. Let f(d) = s*j(d) - b(d). Determine l, given that f(l) = 0.
1, 4
Let b = -6569/2 - -3285. Factor 0 + b*n**3 - 1/2*n**2 + 0*n.
n**2*(n - 1)/2
Let c(d) be the third derivative of 1/10*d**5 - 1/40*d**6 + 0 + 0*d**3 - 1/8*d**4 - 6*d**2 + 0*d. Factor c(q).
-3*q*(q - 1)**2
Let a(f) be the third derivative of f**8/1008 + f**7/336 - f**6/144 + 7*f**5/60 - 5*f**2. Let z(x) be the third derivative of a(x). Factor z(y).
5*(y + 1)*(4*y - 1)
Let a(g) = 12*g**3 - 3*g**2 + 24*g - 6. Let n(l) = -24*l**3 + 5*l**2 - 52*l + 13. Let h(z) = -13*a(z) - 6*n(z). What is q in h(q) = 0?
0, 3/4
Factor -10*t - 44*t**2 + 22*t**2 - 2*t**4 - 7*t**3 - 7*t**3 + 0*t**4.
-2*t*(t + 1)**2*(t + 5)
Let k = -13488/7 - -1927. Factor 2/7*f - 3/7 + k*f**2.
(f - 1)*(f + 3)/7
Let p(f) be the second derivative of -9/2*f**2 + 31*f + 4/15*f**5 + 9/2*f**3 + 0 - 2*f**4. Let p(i) = 0. What is i?
3/4, 3
Let k = 15359/264 + -463/8. Let v(c) be the first derivative of 1/11*c**2 - k*c**3 + 1 + 0*c. Factor v(o).
-2*o*(5*o - 1)/11
Let a(j) = -4*j**4 - 6*j**3 - 8*j**2 + 6*j + 2. Let f(u) = -3*u**4 - 5*u**3 - 7*u**2 + 5*u + 2. Let w(r) = -4*a(r) + 5*f(r). Factor w(b).
(b - 2)*(b - 1)*(b + 1)**2
Factor -1/5*y**3 + 1/5*y - 6/5 + 6/5*y**2.
-(y - 6)*(y - 1)*(y + 1)/5
Suppose 3 + 25 = 2*m. Let y = m - 14. Let y*u + 1/2*u**2 + 9/4*u**3 + 0 + 7/4*u**4 = 0. Calculate u.
-1, -2/7, 0
Let f(u) = 4*u**2 + 186*u - 4602. Let o(r) = r**2 - r + 1. Let y(v) = f(v) - 6*o(v). Factor y(j).
-2*(j - 48)**2
Let d(f) be the third derivative of -f**8/10080 + f**7/504 - f**6/60 - f**5/10 - 4*f**2. Let z(u) be the third derivative of d(u). Factor z(n).
-2*(n - 3)*(n - 2)
Suppose 23 = 6*r + 5. Let z(v) = -17*v**2 - 15*v + 5. Let p(b) = 35*b**2 + 30*b - 10. Let j(t) = r*p(t) + 5*z(t). What is w in j(w) = 0?
-1, 1/4
Suppose -3*b + 12 = b. Factor 17*g**3 - 4*g - 15*g**b + 2*g.
2*g*(g - 1)*(g + 1)
Suppose -11 = -4*d + z, -z + 5 = 3*d + 2. Let y(c) be the first derivative of 15*c**3 + 6 + 39*c**3 - 2 + 8*c + 36*c**d. Factor y(n).
2*(9*n + 2)**2
Let o(g) = -5*g**2 - 11*g + 36. Let d(a) = -9*a**2 - 23*a + 72. Let m(x) = 6*d(x) - 10*o(x). Factor m(f).
-4*(f - 2)*(f + 9)
Let j(t) be the second derivative of -3*t**4/20 - 5*t**3/6 + 3*t**2/5 - 8*t - 1. Factor j(r).
-(r + 3)*(9*r - 2)/5
Let c be (-4)/8 - (11 + 1 - 13). Suppose -1/2*x**2 + 1/4*x**3 + c - 1/4*x = 0. Calculate x.
-1, 1, 2
Let i = -2 + 6. Find g such that -14*g - i*g**2 + g**4 + 16*g - 2*g**3 + 3 + 0*g**3 = 0.
-1, 1, 3
Let n(w) be the third derivative of -w**5/60 - 3*w**4/4 - 27*w**3/2 - 41*w**2. Factor n(q).
-(q + 9)**2
Suppose 0 = -4*r - b - 147, r = 3*b - 48 + 8. Let u = r + 41. Suppose 4/11 - 14/11*t + 28/11*t**3 + 4/11*t**u - 8/11*t**2 - 14/11*t**5 = 0. Calculate t.
