+ 2009. Suppose w(m) = 0. What is m?
0, 4
Solve 47*m - 68*m**3 - 2*m**5 + 7*m - 9*m + 3*m + 22*m + 156*m**2 - 42*m**4 - 114 = 0 for m.
-19, -3, -1, 1
Let x = 15707 - 15707. Let s(c) be the second derivative of x*c**2 - 4/21*c**3 + 1/42*c**4 + 19*c + 0. Find u, given that s(u) = 0.
0, 4
Let g(a) = a**2 + 183*a + 543. Let y be g(-3). Factor 2/7*x - 2/7*x**y + 2/7 - 2/7*x**2.
-2*(x - 1)*(x + 1)**2/7
Solve 376*y**2 + 210*y - 5*y**3 - 2*y**2 - 900*y + 2*y**3 - 1392 + 325*y**2 = 0.
-1, 2, 232
Let a(j) = j**3 - 5*j**2 + 4*j - 2. Let w be a(5). Let h be w*(27/6)/9. Determine r so that -24*r + 3 + h*r + 3*r**2 + 5*r = 0.
1/3, 3
Let y(z) be the first derivative of 1/480*z**5 + 7/192*z**4 + 16 + 0*z + 1/8*z**3 - 11/2*z**2. Let w(h) be the second derivative of y(h). Factor w(a).
(a + 1)*(a + 6)/8
Let k(j) be the third derivative of j**6/240 + 2*j**5/3 - 27*j**4/16 - 3437*j**2. Solve k(a) = 0 for a.
-81, 0, 1
Let k = -234663/4 - -58666. Factor -k*a**2 - 1/4 + 1/2*a.
-(a - 1)**2/4
Factor 310*z**3 + 11*z**4 - 7*z**2 + 13*z**4 + 647*z**2 - 29*z**4.
-5*z**2*(z - 64)*(z + 2)
Let g = 355 - 349. Let d be ((-336)/945)/((-4)/g). What is c in -2/5*c + d*c**2 + 0 - 2/15*c**3 = 0?
0, 1, 3
Let u = 207660818/479843 + 36/36911. Factor u*h + 730/13*h**4 + 50/13*h**5 + 3572/13*h**3 + 6836/13*h**2 + 1682/13.
2*(h + 1)**3*(5*h + 29)**2/13
Suppose -681*d + 306 + 141*d**2 + 6746*d**3 - 13497*d**3 + 6745*d**3 = 0. What is d?
1/2, 6, 17
Factor -6*h - 4*h + h**2 - h - 39 + 13.
(h - 13)*(h + 2)
Let t(q) be the first derivative of q**6/120 - 17*q**5/80 + q**4/2 + 16*q**3/3 - 2*q + 105. Let s(l) be the third derivative of t(l). Factor s(r).
3*(r - 8)*(2*r - 1)/2
Let o be ((-14504)/(-96))/37 - 4. Let d(i) be the third derivative of 0 + 0*i - 25*i**2 - 1/6*i**3 - o*i**4 - 1/60*i**5. Factor d(r).
-(r + 1)**2
Suppose -5*m + 25 = -8*d + 9*d, 2*d = m + 6. Let r**4 + 3*r**m - 223*r**3 - 8*r + 235*r**3 - 4*r**2 - 4*r**5 = 0. What is r?
-1, 0, 1, 2
Factor -56 + 58*s**2 + 869*s**3 - 2*s**4 - 482*s**3 - 441*s**3 + 54*s.
-2*(s - 1)**2*(s + 1)*(s + 28)
Let r(h) be the first derivative of 2*h**3/21 + h**2 + 4731. Factor r(n).
2*n*(n + 7)/7
Let c(g) = -g**2 - 11*g + 5*g + 0 - 13*g + 2. Let b be c(-19). Factor 2*f - 4*f + f**b - f**2 + f**2.
f*(f - 2)
Let y be 138/(-1380) - (36/(-8) - -4). Determine w, given that -1/5*w**3 + 0 - y*w - 3/5*w**2 = 0.
-2, -1, 0
Let a be (-6622)/(-35) + 5/(-25). Let x = a + -185. Solve 0 - 1/4*p**5 + 7/4*p**2 - 1/2*p + 5/4*p**x - 9/4*p**3 = 0.
0, 1, 2
Let a be 15 + 246/(-20) + 1/(-2)*(-12)/(-20). Factor -7/5*t**2 - 16/5*t - 1/5*t**3 - a.
-(t + 2)**2*(t + 3)/5
Let z = -162 + 291. Let j(k) = -k**3 + 2*k**2 + 6*k - 5. Let d be j(3). Solve 129*u - d*u**2 - z*u + 4 = 0.
