q). Factor s(h).
h**2*(h - 5)
Let h(n) = 12*n**2 + 979*n + 570. Let y be h(-81). Let f(g) be the second derivative of -g**4 + 6*g**2 + 1 - 13/2*g**y + 39/20*g**5 + 2*g. Factor f(c).
3*(c - 1)*(c + 1)*(13*c - 4)
Let w(q) be the first derivative of 0*q - 46 - 1/2*q**2 - 5/2*q**3. Determine b so that w(b) = 0.
-2/15, 0
Let i(w) be the second derivative of 1/36*w**4 - 1/12*w**3 - 1/6*w**2 + 0 - 46*w. Factor i(k).
(k - 2)*(2*k + 1)/6
Let b(r) be the first derivative of -20*r**3/3 - 94*r**2 + 352*r - 1162. Factor b(t).
-4*(t + 11)*(5*t - 8)
Let y be (-6)/1 - 300/(-50). Let h(l) be the first derivative of 0*l + 4/9*l**3 + 3 + y*l**2 - 4/15*l**5 + 7/9*l**6 - 7/6*l**4. Let h(z) = 0. Calculate z.
-1, 0, 2/7, 1
Let x(i) be the second derivative of -5*i**4/12 - 1805*i**3/3 - 651605*i**2/2 + 7114*i. Solve x(h) = 0.
-361
Determine c, given that c**5 + 66*c + 216*c + 68*c + 75*c - 328*c**2 + 12*c**4 - 18*c**3 + 232*c - 324 = 0.
-9, 1, 4
Factor -15*a - 3*a**2 - 65*a**3 + 3*a**4 + 43*a**3 + 6*a + 31*a**3.
3*a*(a - 1)*(a + 1)*(a + 3)
Suppose -4*z**4 - 3449246499*z + 7401*z**3 - 9390597*z**2 + 1569*z**3 - 5931027*z**2 + 3814*z**3 - 1630223347204 + 11610564883*z = 0. What is z?
799
Suppose -4*r - m - 27 = -101, -12 = -r + 3*m. Suppose -37*v**4 + 8*v - r*v**4 - 3 - 2 - 78*v - 8*v**2 - 170*v**3 - 172*v**2 = 0. Calculate v.
-1, -1/11
Suppose 4*q = 1 + 19. Suppose n = 21 - q. Let -n*r - 10*r - 55*r**2 - 9*r - 5 - 25*r**3 = 0. What is r?
-1, -1/5
Let m(w) be the first derivative of 3*w**4/4 - 27*w**3 - 600*w**2 - 2052*w - 11719. Factor m(l).
3*(l - 38)*(l + 2)*(l + 9)
Let p(z) be the third derivative of -z**7/105 + 2*z**6/3 - 157*z**5/10 + 117*z**4 - 324*z**3 + 704*z**2. Factor p(t).
-2*(t - 18)**2*(t - 3)*(t - 1)
Let d(h) be the first derivative of 2*h**5/85 - h**4/34 - 8*h**3/17 - 938. Factor d(m).
2*m**2*(m - 4)*(m + 3)/17
Determine o so that -1000/13 - 2/13*o**2 + 90/13*o = 0.
20, 25
Let u(g) be the second derivative of -1/35*g**6 + 0*g**2 + 0*g**3 + 39/70*g**5 + 0 + 0*g**4 + 86*g. Factor u(i).
-6*i**3*(i - 13)/7
Factor -178/11*v**2 + 90/11*v + 0 + 86/11*v**3 + 2/11*v**4.
2*v*(v - 1)**2*(v + 45)/11
Let a(s) be the first derivative of s**4/8 - 3*s**2/4 - 11*s + 42. Let n(x) be the first derivative of a(x). Factor n(h).
3*(h - 1)*(h + 1)/2
Factor 411*w - 29*w**2 - 141*w + 26*w**2.
-3*w*(w - 90)
Let k(p) be the second derivative of -31*p + 0 - 19/4*p**4 - 51/2*p**2 + 3/20*p**5 + 35/2*p**3. Factor k(w).
3*(w - 17)*(w - 1)**2
Let l(u) be the first derivative of 21/2*u**2 - 6/5*u**5 - 6*u - 29 + 21/4*u**4 + 0*u**3. Let v(t) = -t**3 + t**2 - t. Let x(g) = -l(g) - 18*v(g). Factor x(a).
3*(a - 2)*(a + 1)**2*(2*a - 1)
Suppose -88 = 19*g - 41*g. Let f be 14/10 - (-9)/15. Solve 0 + 0*s**3 - 2/9*s - 4/9*s**f + 2/9*s**5 + 4/9*s**g = 0.