-1, 2/7, 1
Suppose 8 = -2*k + 4*k. Suppose -11 = -k*j - 3. Factor 0*p**2 + 2*p + 9*p**j - 12*p**4 - 5*p.
-3*p*(p + 1)*(2*p - 1)**2
Suppose -14/17 - 2/17*r**2 - 16/17*r = 0. What is r?
-7, -1
Find x such that 76*x**3 + x**4 - 3*x**4 - 12*x + 5*x**4 - 67*x**3 = 0.
-2, 0, 1
Let l(i) = 3*i**3 + 60*i**2 + 240*i - 12. Let u(a) = a**2 + 4*a - 1. Let y(j) = l(j) - 12*u(j). Factor y(v).
3*v*(v + 8)**2
Let q be (-6 - -8)/(-2)*-2. Let u(f) be the first derivative of q - 6/7*f - 2/21*f**3 + 4/7*f**2. Determine p so that u(p) = 0.
1, 3
Let g(f) = -3*f**4 + 15*f**3 - 18*f**2 - 6*f. Let s(x) = 3*x**4 - 16*x**3 + 20*x**2 + 7*x. Let t(o) = 7*g(o) + 6*s(o). Let t(p) = 0. Calculate p.
0, 1, 2
Let q(o) be the second derivative of o**5/30 - 13*o**4/6 + 48*o**3 - 324*o**2 + 2*o + 125. Solve q(v) = 0.
3, 18
Let v be (50/125)/(93/45 + (-2)/3). Factor -4/7*j**3 + 0 - v*j - 5/7*j**2 - 1/7*j**4.
-j*(j + 1)**2*(j + 2)/7
Let u(r) = r**5 + r**3 - r**2 + r. Let i(v) = 7*v**5 - 2*v**4 + 7*v**3 - 6*v**2 + 6*v. Let y(k) = -i(k) + 6*u(k). Factor y(w).
-w**3*(w - 1)**2
What is q in 280*q - 12*q**2 + 192 - 5*q**4 - 12*q**3 + 17*q**3 + 9*q**4 - 101*q**3 = 0?
-1, 2, 24
Let y be 2/12 + (-13)/6. Let u(j) = -j**4 + j**3 - 4*j**2 - 6*j - 5. Let k(l) = l**2 + l + 1. Let d(w) = y*u(w) - 10*k(w). Factor d(q).
2*q*(q - 1)**2*(q + 1)
Let p(v) be the first derivative of v**6/2 + 69*v**5/5 + 189*v**4/4 + 61*v**3 + 30*v**2 + 561. Factor p(z).
3*z*(z + 1)**3*(z + 20)
Let v(f) be the third derivative of f**7/420 + 11*f**6/240 - 31*f**5/40 + 51*f**4/16 + 17*f**2. Suppose v(o) = 0. What is o?
-17, 0, 3
Let v(x) be the third derivative of -x**4/6 + x**3/3 + 45*x**2. Let o be v(0). Factor -4/7*w + 4/7*w**o + 1/7.
(2*w - 1)**2/7
Let y be (-1)/((20/(-8) - -3)/(-7)). Let c = 17 - y. Factor 10/3*p**c - 2/3*p**2 - 14/3*p**4 + 0 + 2*p**5 + 0*p.
2*p**2*(p - 1)**2*(3*p - 1)/3
Suppose 8*i + 16 - 64 = 0. Suppose 3*m**3 + 121*m - 241*m + 120*m - i*m**2 = 0. What is m?
0, 2
Let u(x) be the second derivative of 0 + 4/3*x**3 + 2*x**4 + 2/5*x**6 - 45*x + 0*x**2 + 13/10*x**5 + 1/21*x**7. What is t in u(t) = 0?
-2, -1, 0
Let v(h) be the second derivative of -h**4/26 - 10*h**3/39 - 3*h**2/13 - 2*h + 27. Solve v(b) = 0 for b.
-3, -1/3
Let d(k) be the third derivative of 7*k**6/40 + k**5/2 + 7*k**4/24 - 5*k**3/6 + 16*k**2. Let r(g) = -g**3 - g**2 + 1. Let z(f) = -4*d(f) - 12*r(f). Factor z(m).
-4*(m + 1)*(3*m + 2)*(6*m - 1)
Let t(w) = 3*w**3 + 108*w**2 + 117*w + 6. Let x(r) = -2*r**3 - 108*r**2 - 116*r - 5. Let k(g) = 5*t(g) + 6*x(g). Find d such that k(d) = 0.
-1, 0, 37
Let x(k) be the second derivative of -k**9/18144 + k**7/5040 - 11*k**3/6 - 4*k. Let p(b) be the second derivative of x(b). Determine c so that p(c) = 0.
