 o(p). Determine c so that j(c) = 0.
-2, 1
Suppose 43*c + 112 = 27*c. Let n be 10 + 28/c - 4. Suppose 1/11*w**n + 0 + 2/11*w = 0. Calculate w.
-2, 0
Suppose -12 + 3/4*n**3 + 6*n**2 - 7*n - 1/4*n**4 = 0. What is n?
-4, -1, 2, 6
Let i(p) be the first derivative of -36 - 3*p + 1/8*p**3 + 3/8*p**2. Factor i(j).
3*(j - 2)*(j + 4)/8
Let v(j) be the second derivative of -j**5/70 + 100*j**3/21 + 2*j + 3942. Factor v(q).
-2*q*(q - 10)*(q + 10)/7
Suppose -41*v = -40*v - 12. Let n(c) be the third derivative of v*c**2 + 0*c + 1/420*c**6 - 2/21*c**3 + 0 + 0*c**5 - 1/28*c**4. Let n(p) = 0. Calculate p.
-1, 2
Suppose 10*f - 5*f = 2*l + 5, 5*f - 15 = 0. Let q be 5 - l/(-15)*-15. Factor 3*t**3 + 3/4*t**4 + 0*t + q + 0*t**2.
3*t**3*(t + 4)/4
Suppose -2*f + 2*d = 2*f - 98, -2*d = -5*f + 122. Factor 78 - 105 - f*k**2 + 67 + 12*k + 4*k**3.
4*(k - 5)*(k - 2)*(k + 1)
Let g be (-118)/(-472)*(1 + -1). Let k(u) be the second derivative of -5/4*u**4 + 25/6*u**3 + g + 2*u + 5*u**2. Factor k(b).
-5*(b - 2)*(3*b + 1)
Let a(l) be the third derivative of 30*l**2 - 1/120*l**4 + 0 + 1/300*l**5 + 0*l**3 - 2*l. Solve a(k) = 0.
0, 1
Suppose 2/5*n**2 + 362/5*n + 0 = 0. Calculate n.
-181, 0
Let t(h) be the second derivative of -1/4*h**4 + 3*h - 6*h**2 + 1/14*h**7 + 16 + 4*h**3 - 3/4*h**5 + 1/10*h**6. Factor t(u).
3*(u - 1)**3*(u + 2)**2
Let l(v) = 4*v**2 + 2792*v + 484420. Let w(k) = 4*k + 2. Let r(c) = l(c) - 2*w(c). What is i in r(i) = 0?
-348
Suppose -108*w + 111*w - 12 = 0. Let y(v) be the first derivative of -6*v**2 - 1/8*v**w - 3/2*v**3 - 8*v + 4. Suppose y(h) = 0. What is h?
-4, -1
Let h be (-20 - -25 - (1 + 8)) + 28. Let w(u) be the third derivative of 0 + 1/6*u**6 + h*u**2 + 2/105*u**7 + 7/15*u**5 + 1/2*u**4 + 0*u**3 + 0*u. Factor w(i).
4*i*(i + 1)**2*(i + 3)
Let y(s) be the second derivative of -s**6/45 + s**5/12 + 28*s**4/9 + 17*s**3/6 - 9*s**2 - 2778*s. Determine j, given that y(j) = 0.
-6, -1, 1/2, 9
Let m = 18 + -34. Let q = m - -34. Find y such that q*y + 4*y**2 + y**2 - 23*y - 10 = 0.
-1, 2
Let w(x) be the second derivative of -x**8/8400 - x**7/1050 - x**6/450 + 55*x**3/6 - 4*x - 2. Let f(g) be the second derivative of w(g). Factor f(l).
-l**2*(l + 2)**2/5
Let x = 10 - 6. Let h = -14459 + 14469. Find l, given that 6*l**x + l**2 + 3*l**2 - h*l**4 + 2*l**3 - 4*l + 2*l**3 = 0.
-1, 0, 1
Let o(z) = -28*z**2 + 657*z + 321. Let j(f) = -3*f**2 - 8*f + 35*f - 6*f**2 + 108 + 192*f. Let b(r) = 17*j(r) - 6*o(r). Factor b(a).
3*(a - 15)*(5*a + 2)
Suppose -100*g - 552 = -104*g. Suppose 14*l + g = 180. Let -8/5*i + 2/5*i**l - 2/5*i**2 + 8/5 = 0. Calculate i.
-2, 1, 2
Let c(k) = -k**2 + 2*k - 2. Let z(d) = -3*d**2 - 76*d - 160. Let s(p) = -6*c(p) + 3*z(p). Solve s(u) = 0.
