 be the second derivative of 3*l**5/40 - l**4/4 - 9*l**3/4 + 27*l**2/2 + 2*l - 4. Let b(c) = 0. What is c?
-3, 2, 3
Let w = 284/933 - -9/311. Factor w*t**2 + 1 - 4/3*t.
(t - 3)*(t - 1)/3
Let i(o) be the second derivative of -2/27*o**4 + 3*o - 1/27*o**3 + 0 + 1/30*o**5 + 2/9*o**2. Let i(r) = 0. What is r?
-2/3, 1
Let p(a) = -a**2 - 7*a + 3. Let j be p(-6). Let m be 0 + -2 - (5 - j). Let 6 - 3*g**m + 0 + 0 + 0 - 3*g = 0. Calculate g.
-2, 1
Let x(r) be the second derivative of r**6/1620 + r**5/135 - r**4/9 - 13*r**3/6 + 11*r. Let v(u) be the second derivative of x(u). Factor v(h).
2*(h - 2)*(h + 6)/9
Let y(r) be the first derivative of r**6/120 - r**5/15 + r**4/6 + 13*r**2 + 27. Let f(o) be the second derivative of y(o). Determine j, given that f(j) = 0.
0, 2
Let g(h) be the third derivative of 0 - 1/60*h**5 - 50/3*h**3 + 5/6*h**4 + 34*h**2 + 0*h. Determine x so that g(x) = 0.
10
Let v(k) be the first derivative of -k**8/420 - k**7/105 - 10*k**3 + 24. Let r(l) be the third derivative of v(l). Factor r(o).
-4*o**3*(o + 2)
Let o = -1861 + 1863. Suppose -2/15*a**o - 2/15*a + 2/15 + 2/15*a**3 = 0. Calculate a.
-1, 1
Let x(i) be the third derivative of i**7/630 - i**6/36 - i**5/60 + 35*i**4/18 + 98*i**3/9 + 42*i**2. Factor x(k).
(k - 7)**2*(k + 2)**2/3
Let h = -1490 + 1491. Let d(o) be the first derivative of 1/6*o**4 + 0*o + 0*o**2 - 2/9*o**3 - h. Factor d(f).
2*f**2*(f - 1)/3
Let z = 381607/72 + -5300. Let n = z - -1/8. Factor -2/3*f + 0 - 4/3*f**4 - n*f**5 - 20/9*f**2 - 8/3*f**3.
-2*f*(f + 1)**3*(f + 3)/9
Factor 448*d + 2/3*d**3 + 768 + 100/3*d**2.
2*(d + 2)*(d + 24)**2/3
Let h(g) be the second derivative of 9/4*g**4 + 7/2*g**3 + 3*g**2 - 3*g + 0 + 1/10*g**6 + 3/4*g**5. Let h(z) = 0. Calculate z.
-2, -1
Suppose -2*c = c - p - 2, -3*c + 5*p - 14 = 0. Let h = -49/11 + 365/77. What is z in -h + 3/7*z - 1/7*z**c = 0?
1, 2
Suppose -40 = 2*h - t, 2*h + 5*t = 2*t - 48. Let w be (12/(-7))/(6/h). Find n, given that -9*n**3 + 4*n**2 - w*n**3 - 10*n**2 = 0.
-2/5, 0
Let c(j) be the second derivative of 0*j**2 - 1/42*j**6 + 0*j**4 + 1/70*j**5 + 1/98*j**7 - 11*j + 0 + 0*j**3. Factor c(k).
k**3*(k - 1)*(3*k - 2)/7
Let q be (-4)/(-22) - 15/(-825). Let i be 2/6*6/10. Factor -2/5 + q*l + i*l**2.
(l - 1)*(l + 2)/5
Let i(a) be the first derivative of -46*a**5/45 + 47*a**4/9 - 82*a**3/9 + 56*a**2/9 - 8*a/9 + 376. Solve i(u) = 0 for u.
2/23, 1, 2
Factor 148/7*y**2 + 152/7*y + 32/7 + 4*y**3.
4*(y + 1)*(y + 4)*(7*y + 2)/7
Let q(j) = -j**2 - 9*j + 12. Let g be q(-10). Suppose 2*m**g - 5*m**2 - 2*m**2 + 2 - 9*m = 0. Calculate m.
-2, 1/5
Let g(l) = 25*l**3 + 16*l**2 - 119*l - 192. Let w(i) = 6*i**3 + 4*i**2 - 30*i - 48. Let u = -25 - -27. Let b(m) = u*g(m) - 9*w(m). Solve b(p) = 0 for p.
-2, 3
Let p(c) be the third derivative of 0*c - 3*c**2 + 0 - 5/12*c**4 + 4/3*c**3 + 1/30*c**5. Factor p(x).