-1, 0, 1
Suppose -309 = -3*c - 12. Let a = 101 - c. Let 2/15 + 2/15*l**a + 4/15*l = 0. Calculate l.
-1
Let b(t) be the third derivative of -t**7/168 + t**6/24 - 5*t**4/6 - 4*t**3/3 - 5*t**2. Let r(k) be the first derivative of b(k). Find c such that r(c) = 0.
-1, 2
Let k = -29/45 - -59/45. Let o(h) be the second derivative of -k*h**2 - 1/18*h**4 + 0 + 1/3*h**3 + 10*h. Find u such that o(u) = 0.
1, 2
Let i(v) be the third derivative of 1/2352*v**8 + 0*v + 0 + 0*v**4 + 1/210*v**5 + 2/735*v**7 - v**2 + 1/168*v**6 + 0*v**3. Factor i(k).
k**2*(k + 1)**2*(k + 2)/7
Find f, given that 0*f + 10*f**2 + 35/2*f**3 + 0 + 5*f**4 - 5/2*f**5 = 0.
-1, 0, 4
Let m = 361/5 + -72. Let a be (10*9/(-54))/((-10)/12). Factor 0*k**a + m*k**4 + 0 + 0*k + 1/5*k**3.
k**3*(k + 1)/5
Let o(z) be the first derivative of -1/16*z**4 + 1/6*z**3 - 19 - 1/8*z**2 + 0*z. Factor o(d).
-d*(d - 1)**2/4
Let l(g) = 2*g + 19. Let p be l(-6). Let a = 9 - p. Find y such that 29 + a*y**2 + 2*y - 14 - 19 = 0.
-2, 1
Let t(w) be the second derivative of w**7/315 - w**6/360 + w**2 - 6*w. Let p(c) be the first derivative of t(c). Factor p(o).
o**3*(2*o - 1)/3
Let p(u) be the first derivative of 25/24*u**4 + 5/18*u**3 + 0*u + 5/9*u**6 + 0*u**2 + 12 + 4/3*u**5. Suppose p(r) = 0. Calculate r.
-1, -1/2, 0
Let t(r) be the third derivative of r**8/784 - 39*r**7/490 + 2*r**6 - 170*r**5/7 + 750*r**4/7 + 5000*r**3/7 + 27*r**2 - 1. Let t(k) = 0. Calculate k.
-1, 10
Let p(q) be the first derivative of 1/3*q**4 - 2/3*q**3 - 1 - q**2 + 4/3*q. Find f such that p(f) = 0.
-1, 1/2, 2
Suppose 5*g = -2*i, 0 = -i + 27*g - 31*g. Let -1/2*b**2 + 0*b + i = 0. What is b?
0
Let g be 3 + 4/2 + -3. Let m(v) = -v**2 - 3*v + 3. Let j be m(-3). What is f in g + f**2 - 2 + 12*f - 10*f - j*f**3 = 0?
-2/3, 0, 1
Let t(i) be the first derivative of i**6/165 - i**5/330 - i**4/12 - 2*i**3/11 + 4*i**2 + 10. Let f(h) be the second derivative of t(h). Factor f(c).
2*(c - 2)*(c + 1)*(4*c + 3)/11
Suppose -14/9*n**5 + 8*n**2 + 12*n**4 + 0 - 206/9*n**3 + 40/9*n = 0. Calculate n.
-2/7, 0, 1, 2, 5
Factor 6/5*g + 4/5 + 0*g**2 - 2/5*g**3.
-2*(g - 2)*(g + 1)**2/5
Factor -2*l - 1/2*l**3 - 6 + 7/2*l**2.
-(l - 6)*(l - 2)*(l + 1)/2
Let d be (2/2 - 6)*3/(-5). Let t = -48 - -145/3. Factor 0 + t*c**2 + 1/6*c**d + 1/6*c.
c*(c + 1)**2/6
Let l(z) be the first derivative of z**3/8 + 39*z**2/2 + 1014*z + 133. Find d such that l(d) = 0.
-52
Let d be (324/63 - 5)*0. Let x(p) be the second derivative of -1/13*p**3 + 1/78*p**4 - 7*p + d + 2/13*p**2. Factor x(i).
2*(i - 2)*(i - 1)/13
Factor 27/5*k**4 + 0*k + 0 - 63/5*k**3 + 3/5*k**5 + 33/5*k**2.
3*k**2*(k - 1)**2*(k + 11)/5
Let w = 1234/5 - 2393/10. Solve 65/2*b + w + 10*b**2 = 0.
-3, -1/4
Let k(r) = r**3 - 11*r**2 + r - 11. Let y be k(11). Factor -24*s**2 - 4 - 21*s + y - 7*s.
-4*(s + 1)*(6*s + 1)
Let f = 1/606 + 9689/4242. Facto