-1, 1
Let d(r) be the third derivative of 5*r**7/42 + r**6/3 - r**5/6 - 5*r**4/3 - 5*r**3/2 - 778*r**2. Factor d(h).
5*(h - 1)*(h + 1)**2*(5*h + 3)
Let f(y) be the second derivative of 67*y + 1/2*y**3 - 9/2*y**2 + 0 + 3/16*y**4 - 3/80*y**5. Factor f(s).
-3*(s - 3)*(s - 2)*(s + 2)/4
Let r(h) = 8*h**2 - 155*h - 54. Let q be r(20). Suppose 19*t - 30 - q = 0. Factor 4/15*b**t + 0 + 0*b + 0*b**2 - 2/15*b**5 + 0*b**3.
-2*b**4*(b - 2)/15
Let g be (-7728)/(-168) + (-344)/8. Factor 0 + 10/19*v**2 + 8/19*v + 2/19*v**g.
2*v*(v + 1)*(v + 4)/19
Let u(x) be the first derivative of -3*x**5/80 + x**4 + x**3/8 - 6*x**2 + 140*x - 263. Let v(g) be the first derivative of u(g). Suppose v(r) = 0. Calculate r.
-1, 1, 16
Let l = -525231/20 - -26262. Let x(b) be the second derivative of 0 + 6*b**2 - 33*b + l*b**5 - 4*b**3 + 1/4*b**4. Find q such that x(q) = 0.
-2, 2/3, 1
Let w = -425 - -427. Suppose -w*o - 7*o = 2*o. What is k in o - 69/2*k**4 - 15/2*k**5 - 45*k**3 - 6*k**2 + 12*k = 0?
-2, -1, 0, 2/5
Let a(y) = 5*y + 206 - 192 - y**2 - 9*y. Let n(c) = 2. Let t(v) = 3*a(v) - 21*n(v). Factor t(m).
-3*m*(m + 4)
Let a = 84661/2 + -29728. Solve 355*p - a - 5/2*p**2 = 0 for p.
71
Find u, given that 30*u**3 - 40/3*u**2 - 8*u - 2*u**5 + 0 - 20/3*u**4 = 0.
-6, -1/3, 0, 1, 2
Let z(u) = -u**3 - 30*u**2 - 19*u + 108. Let x be z(-28). Let q = x + 2792/3. Factor -4/9*w**4 + 4/3 + 0*w**3 - 32/9*w + q*w**2.
-4*(w - 1)**3*(w + 3)/9
Let p(g) be the second derivative of -g**4/3 + 473*g**3/12 - 59*g**2/4 - 2029*g. Suppose p(v) = 0. What is v?
1/8, 59
Let o(k) be the second derivative of k**5/5 - 16*k**4/3 + 110*k**3/3 + 1538*k + 5. Factor o(y).
4*y*(y - 11)*(y - 5)
Let o(r) be the second derivative of -r**4/12 + 13*r**3/6 - 11*r**2 - 3*r + 24. Solve o(l) = 0.
2, 11
Let b be (-6)/30*1 - (880/100 - 11). Factor -1/3*g**3 + 10/3*g - 8/3 - 1/3*g**b.
-(g - 2)*(g - 1)*(g + 4)/3
Let t = -21823 - -458287/21. Let l(q) be the second derivative of 1/42*q**4 + 0*q**2 + t*q**3 + 0 - 32*q. Factor l(s).
2*s*(s + 4)/7
Let 9408 + 36*t**3 - 9716*t + 820/3*t**2 - 4/3*t**4 = 0. What is t?
-16, 1, 21
Let m(j) be the first derivative of -44*j**5 + 845*j**4/4 + 145*j**3/3 - 10*j**2 + 1815. Suppose m(s) = 0. What is s?
-1/4, 0, 1/11, 4
Let g = 621281/724787 - 5/103541. Find a such that 4/7 + 2/7*a**2 - g*a = 0.
1, 2
Let o = 829/5 - 165. Let f(t) be the first derivative of -4/15*t**3 - 1/40*t**4 - o*t**2 + 0*t + 4. Factor f(s).
-s*(s + 4)**2/10
Let v = 446259 + -5804587/13. Let f = v + 248. Let 0 - 6/13*n + f*n**2 + 2/13*n**3 = 0. Calculate n.
-3, 0, 1
Suppose -4*r - 314*c + 8 = -312*c, r - 12 = -3*c. Find i such that -1/4*i**5 + 0 - 1/2*i**4 + 1/4*i**3 + 1/2*i**2 + r*i = 0.
-2, -1, 0, 1
Let j(o) be the second derivative of -41/72*o**4 + 133/36*o**3 + 1/40*o**5 + 49/12*o**2 + 0 + 10*o. Factor j(l).
