) be the first derivative of j(t). Factor w(x).
-(x + 1)*(x + 26)/6
Let b be (-3594)/5990*(-40)/(-18) + (0 - 164/(-114)). Factor 148/19*i - b*i**2 - 2738/19.
-2*(i - 37)**2/19
Determine p, given that -8*p**3 + 6*p**3 + 28*p + 10*p**2 + 26 + 9*p + 2*p**3 - p**3 = 0.
-2, -1, 13
Let q(s) = 8*s**3 + 4*s - 2*s**4 + 250*s**2 - 268*s**2 - 8*s. Let m(a) = 4*a**4 - 15*a**3 + 36*a**2 + 9*a. Let r(t) = 4*m(t) + 9*q(t). Factor r(h).
-2*h**2*(h - 3)**2
Suppose j + 2*r = -8, 2*j = -35*r + 37*r + 14. Factor 10*y**j + 5*y**2 + 5*y**3 + 80*y + 35*y**2.
5*y*(y + 2)*(y + 8)
Let j be 6/4*(16 - (-6 + 8)). Factor 20 + 6*s + 20*s**3 - 10*s**2 - j*s - 5*s**5 - 10.
-5*(s - 1)**3*(s + 1)*(s + 2)
Let v(b) be the second derivative of -8*b - 1/9*b**3 + 4 + 1/72*b**4 + 1/4*b**2. Solve v(z) = 0 for z.
1, 3
Let s be ((-15)/10)/((-5)/2) - -1. Find w, given that 0*w + 4/5*w**2 + w**4 + 0 - 1/5*w**5 - s*w**3 = 0.
0, 1, 2
Suppose -11*r = -21*r + 110. Let j - r*j + 4*j**2 - 80 - 22*j = 0. Calculate j.
-2, 10
Let a(q) be the third derivative of -53/15*q**3 + 13/15*q**4 + 0 - 114*q**2 + 1/150*q**5 + 0*q. Factor a(h).
2*(h - 1)*(h + 53)/5
Determine f, given that -1507/7 + 1508/7*f - 1/7*f**2 = 0.
1, 1507
Let v(x) be the second derivative of 3*x**7/112 - 3*x**6/80 - 37*x**5/160 + 37*x**4/96 + x**3/12 - x**2/4 - 15*x - 171. Suppose v(f) = 0. What is f?
-2, -1/3, 1/3, 1, 2
Factor -92 - 47*n - 1/2*n**2.
-(n + 2)*(n + 92)/2
Suppose -o + 5*x + 58 = -0*o, -2*o + 3*x + 123 = 0. Let n = 200 - 106. Factor 8*b - 119 - 10*b**2 + n - o*b.
-5*(b + 5)*(2*b + 1)
Factor 34/7*w**2 + 24/7 + 110/7*w.
2*(w + 3)*(17*w + 4)/7
Factor 0*f + 0 + 448/5*f**5 - 48/5*f**4 + 1/5*f**2 - 9/5*f**3.
f**2*(7*f + 1)*(8*f - 1)**2/5
Let u be 2/100*(-345)/(-322). Let o(y) be the second derivative of 3/7*y**2 + 3/14*y**3 - 13*y + 0 + 0*y**4 - u*y**5. Let o(d) = 0. What is d?
-1, 2
Let u(c) = -c**3 + 182*c**2 + 179*c + 734. Let b be u(183). Factor -33/7*n - 3/7*n**b - 30/7.
-3*(n + 1)*(n + 10)/7
Let d(v) be the second derivative of 0 - 1/70*v**6 + 15/28*v**4 - 40*v + 0*v**2 + 9/70*v**5 - 50/7*v**3. Suppose d(p) = 0. Calculate p.
-4, 0, 5
Let z(r) be the second derivative of -4/15*r**3 + 1/25*r**6 + 69*r + 2/5*r**4 + 0*r**2 + 0 - 11/50*r**5. Solve z(n) = 0.
0, 2/3, 1, 2
Let b = 348 + -300. Factor -4*s**3 + 4*s**3 - b*s + 0*s**3 - 51*s**2 - 3*s**3.
-3*s*(s + 1)*(s + 16)
Let h(w) be the second derivative of 1/70*w**5 - 4 - 12*w + 16/21*w**3 + 5/21*w**4 + 0*w**2. Factor h(r).
2*r*(r + 2)*(r + 8)/7
Let y = -4971/40 + 163391/40. Suppose -y + 89*s - 1/2*s**2 = 0. Calculate s.
89
Factor 255 + 285 + 637*d**2 - 528 + 282*d**3 - 166*d**2 + 236*d + 35*d**4.
(d + 1)**2*(d + 6)*(35*d + 2)
Suppose 1625 + 4855 = 4*p. Let o = 5723 + -5721. Factor b**2 + b**4 + o*b**3 + p*b - 1620*b.
b**2*(b + 1)**2
Let a(l) be the second derivative of -1/45*l**5 - 7/54*l**4 - 4/27*l**3 + 122*l + 1/135*l**6 + 0 + 0*l**2. Let a(m) = 0. What is m?
-1, 0, 4
Let a(q) = -2*q**3 - 14*q**2 + 496*q - 2046. Let l(i) = 2*i**3 + 14*i**2 - 498*i + 2042. Let m(w) = -4*a(w) - 3*l(w). Solve m(d) = 0.