2*(x - 4)*(x - 1)
Suppose 4*s + q = 29, 7*q + 24 = 4*s + 3*q. Let t(c) = -3*c**3 - 9*c**2 - 4*c + 16. Let d(o) = -o**3 - 3*o**2 - o + 5. Let g(n) = s*d(n) - 2*t(n). Factor g(z).
-(z - 1)*(z + 1)*(z + 3)
Let g(n) be the third derivative of -n**6/420 + 4*n**5/105 + 19*n**4/84 + 10*n**3/21 + 23*n**2 + 6. Let g(i) = 0. What is i?
-1, 10
Let w(z) be the second derivative of 0 - 1/72*z**4 - z + 1/3*z**3 - 1/540*z**6 + 1/120*z**5 + 0*z**2. Let i(m) be the second derivative of w(m). Factor i(l).
-(l - 1)*(2*l - 1)/3
Let x = -153 - -463/3. Let h be (6/(-5))/(306/(-20) + 150/10). Factor 2/3*p**3 + 0*p**2 + 0*p + x*p**h + 2/3*p**5 + 0.
2*p**3*(p + 1)**2/3
Let a(i) be the first derivative of -i**7/168 + i**6/24 - i**5/12 + 2*i**3 - 2. Let t(g) be the third derivative of a(g). Determine c so that t(c) = 0.
0, 1, 2
Let t = -4707903439/1910 + 2464871. Let y = t - -2/191. Find c, given that y*c**2 + 1/10*c**4 + 1/5*c**5 - 7/10*c**3 + 1/2*c - 1/5 = 0.
-2, -1, 1/2, 1
Suppose -127*q + 126*q = -165. Let n be -2 + 368/154 + 30/q. Factor -2/7*z**2 - n - 6/7*z.
-2*(z + 1)*(z + 2)/7
Let v(r) = -21*r**3 - 56*r**2 - 45*r - 14. Let y(i) = 64*i**3 + 169*i**2 + 135*i + 41. Let w(o) = 11*v(o) + 4*y(o). Factor w(z).
5*(z + 1)**2*(5*z + 2)
Let a(v) be the second derivative of 8/5*v**5 - 2/15*v**6 - 13*v + 0*v**2 + 0*v**3 - 16/3*v**4 + 0. Factor a(x).
-4*x**2*(x - 4)**2
Let l be 3 + (-21)/(-14)*(-296)/(-6). Let p = l - 536/7. Solve -6/7*j**3 + 0*j**4 + 0 + p*j + 0*j**2 + 3/7*j**5 = 0.
-1, 0, 1
Suppose -5 = -5*l + 2*j - 7*j, 2*l - j = 11. Let f(x) be the second derivative of 0*x**2 + 0*x**3 - 1/10*x**6 + 5*x + 0 + 0*x**l + 3/20*x**5. Factor f(u).
-3*u**3*(u - 1)
Let y = 2395 + -4789/2. Let -x**2 + 0 + 1/2*x**3 + y*x = 0. What is x?
0, 1
Let p(x) be the second derivative of -x**7/105 + x**6/60 + x**5/15 + 4*x**2 + 8*x. Let m(g) be the first derivative of p(g). Factor m(v).
-2*v**2*(v - 2)*(v + 1)
Factor 0 + 2/7*t**2 + 22/7*t.
2*t*(t + 11)/7
Let z = 6 + -5. Suppose 5*h + 2*l = -3*l + 35, -4*l + 16 = -2*h. Let -2/3*a - 1/3*a**h + z = 0. What is a?
-3, 1
Let h be ((-40)/6)/(6/81). Let y be ((-48)/32)/(h/8). Factor 2/15*o**3 + 0 - y*o**2 - 4/15*o.
2*o*(o - 2)*(o + 1)/15
Suppose 3/8*y**2 + 1/8*y - 1/8*y**3 - 3/8 = 0. What is y?
-1, 1, 3
Let a be 7/2*(-5 + (-78)/(-14)). Factor -566 + 9*m + 580 - m**a + 2*m**2.
(m + 2)*(m + 7)
Factor 578/3 + 1/6*c**2 + 34/3*c.
(c + 34)**2/6
Let i(n) be the second derivative of 6*n**2 + n**4 + 11/3*n**3 - 8*n + 1/10*n**5 + 0. Suppose i(l) = 0. What is l?
-3, -2, -1
Let o = -14 - -22. Suppose -11 = 2*f + 4*c - 1, 5*c = -4*f - o. Factor -1/4*i + 2*i**2 - 1/2 - 5/4*i**f.
-(i - 1)**2*(5*i + 2)/4
Let t(i) = -7*i**2 + 12*i - 36. Let y(x) = 8*x**2 - 12*x + 36. Let k be (-39)/(-6) - (-1)/(-2). Let n(h) = k*y(h) + 7*t(h). Suppose n(z) = 0. What is z?