-1, 0, 1
Suppose 10 = 38*l - 36*l. Suppose 4*i - 20 = 2*p - l*p, -i - 3*p = -14. Solve -1 - 27*f**i - 5 - 141 + 66*f - 192*f = 0 for f.
-7/3
Let d = 8857/7 - 35421/28. Let z = -30 + 121/4. Let -d*r**3 + 3/4*r**2 - 3/4*r + z = 0. Calculate r.
1
Let f(u) be the first derivative of -u**5/30 - 3*u**4/2 - u**2 - 58*u + 80. Let d(g) be the second derivative of f(g). Determine t so that d(t) = 0.
-18, 0
Let g(w) = 14*w**2 - 29*w - 241. Let a(v) = 5*v**2 - 9*v - 80. Let d(m) = 11*a(m) - 4*g(m). Let n be d(21). Solve 2/3*x**2 - 4/3*x + n = 0 for x.
0, 2
Let b(p) be the first derivative of -9583*p**4/16 + 13357*p**3/6 - 680*p**2 + 72*p + 8266. Factor b(c).
-(7*c - 18)*(37*c - 4)**2/4
Suppose 18*w - 129 = -21. Find y such that 18*y**2 - 9 + 3*y**5 - 5*y**3 - 6*y**3 + 3*y + w*y**3 - 9*y**4 - y**3 = 0.
-1, 1, 3
Solve 48*d**3 - 124*d**2 - 32*d**3 - 12*d**3 + 240 + 53*d + 59*d = 0 for d.
-1, 2, 30
Let s(t) = t**2 - 11*t + 2. Let k(l) = l**3 + 6*l**2 + 3*l + 29. Let f be k(-6). Let b be s(f). Solve -1/3*i**b - 1/3*i + 2/3 = 0 for i.
-2, 1
Let b(d) be the third derivative of 1/48*d**5 + 9*d**2 - 5/6*d**3 - 1/2880*d**6 + 0 - 25/48*d**4 + 0*d. Let o(u) be the first derivative of b(u). Factor o(a).
-(a - 10)**2/8
Let i(m) be the third derivative of 0*m + 26 - 1/1155*m**7 + 1/330*m**6 - 1/616*m**8 + 0*m**5 + 2*m**2 + 0*m**3 + 0*m**4. Factor i(v).
-2*v**3*(v + 1)*(3*v - 2)/11
Suppose 95 = 9*y + 50. Let z(n) be the third derivative of 0*n + 5*n**2 - 1/12*n**4 + 4/15*n**3 + 0 + 1/150*n**y. Factor z(k).
2*(k - 4)*(k - 1)/5
Let l = 112 + -109. Factor -54*o**2 - 96*o - 390*o**l + 387*o**3 + 0*o.
-3*o*(o + 2)*(o + 16)
Let v(w) be the first derivative of -5*w**3 + 603*w**2 - 480*w - 11670. Factor v(g).
-3*(g - 80)*(5*g - 2)
Let l(z) be the second derivative of 2 + 10*z + 1/6*z**4 - 1/12*z**6 + 3/20*z**5 - 2/3*z**3 + 0*z**2 + 1/84*z**7. Factor l(o).
o*(o - 2)**3*(o + 1)/2
Let h be ((5 - 4) + -1)/2. Let n(w) = -3*w + h - 4*w - 1 - 6 - 13*w**2. Let x(f) = 4*f**2 + 2*f + 2. Let i(b) = 4*n(b) + 14*x(b). Factor i(z).
4*z**2
Solve -158*x - 2/5*x**2 + 792/5 = 0 for x.
-396, 1
Let s(w) be the second derivative of -w**4/3 + 56*w**3 - 328*w**2 - w + 61. Factor s(q).
-4*(q - 82)*(q - 2)
Let h(g) be the third derivative of g**6/660 - 7*g**5/165 + 7*g**4/132 + 26*g**3/11 - 5*g**2 + 44*g. Let h(d) = 0. What is d?
-2, 3, 13
Let a = 4392911/5 - 878582. Find x such that 605 + 22*x + a*x**2 = 0.
-55
Let c(i) = -40*i**2 + 35*i - 34. Let t(y) = 52*y**2 - 36*y + 36. Let b(v) = 4*c(v) + 3*t(v). Find p, given that b(p) = 0.
1, 7
Let j(t) = -27*t**3 + 3*t + 69*t**3 - 3*t**2 - 43*t**3 + 9. Let q be j(-3). Find g such that -1/5*g**2 - 8/5*g**4 + 4/5*g**5 + g**3 + 0*g + q = 0.
0, 1/2, 1
Let u(n) be the first derivative of -2*n**5/75 + 2*n**4/15 + 26*n**3/45 - 28*n**2/15 - 8*n + 876. Let u(k) = 0. What is k?
