3. Factor -1 - 4*b**2 - 2*b**3 + 2*b + 2 + 1 + m.
-2*(b - 1)*(b + 1)*(b + 2)
Let d(l) be the first derivative of -l**8/588 - 2*l**7/735 + l**6/105 - 5*l**2 + 3. Let y(v) be the second derivative of d(v). Determine t so that y(t) = 0.
-2, 0, 1
Let q(b) be the first derivative of b**2 - b + 2. Let i be q(2). Factor -u + u**i + u**3 + 2*u**2 + u.
2*u**2*(u + 1)
Let a(f) be the third derivative of -f**8/1680 + f**7/84 + f**6/40 - 2*f**5/15 - 5*f**4/8 - 19*f**2. Let y(b) be the second derivative of a(b). Factor y(n).
-2*(n - 8)*(n + 1)*(2*n - 1)
Let c(h) be the first derivative of -7*h**6/9 - 16*h**5/3 + 2*h**4 + 49. Factor c(u).
-2*u**3*(u + 6)*(7*u - 2)/3
Let g(a) be the first derivative of -a**6/21 - 18*a**5/35 - 13*a**4/7 - 12*a**3/7 + 27*a**2/7 + 54*a/7 - 197. Solve g(x) = 0 for x.
-3, -1, 1
Suppose 57/4*a - 397/8*a**2 + 57/2*a**3 - 9/8 - 9/2*a**4 = 0. Calculate a.
1/6, 3
Let o = -18 - -19. Suppose -r + o = -1. Factor 12*v - 3*v**2 - 4*v - v**r - 60*v**3 - 76*v**4 - 28*v**5.
-4*v*(v + 1)**3*(7*v - 2)
Let i = -70 + 421/6. Let v(m) be the second derivative of 0*m**2 + 1/3*m**4 + 4*m + 1/42*m**7 + 0 + i*m**3 + 3/10*m**5 + 2/15*m**6. Factor v(u).
u*(u + 1)**4
Let o(u) be the first derivative of -u**5/3 - 5*u**4/2 - 20*u**3/3 - 25*u**2/3 - 5*u - 2. Factor o(p).
-5*(p + 1)**3*(p + 3)/3
Let y(j) be the third derivative of -3/100*j**5 + 0 + j + 6/5*j**3 - 2*j**2 - 2/5*j**4. Factor y(w).
-3*(w + 6)*(3*w - 2)/5
Let 7/3*t**4 - 8/3 - 1/3*t**5 + 14/3*t - 13/3*t**3 + 1/3*t**2 = 0. What is t?
-1, 1, 2, 4
Suppose 2*o - 3*a + 0*a = 20, -4*a - 29 = -3*o. Find w such that 4*w**2 - 6*w**2 - 15 + o*w**2 - 10*w = 0.
-1, 3
Suppose j - 12 = -2*j. Suppose 5 = -5*k - 5*d, 0 = -0*k + k + j*d + 10. Factor -3 - k*n**2 + 9 + 2*n**4 - 6.
2*n**2*(n - 1)*(n + 1)
Factor -5202/11*u - 2/11*u**3 + 0 + 204/11*u**2.
-2*u*(u - 51)**2/11
Let m(b) be the second derivative of -2/21*b**7 + 9*b - 16/15*b**6 - 5*b**5 + 0 - 16*b**2 - 38/3*b**4 - 56/3*b**3. Let m(r) = 0. Calculate r.
-2, -1
Let l(i) = -14*i**2 + 594*i + 135. Let w(a) = -22*a**2 + 891*a + 204. Let d(o) = -7*l(o) + 5*w(o). Factor d(k).
-3*(k - 25)*(4*k + 1)
Let u(g) be the second derivative of g**4/108 - 19*g**3/18 - 623*g. Solve u(l) = 0 for l.
0, 57
Let x be (-988)/9 - (-1 + (5 - -1)). Let y = x + 115. Factor 2/9*k**3 - 2/9*k + 2/9 - y*k**2.
2*(k - 1)**2*(k + 1)/9
Let d(n) be the second derivative of n**8/16800 - n**7/6300 - 3*n**4/4 + 10*n. Let l(f) be the third derivative of d(f). Suppose l(g) = 0. What is g?
0, 1
Let d(i) be the third derivative of -1/20*i**5 - 1/40*i**6 + 1/112*i**8 + 0 + 0*i**3 + 0*i + 0*i**4 - 5*i**2 + 1/70*i**7. Determine v so that d(v) = 0.
-1, 0, 1
Let w(d) be the third derivative of d**8/2520 - 2*d**7/175 + 47*d**6/900 - d**5/15 + 50*d**2. Solve w(q) = 0.