(l - 7)**2*(3*l + 1)/6
Let z(g) be the third derivative of -941*g**6/24 + g**5/6 + 4705*g**4/24 - 5*g**3/3 + 4009*g**2. Factor z(y).
-5*(y - 1)*(y + 1)*(941*y - 2)
Let v(l) be the third derivative of l**8/84 - 44*l**7/105 - l**6/15 + 472*l**5/5 + 915*l**4/2 + 900*l**3 - 1163*l**2. Find x, given that v(x) = 0.
-6, -1, 15
Let w(b) be the second derivative of -b**4/32 + 67*b**3/16 + 51*b**2/4 - 2*b + 33. Let w(r) = 0. What is r?
-1, 68
Let i(g) be the third derivative of -g**6/72 + 17*g**5/12 - 1445*g**4/24 + 29*g**3/3 + 23*g**2. Let s(d) be the first derivative of i(d). Solve s(y) = 0.
17
Suppose -7/4*m + 0 - 1/8*m**4 - 5/8*m**2 + m**3 = 0. What is m?
-1, 0, 2, 7
Let h(x) be the second derivative of -56/33*x**3 + 12/11*x**2 + 5/22*x**5 - 103 - 2*x + 5/6*x**4. Factor h(y).
2*(y + 3)*(5*y - 2)**2/11
Let u(s) be the first derivative of -4*s**5/5 + 14*s**4 - 140*s**3/3 - 100*s**2 + 639. Let u(l) = 0. What is l?
-1, 0, 5, 10
Let w(g) be the third derivative of -g**6/480 - 21*g**5/80 - 341*g**4/32 - 961*g**3/24 - 605*g**2. Suppose w(z) = 0. What is z?
-31, -1
Let l(k) be the first derivative of 5*k**2/2 + 105*k + 160. Let h be l(-21). Factor 0*r + h + 1/4*r**2.
r**2/4
Factor -22*h**2 - 93*h**2 + 139*h**2 - 22*h**2 - 44*h.
2*h*(h - 22)
Let a(x) = 3*x**3 + 3*x**2 - 7*x + 3. Let r be a(1). Let 12*o**4 + 58*o**3 - 2*o**3 + 24*o + 40*o**2 + 41*o**2 - 13*o**r = 0. What is o?
-3, -1, -2/3, 0
Let k be 4/46 - 114/1311. Let a(u) be the third derivative of -1/2*u**4 - 1/70*u**7 - 2*u**3 + 3/20*u**5 + k*u + 1/20*u**6 + 9*u**2 + 0. Factor a(o).
-3*(o - 2)**2*(o + 1)**2
Let v be 4/12 - (-16)/6. Factor 45*w**2 + 7*w**3 + 9*w**4 - 8*w**4 - 19*w**v - 50*w.
w*(w - 5)**2*(w - 2)
Let b be (28/(-630)*66)/((-1)/5 + 43 + -44). Factor -8/9*f + b*f**3 - 16/9*f**2 + 0 - 2/3*f**4.
-2*f*(f - 2)**2*(3*f + 1)/9
Let q(w) = 1750*w + 5252. Let p be q(-3). Let m(n) be the first derivative of -9 + 256/7*n - 96/7*n**p - 20/7*n**3 - 1/7*n**4. Factor m(g).
-4*(g - 1)*(g + 8)**2/7
Solve -621/7*h**2 + 1020/7 - 3/7*h**4 + 120/7*h**3 + 276/7*h = 0 for h.
-1, 2, 5, 34
Let j(d) be the first derivative of -3*d**4/16 + 99*d**3/2 - 29403*d**2/8 - 1100. Factor j(a).
-3*a*(a - 99)**2/4
Suppose 26*w = 21*w - 3135. Let q = w + 630. Solve 3/2*s**2 + 0*s - 2 + 1/2*s**q = 0 for s.
-2, 1
Factor 0*d + 0*d**2 - 1/3*d**4 + 38*d**3 + 0.
-d**3*(d - 114)/3
Let d = -761511 + 761515. Let 0 + 2/13*c**5 + 0*c + 36/13*c**2 + 12/13*c**d - 50/13*c**3 = 0. What is c?
-9, 0, 1, 2
Factor 102*c - 7752075*c**3 - 5*c**4 + 75*c**2 + 7752177*c**3 - 370*c**2.
-c*(c - 17)*(c - 3)*(5*c - 2)
Let j(q) be the first derivative of 4*q**5/5 + 11*q**4 - 16*q**3 + 220. Let j(m) = 0. Calculate m.
-12, 0, 1
Suppose 48 = 19*a - 11*a. Let c(o) be the second derivative of 0 -