6
Let p = -8 - -9. Factor 1 + p - 257*m**2 + 8*m - 5 + 268*m**2.
(m + 1)*(11*m - 3)
Let t(x) = 13*x**5 - 5*x**4 + 68*x**3 - 56*x**2 + 35*x + 11. Let v(n) = n**5 + n**4 + 2*n**3 + n + 1. Let j(d) = 2*t(d) - 22*v(d). Let j(o) = 0. What is o?
0, 1, 2, 3
Let c be -2 + 2 + 5/(100/60). Factor -3/2*t**2 - 1 + 1/2*t**4 + 5/2*t - 1/2*t**c.
(t - 1)**3*(t + 2)/2
Suppose -9 = 3*p + 3*g, -g + 1 = -2*p - 2*g. Suppose -4 = -0*n - p*n + 3*j, 5*n + 2*j - 10 = 0. Let -2/7*c**n - 2/7 - 4/7*c = 0. Calculate c.
-1
Find b, given that 93*b - 9/7*b**2 - 216/7 = 0.
1/3, 72
Let k = 19886 - 19882. Factor 3/2*a**k + 0*a + 0 - 5/2*a**3 - a**2.
a**2*(a - 2)*(3*a + 1)/2
Let f(g) = -11*g**4 - 97*g**3 + 141*g**2 - 18*g + 5. Let d(v) = v**4 - v**3 + v**2 + 2*v + 1. Let b(o) = 5*d(o) - f(o). Factor b(a).
4*a*(a - 1)*(a + 7)*(4*a - 1)
Let b(n) = -n**2 + 6*n - 2. Let z be b(5). Factor 2 - 11*f**2 - 4*f - 4*f**3 + 3*f**4 - z*f**2 + 1.
(f - 3)*(f + 1)**2*(3*f - 1)
Let q(u) = -5*u**3 + 2*u**2 + 1. Let r(a) = -5*a**3 - 311*a**2 + 4455*a + 16337. Let i(x) = 2*q(x) - r(x). Let i(n) = 0. Calculate n.
-3, 33
Factor -r**4 - 13*r - 19*r - 10*r**3 - 3*r**4 + 2*r**5 + 64*r**2 - 20*r**3.
2*r*(r - 4)*(r - 1)**2*(r + 4)
Let -190*w + 57*w**2 + 123*w**2 + 65 + 8*w**3 - 5*w**4 - 58*w**3 + 0*w**4 = 0. Calculate w.
-13, 1
Let x = -11695 + 736808/63. Let r = x - 2/9. Factor 0 - 1/7*w**4 + r*w**2 + 0*w**3 + 0*w.
-w**2*(w - 1)*(w + 1)/7
Suppose -7*x - 6 = -8*x. Let k(j) be the second derivative of 4*j + 0*j**2 + 9/20*j**5 + 1/10*j**x + 0 + 0*j**3 + 1/2*j**4. Suppose k(r) = 0. Calculate r.
-2, -1, 0
Solve -3*r**4 - 57*r**3 - 28 + 57*r + 38*r**2 - 5 - 40 + 13 + 25*r**2 = 0.
-20, -1, 1
Let a(y) = 6*y**5 + 3*y**4 - 35*y**3 + 37*y**2 - 9*y. Let n(h) = 24*h**5 + 12*h**4 - 141*h**3 + 150*h**2 - 36*h. Let l(q) = -9*a(q) + 2*n(q). Solve l(g) = 0.
-3, 0, 1/2, 1
Let f be 158/(-336)*-4 + (-3)/7. Let g = f + 1/21. Factor -g*k + 3/4 - 9/4*k**2.
-3*(k + 1)*(3*k - 1)/4
Suppose 32/5*t**2 - 6/5*t**3 + 74/5*t - 28/5 = 0. Calculate t.
-2, 1/3, 7
Let z(w) be the second derivative of w**6/6 + 109*w**5 + 59405*w**4/2 + 12950290*w**3/3 + 705790805*w**2/2 + 158*w. Factor z(h).
5*(h + 109)**4
Let g(y) be the second derivative of -y**5/90 + 5*y**4/54 + 14*y**3/27 + 3*y + 14. Determine t, given that g(t) = 0.
-2, 0, 7
Let w(i) be the third derivative of i**5/12 - 115*i**4/24 + 87*i**2. Factor w(l).
5*l*(l - 23)
Let r(p) = -2*p**4 + 2*p**3 - p - 1. Let n(t) = 14*t**4 - 146*t**3 + 1156*t**2 + 5*t + 5. Let o(a) = -n(a) - 5*r(a). Factor o(d).
-4*d**2*(d - 17)**2
Let a(s) = -6*s**5 + 13*s**4 - 11*s**3 - 31*s**2 - 7*s + 7. Let k(z) = z**5 + z**