-2, 3, 5
Let n(u) be the first derivative of -1/15*u**3 + 196 - 13/5*u + 7/5*u**2. Factor n(b).
-(b - 13)*(b - 1)/5
Factor 4*k + k**2 + 48*k + 2142 - 2151 + 11*k**2.
(2*k + 9)*(6*k - 1)
Let b(s) be the third derivative of -15*s**6/32 - 41*s**5/16 + 11*s**4/6 - s**3/2 - 104*s**2 + 3*s. Factor b(v).
-(v + 3)*(15*v - 2)**2/4
Let f(t) = -t**4 + 18*t**3 + 49*t**2 - 140*t + 78. Let p(b) = -4*b**4 + 72*b**3 + 197*b**2 - 558*b + 311. Let m(k) = 9*f(k) - 2*p(k). Factor m(x).
-(x - 20)*(x - 1)**2*(x + 4)
Let o(u) be the second derivative of -1/98*u**7 - 41/14*u**3 + 0 - 15/7*u**2 - 16/7*u**4 - 69/70*u**5 - 165*u - 1/5*u**6. Factor o(l).
-3*(l + 1)**4*(l + 10)/7
Let m(w) = -1092662*w + 325. Let t be m(-5). Solve -5*i**3 + t + 1208*i**2 - 148965*i - 10170*i + 337*i**2 = 0 for i.
103
Let b = 368 + -158. Factor -4*g + g**4 - 208*g**3 + 4 - 7*g**2 + b*g**3 + 4*g**2.
(g - 1)**2*(g + 2)**2
Suppose 17*a = -3*l + 37, 3*a = -14*l + 10*l + 10. Let 3/7*i**3 + 0*i + 0 - 6*i**a = 0. Calculate i.
0, 14
Let l(g) be the third derivative of g**8/2184 - g**7/91 + 21*g**6/260 - 17*g**5/78 + 3*g**4/13 + 548*g**2. Solve l(q) = 0 for q.
0, 1, 4, 9
Let j = -116726 - -817084/7. Factor -j*h**3 + 12/7*h**2 - 22/7*h + 12/7.
-2*(h - 3)*(h - 2)*(h - 1)/7
Let v(h) be the third derivative of 17*h**5/12 + 55*h**4/3 + 25*h**3/2 + 8900*h**2. Factor v(r).
5*(r + 5)*(17*r + 3)
Suppose 0 = 5*f + 8 - 33. Let d(t) = -t**2 + 38*t - 278. Let i be d(28). Factor -15*k**3 - 9*k**i - f*k**4 + 12*k**2 - 13*k**2.
-5*k**2*(k + 1)*(k + 2)
Factor -2/3*h**2 + 20*h - 352/3.
-2*(h - 22)*(h - 8)/3
What is b in 15*b**5 + 19*b - 19*b - 34*b**5 + 22*b**5 + 2*b**3 - 5*b**4 = 0?
0, 2/3, 1
Let i(l) be the third derivative of -l**7/420 - l**6/48 - l**5/20 + l**4/12 + 2*l**3/3 + 946*l**2. Factor i(j).
-(j - 1)*(j + 2)**3/2
Let b be (0 + 4/5)*(9 - -1 - 5). Let l(i) be the second derivative of -1/84*i**7 + 0 + 0*i**6 + 0*i**3 + 1/40*i**5 + 0*i**b + 0*i**2 - 16*i. Factor l(u).
-u**3*(u - 1)*(u + 1)/2
Factor -527/5*a + 1/10*a**2 + 277729/10.
(a - 527)**2/10
Let u(g) be the second derivative of -5/6*g**4 - 4*g**2 + 4*g**3 + 0 - 53*g. Factor u(y).
-2*(y - 2)*(5*y - 2)
What is p in -24*p**2 + 83874*p**4 - 5*p**3 - 83875*p**4 - 5*p**3 = 0?
-6, -4, 0
Let w = 16604 - 16600. Let r(n) be the first derivative of -8/21*n**3 - w - 3/7*n**2 - 1/14*n**4 + 0*n. Find t, given that r(t) = 0.
-3, -1, 0
Suppose -4*d - 23 + 108 = -j, d + 3*j = 18. Factor 15*z**3 - 63*z**3 + 3*z**2 + 21*z**3 + 3*z**4 + d*z**3.
3*z**2*(z - 1)**2
Let h(n) be the first derivative of 3*n**6/8 - 81*n**5/40 - 317*n**4/32 - 11*n**3/8 + 315*n**2/16 + 49*n/4 + 2695. Let h(m) = 0. Calculate m.
-2, -7/6, -1/3, 1, 7
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