0, 1, 2, 15
Let z(x) be the first derivative of 14*x**3/27 + 20*x**2/9 - 2*x/3 + 115. Factor z(w).
2*(w + 3)*(7*w - 1)/9
Let j be -1*(5 + -3)/2. Let b(u) = u**2 - 1. Let i be b(j). Factor -2*x + i*x + 4*x**2 + 1 - 2*x**2 - x**2.
(x - 1)**2
Suppose -6*b = -4 - 44. Let -8*g**3 - 2782*g**2 - b - 20*g + 2766*g**2 + 4*g**3 = 0. Calculate g.
-2, -1
Suppose -2*y = -7*y + 30. Let o be (7 - (y - 2)) + 0/3. Solve 1/2*d + 0 - 3/4*d**2 + 1/4*d**4 + 0*d**o = 0.
-2, 0, 1
Let h = -55 - -80. Let q(m) = 85*m**3 - 205*m**2 - 60*m + 155. Let w(s) = 7*s**3 - 17*s**2 - 5*s + 13. Let t(c) = h*w(c) - 2*q(c). Solve t(v) = 0 for v.
-1, 1, 3
Let n(i) be the third derivative of 3/2*i**6 + 0 + 17/105*i**7 + 1/168*i**8 + 18/5*i**5 + 0*i + 0*i**3 - 18*i**4 + 20*i**2. Factor n(k).
2*k*(k - 1)*(k + 6)**3
What is v in -9/2 - 27/4*v - 5/2*v**2 - 1/4*v**3 = 0?
-6, -3, -1
Let f = 38 - 30. Let k = 5 + -2. Suppose 65*l + 150*l**2 + f + 23*l + 125*l**k - 28*l = 0. Calculate l.
-2/5
Let 39*u**4 + 48*u**3 + 54*u + 69*u - 3*u**4 - 4*u**5 - 136*u**3 + 5*u = 0. What is u?
-1, 0, 2, 4
Let s(k) be the third derivative of -k**5/60 + 53*k**4/4 - 8427*k**3/2 - 461*k**2. Solve s(o) = 0.
159
Let c(i) be the second derivative of -i**5/40 - 115*i**4/24 + 233*i**3/12 - 117*i**2/4 + 91*i. Determine n so that c(n) = 0.
-117, 1
Let v(i) be the first derivative of i**6/66 - 4*i**5/55 + 3*i**4/44 + 4*i**3/33 - 2*i**2/11 - 532. Determine m, given that v(m) = 0.
-1, 0, 1, 2
Factor -1/4*b**4 - b**3 - b - 1/4 - 3/2*b**2.
-(b + 1)**4/4
Let r(u) = -3*u**2 - 29*u + 12. Let n be r(-10). Let h be (7/(-28) - 14/(-8))*n. Find s such that 1/4*s**h + 1/2*s + 0 - 7/4*s**4 - 3/4*s**5 + 7/4*s**2 = 0.
-2, -1, -1/3, 0, 1
Let k be -1 + 4 - (1 - (8 - -18)). Suppose x - 31 = -k. Suppose 2*g**2 - 2*g**x + 0 + 2/3*g**4 - 2/3*g = 0. Calculate g.
0, 1
Let f be 759/138 - (5/2 + 0). Determine n, given that -3*n**2 - 3/2 - 15/4*n - 3/4*n**f = 0.
-2, -1
Let r(y) be the first derivative of y**5/15 - 13*y**4/12 + 4*y**3/3 - 207. Let r(t) = 0. What is t?
0, 1, 12
Let f(m) = m**3 - m**2 - 2*m + 2. Let s be f(1). Let x(d) be the third derivative of -3*d**2 + 0*d + s - 1/32*d**4 + 1/240*d**5 + 1/12*d**3. Factor x(h).
(h - 2)*(h - 1)/4
Let r(d) be the third derivative of -d**8/56 - d**7/105 + d**6/3 - 2*d**5/5 + 2*d**2 - 5*d. Determine n so that r(n) = 0.
-3, 0, 2/3, 2
Suppose 0 = -s - s - 4*m + 4, 5*s - m - 10 = 0. Suppose o = s*o + 2*o. Factor 4/3*n**2 + o - 2/3*n**3 - 2/3*n.
-2*n*(n - 1)**2/3
Let r = 3481 - 17403/5. Determine q, given that 1/5*q**3 - r - 3/5*q + 0*q**2 = 0.
-1, 2
Suppose 5*o - 3 = 2*o. Suppose 5*k + 0*j - 5 = -3*j, 3 = 3*k + 5*j. What is m in 0 + k + o + 2 + 4*m**2 + 8*m = 0?
-1
Let r = 111 - 63. What is z in r + 0*z**2 - 8*z**2 + 11*z**2 + 24*z = 0?