-78, -2
Let b(w) = w**3 + 9*w**2 - w - 31. Let s = 0 - -2. Let m(a) = 675199*a**2 + 2 - 6 + 0 - 675197*a**2 - 2. Let r(i) = s*b(i) - 11*m(i). Factor r(t).
2*(t - 2)*(t - 1)*(t + 1)
Suppose 4*l = -4*t + 185 - 137, -4*t = -2*l - 24. Factor -2/9*r**3 - 32/3*r + 26/9*r**2 + t.
-2*(r - 6)**2*(r - 1)/9
Let 648 - 11/2*s**3 + 190*s**2 - 1/2*s**4 - 678*s = 0. What is s?
-27, 2, 12
Let c(i) = -2*i**3 + 10*i**2 + 11*i + 6. Let k be c(6). What is z in -136*z + z**2 - 95*z + k*z**2 - 328 + 4297 + 105*z = 0?
63
Let q(f) be the first derivative of 77 - 3/11*f**2 + 2/33*f**3 + 4/11*f. Let q(c) = 0. What is c?
1, 2
Let o(k) be the first derivative of -13/2*k**2 - 4 + 2/9*k**3 - 1/12*k**4 + 0*k + 1/90*k**5. Let j(u) be the second derivative of o(u). Factor j(r).
2*(r - 2)*(r - 1)/3
Suppose 2 - 2*i**4 + 1549*i**2 + i**3 - 4*i**4 - 785*i**2 - 15*i - 746*i**2 = 0. Calculate i.
-2, 1/6, 1
Let v(n) = -n - 2. Suppose -3*i - 3 = 9, 2*q + 2*i + 18 = 0. Let h be v(q). Solve 8*m + 10*m**2 + 13 + h - 9*m**2 = 0 for m.
-4
Let y(c) = 28*c - 364. Suppose d + 5 = 0, -5*a + 4*a - 12 = 5*d. Let r be y(a). Factor 0 + r*o + o**3 - 2/3*o**2 - 1/3*o**4.
-o**2*(o - 2)*(o - 1)/3
Find v, given that 9216/7 + 4/7*v**3 + 9600/7*v + 388/7*v**2 = 0.
-48, -1
Let o(v) be the second derivative of -v**7/126 - 29*v**6/45 - 359*v**5/30 + 884*v**4/9 - 4681*v**3/18 + 961*v**2/3 - 5*v - 382. Suppose o(l) = 0. What is l?
-31, 1, 2
Let a(v) be the first derivative of v**8/84 - 4*v**7/105 + v**6/30 + 54*v**2 - 23. Let o(l) be the second derivative of a(l). Solve o(b) = 0.
0, 1
Let g(k) = 3*k**2 - 19*k. Let w(t) = -562*t**2 + 2*t - 7*t + 563*t**2 + 2*t. Let l(u) = -g(u) + 2*w(u). Let l(r) = 0. Calculate r.
0, 13
Determine t, given that -18686 + 2*t**5 - 844*t**2 + 18558 - 680*t - 245*t**3 + 100*t**4 - 46*t**2 + 5*t**5 = 0.
-16, -1, -2/7, 4
Let 1036/13*k - 2/13*k**3 + 0 - 134/13*k**2 = 0. What is k?
-74, 0, 7
Factor -555*c + 124 - 5*c**3 - 375 - 49*c**2 - 406 + 27 - 81*c**2.
-5*(c + 2)*(c + 3)*(c + 21)
Let a = -2544/7 - -364. Suppose -71*o + 45*o = -63*o + 148. Let 2/7*i**3 - 2/7*i**o + 0*i + a*i**2 + 0 = 0. Calculate i.
-1, 0, 2
Let v = -330 - -358. Factor 3*x**4 - 8 - 55*x**3 + 18*x**2 + 62*x**3 - 7*x**4 - v*x.
-(x - 2)**2*(x + 2)*(4*x + 1)
Let s(y) be the first derivative of y**6/60 - y**5/15 + y**4/12 - 17*y**2/2 - 17. Let w(l) be the second derivative of s(l). Solve w(p) = 0 for p.
0, 1
Let h be 56/3*(-15)/(-10). Let w = -56 + 58. Factor -h*v**w + 107*v**3 - 82*v**3 + 2*v - 6*v**4 - v + 3*v.
-v*(v - 2)**2*(6*v - 1)
Let m(t) be the second derivative of t**5/240 - 11*t**4/48 + 121*t**3/24 + 69*t**2/2 + 12*t + 4. Let y(a) be the first derivative of m(a). Solve y(w) = 0.
11
Let j = 239 + -237. Determine z, given that -28*z**4 - 45*z**3 - 3*z**3 + 12*z**3 + z**j - 9*z**2 = 0.