-21, 7
Let l(n) be the second derivative of n**6/120 + 37*n**5/80 - 77*n**4/12 + 3639*n. Factor l(v).
v**2*(v - 7)*(v + 44)/4
Let g be ((-34225)/2220)/(-1 - (-2)/(-8)) - 7. Suppose g*c + 6 - 2/3*c**2 = 0. What is c?
-1, 9
Let m(p) be the first derivative of 0*p + 7/4*p**3 + 60 + 1/24*p**6 - 9/4*p**2 - 1/4*p**5 + 1/16*p**4. Solve m(o) = 0 for o.
-2, 0, 1, 3
Let f(d) be the third derivative of d**5/20 - 13*d**4/8 - 70*d**3 + 5*d**2 + 312. Factor f(a).
3*(a - 20)*(a + 7)
Factor -1359*z**4 + 144*z - 144*z**2 - 1361*z**4 + 44*z**3 + 2716*z**4.
-4*z*(z - 6)*(z - 3)*(z - 2)
Let i = 10412 + -416477/40. Let f(p) be the second derivative of 0*p**2 + 0 + 8*p - i*p**5 + 0*p**3 + 3/8*p**4. Suppose f(h) = 0. Calculate h.
0, 3
Let c(o) be the first derivative of o**4 - 340*o**3/3 + 3854*o**2 - 20172*o - 103. What is v in c(v) = 0?
3, 41
Let r(d) be the third derivative of d**8/1008 + 11*d**7/630 + 2*d**6/45 + 16*d**5/15 - d**2 + 15*d. Let z(q) be the third derivative of r(q). Factor z(s).
4*(s + 4)*(5*s + 2)
Factor -4*m**2 + 96 + 122*m**3 - 12 + 122*m + 40*m**2 - 124*m**3.
-2*(m - 21)*(m + 1)*(m + 2)
Let j be 5/(-14)*(728/(-16) - -14) + -11. Factor 0 + 1/4*p**3 - 1/2*p**2 + j*p.
p*(p - 1)**2/4
Let s be ((-21)/(-7))/(12/(-4)). Let b(j) = 6*j**2 - 12*j + 18. Let z(n) = n**2. Let u = 3 - -1. Let y(o) = s*b(o) + u*z(o). Solve y(k) = 0 for k.
3
Let q = 60 + -58. Factor -2*w**2 + 9*w**2 - 6*w**q - 5*w**2.
-4*w**2
Let f be 108/1998 + ((-882)/(-111) - 7). Determine n, given that -1/2*n**2 + 3/2*n - f = 0.
1, 2
Let k = 92/613 + -996187/8582. Let m = -231/2 - k. Suppose 3/7*u**3 + 3/7*u**2 - 3/7 - m*u = 0. What is u?
-1, 1
Let s(h) be the third derivative of -h**5/30 - 133*h**4/2 - 53067*h**3 + 1354*h**2. Factor s(d).
-2*(d + 399)**2
Suppose -6*k + 4*k - u - 425 = 0, 5*k + 1070 = -4*u. Let z be -1 - k/56*4/10. Find c such that 3/2*c**2 + c + z*c**3 + 0 = 0.
-2, -1, 0
Factor 12/5 + 1/5*c**3 - 4/5*c - 3/5*c**2.
(c - 3)*(c - 2)*(c + 2)/5
Let l be ((-79)/711)/((-24)/168). Determine p so that -1/9*p**3 - 2/3*p + 0 - l*p**2 = 0.
-6, -1, 0
Let k(f) be the first derivative of 3*f**4 + 37*f**3/15 - 21*f**2/10 + 2*f/5 + 378. Factor k(a).
(a + 1)*(4*a - 1)*(15*a - 2)/5
Let a be (-160)/(-7) - (153 + -148)*(-4)/(-5). Factor -4*j**3 + 8 - 216/7*j**2 - a*j.
-4*(j + 1)*(j + 7)*(7*j - 2)/7
What is s in -30/13 + 2/13*s**2 - 28/13*s = 0?
-1, 15
Let l be (-5)/(-9)*(9 - (-38526)/20). Let i = -1075 + l. Factor -5/6*r**3 - 1/6*r**2 + 0 - 1/2*r**4 + i*r.
-r*(r + 1)**2*(3*r - 1)/6
Let f(i) = 6*i**2 + 44*i - 17. Let k be f(-6). Let r be 39/k + 93/105. Let -9/7*y**3 - 12/7*y**2 + 3/7*y**5 + r*y**4 + 0 - 4/7*y = 0. Calculate y.
-1, -2/3, 0, 2
Let g(m) be the third derivative of m**8/448 - m**7/40 - m**6/5 + m**5/10 + 7*m**4/2 + 10*m**3 - 1168*m**2. Determine q, given that g(q) = 0.
-2, -1, 2, 10
Let l(w) be the third derivative of w**8/112 - 3*w**7/35 - w**6/40 + 3*w**5/10 + 6*w**2 - 35*w. Factor l(n).
3*n**2*(n - 6)*(n - 1)*(n + 1)
Factor 786*r**2 + 174*r**3 - 3*r**4 - 4860 - 97230*r - 2685*r**2 + 103818*r.
-3*(r - 45)*(r - 6)**2*(r - 1)
Let a(v) = 81*v - 807. Let g be a(10). Suppose -51*x + 202 + 53 = 0. Find w such that 5 - 17*w - 1/5*w**x - 58/5*w**g + 13/5*w**4 + 106/5*w**2 = 0.
1, 5
Let u = -71659/12 - -5972. Let j(n) be the second derivative of 0*n**2 + 0 + 0*