-4
Let n be 28/3 + (-28)/(-42). Suppose 59*t + 2*t**2 - 5*t + t**4 + 34*t**2 + 0*t**4 + 27 + n*t**3 = 0. What is t?
-3, -1
Suppose 8 + 28 = -6*l. Let q be ((-92)/(-69))/((-2)/l). Factor 5*k**3 + 4*k**3 - 4*k**4 + 0*k**q - 2*k**2.
-k**2*(k - 2)*(4*k - 1)
Let i(n) be the first derivative of n**5/300 - n**4/6 + 10*n**3/3 - 25*n**2/2 - 23. Let a(t) be the second derivative of i(t). Factor a(f).
(f - 10)**2/5
Let w(k) be the first derivative of 15/2*k**2 - 14 - 10*k - 5/3*k**3. Factor w(m).
-5*(m - 2)*(m - 1)
Suppose -2*c + r + 16 = -2*r, -4*c - 3*r = -14. Let a be (-8)/c*-1 - (-66)/165. Find u, given that -1/2*u**a + 0 + 3/2*u = 0.
0, 3
Let c = 11918 + -71507/6. Solve 1/6*i**4 - 1/3*i**3 - c*i**2 + 0 + 1/3*i = 0 for i.
-1, 0, 1, 2
Let l(y) be the third derivative of -y**6/30 + y**5/15 + y**4/3 + 2*y**2 - 30. Solve l(a) = 0.
-1, 0, 2
Let q(b) be the first derivative of -7*b**4/36 + 5*b**3/18 + b**2/3 - 9*b + 6. Let u(z) be the first derivative of q(z). Factor u(t).
-(t - 1)*(7*t + 2)/3
Let l(o) = -12*o - 2. Let v be l(3). Let y = v + 50. Factor a**3 - 123 + a**3 + 6*a**2 + 54*a + 177 + y*a**2.
2*(a + 3)**3
Suppose 4*c + 147*c**2 - 2*c - 2*c - 297553*c**5 + 297548*c**5 - 287*c**3 + 73*c**4 = 0. What is c?
0, 3/5, 7
Let t(m) be the third derivative of -2197*m**7/210 - 169*m**6/20 - 13*m**5/5 - m**4/3 + 46*m**2. Determine p so that t(p) = 0.
-2/13, 0
Suppose 2*t + q + 1 = 0, -28*t + 33*t + 5*q + 15 = 0. Factor 4/7*o**t - 8/7*o - 32/7.
4*(o - 4)*(o + 2)/7
Let n(a) = 4*a - 35. Let g(u) = 36*u - 312. Let c(z) = -3*g(z) + 28*n(z). Let j be c(11). Determine w so that 4/9*w**2 - 4/9 + j*w = 0.
-1, 1
Suppose -12 = 2*g, -23 = -2*l + 4*g + 9. Factor -1/3*b**5 - b**l + 0*b - b**3 - 1/3*b**2 + 0.
-b**2*(b + 1)**3/3
Factor 0*d**3 - 10 + 10 - 5 - 16*d - 7 + 8*d**2 + 16*d**3 + 4*d**4.
4*(d - 1)*(d + 1)**2*(d + 3)
Let x(w) be the second derivative of w**6/40 - w**5 + 25*w**4/2 - 15*w**2 + 33*w. Let g(o) be the first derivative of x(o). What is l in g(l) = 0?
0, 10
Let s(m) = 3*m**2 + 5*m + 8. Let q(u) = -3*u**2 - 3*u - 9. Let x(k) = 2*q(k) + 3*s(k). Determine z, given that x(z) = 0.
-2, -1
Let y(i) = 3*i**2 + 4*i - 4. Let s(q) = -q**2 + q + 2. Let b be s(3). Let z be y(b). Solve 4*o**2 + 22*o**4 + 4 + 8*o**2 + 6*o**5 + z*o**3 - 2*o - 6 = 0 for o.
-1, 1/3
Let j(d) = -8*d**4 + 14*d**3 - 3*d**2 - 4*d + 1. Let z(u) = 7*u**4 - 13*u**3 + 3*u**2 + 5*u - 2. Let f = 126 - 121. Let r(v) = f*z(v) + 4*j(v). Factor r(q).
3*(q - 2)*(q - 1)**2*(q + 1)
Let d(p) = -15*p**2 - 13*p - 8. Let j(c) = 7*c**2 + 6*c + 3. Let y(t) = -2*d(t) - 5*j(t). Factor y(i).
-(i + 1)*(5*i - 1)
Let v(z) be the first derivative of z**4/4 - 3*z**2/2 + 2*z + 108. Factor v(x).
(x - 1)**2*(x + 2)
Let i(t) be the second derivative of -