-1, -2/7, 0
Let q(f) be the second derivative of -3*f**5/160 + 19*f**4/32 - 25*f**3/8 + 6*f**2 + 121*f - 49. Suppose q(u) = 0. Calculate u.
1, 2, 16
Let r be (-1 + 0)/((-4)/16) + -2. Factor 0*s + s + 28*s + 65*s - 14*s**r + 28.
-2*(s - 7)*(7*s + 2)
Let a(j) be the second derivative of j**7/21 + 2*j**6/5 - 13*j**5/5 + 2*j**4 + 25*j**3/3 - 18*j**2 + 8*j + 54. Determine y, given that a(y) = 0.
-9, -1, 1, 2
Let t(d) = d + 14. Let w be t(-11). Let l(x) = x**3 - 99*x**2 + 82*x + 1570. Let k be l(98). Factor -6/7*s**4 + 0*s**w - 3/7*s**5 + 3/7*s + 6/7*s**k + 0.
-3*s*(s - 1)*(s + 1)**3/7
Let y = -76 - -81. Let z(v) = v**3 - 2*v**2 + 3*v - 9. Let x be z(y). Determine r, given that x*r - 4*r**2 - 153*r + 16 + 72*r = 0.
-2, 2
Let l = -19 - -29. Suppose -4*g - 5*x - 8 = -36, -3*g + 2*x - 2 = 0. Factor -8*n**g - l - 10*n - 25*n + 0*n - 7*n.
-2*(n + 5)*(4*n + 1)
Let y(j) be the third derivative of j**7/2520 - 7*j**6/720 + j**5/10 + 205*j**4/24 + 198*j**2. Let u(f) be the second derivative of y(f). Factor u(h).
(h - 4)*(h - 3)
Let q(t) be the second derivative of t**5/5 + 4*t**4/3 - 14*t**3 + 1203*t. Find x, given that q(x) = 0.
-7, 0, 3
Let r(t) be the second derivative of t**4/132 + 31*t**3/33 - 195*t**2/22 + 2994*t. Factor r(n).
(n - 3)*(n + 65)/11
Suppose 0*y - 18 = -6*y. Let -28 - 5*a**4 + 40*a**y - 44870*a**2 + 44755*a**2 + 140*a - 32 = 0. Calculate a.
1, 2, 3
Factor -25 - 205/6*z + 1/2*z**3 + 16/3*z**2.
(z - 5)*(z + 15)*(3*z + 2)/6
Let k(o) be the third derivative of -o**5/120 - 23*o**4/16 - 45*o**3 + o**2 + 933*o. Factor k(n).
-(n + 9)*(n + 60)/2
Let g be 3/(-5) + (-22)/(440/(-92)). Let y be 13 + -5 + (-1 - g). Suppose y + 69/4*o - 27/4*o**3 + 45/2*o**2 = 0. Calculate o.
-1/3, 4
Let t(x) be the second derivative of -x**6/90 + x**5/5 + 8*x**4/3 + 233*x**3/6 - 5*x + 16. Let y(w) be the second derivative of t(w). What is o in y(o) = 0?
-2, 8
Let s(c) be the third derivative of 0*c**3 + 1/112*c**8 + 0*c**5 + 0 + 0*c**4 + 2/5*c**6 - 67*c + 4/35*c**7 + c**2. Factor s(m).
3*m**3*(m + 4)**2
Let u(h) = -h**2 + 7*h - 8. Let b be u(5). Factor -968*t - 78*t**2 - 37 - 10*t**b - 2*t**3 + 37.
-2*t*(t + 22)**2
Let o(i) be the first derivative of -1/5*i**5 + 0*i**2 - 7/3*i**3 + 0*i - 4 - 2*i**4. Factor o(j).
-j**2*(j + 1)*(j + 7)
Let p(x) be the first derivative of -4*x**3/9 + 1688*x**2/3 - 712336*x/3 + 2948. Factor p(d).
-4*(d - 422)**2/3
Let 0*x**3 + 0 + 0*x**2 + 0*x + 3/2*x**4 - 1/2*x**5 = 0. Calculate x.
0, 3
Let n = -2 - -2. Suppose -269534*q + 269540*q = 0. What is f in -1/2*f**4 + n*f**2 + q + 0*f - f**3 = 0?
-2, 0
Let k(o) = 85*o - 338. Let q be k(4). Suppose 2*b = 3*v + 15, -4*b + 0*b - 5*v = 3. Let -48*x**b + x + 49*x**3 - q*x = 0. Calculate x.
-1, 0, 1
Let f = 1065 + -1055. Suppose -f*p + 31 = 11. Factor -5/3*