z(r) be the third derivative of -1/4*r**4 - 1/35*r**7 + 1/15*r**5 + 0 + 1/30*r**6 + 1/168*r**8 + 1/3*r**3 + 0*r + 5*r**2. Determine l, given that z(l) = 0.
-1, 1
Suppose 2*c + 5*b = 26, 0*c - 5*c - 1 = -4*b. Let o(a) be the first derivative of 0*a + 0*a**2 + 2/3*a**c + 1. Solve o(x) = 0.
0
Let v(k) = -6*k**2 + 6*k + 10. Let i(c) = c**2 - c - 1. Let m(s) = -2*i(s) - v(s). Factor m(x).
4*(x - 2)*(x + 1)
Let b = 95/9 - 10. Let u(s) be the second derivative of 0 - 1/9*s**4 - b*s**3 - s - 2/3*s**2. Factor u(q).
-2*(q + 2)*(2*q + 1)/3
Let r = 11 + -17. Let m be (-65)/(-20) - r/(-2). Factor -1/4*w**2 - m*w + 0.
-w*(w + 1)/4
Let k = -36 + 36. Let v(x) be the third derivative of 0*x**3 + x**2 + 0 - 1/48*x**4 + k*x + 1/240*x**6 + 0*x**5. Factor v(l).
l*(l - 1)*(l + 1)/2
Suppose -3*m + 24 = 3*m. Factor 5*q**2 - 3*q**2 + 9*q - 9*q + 2*q**4 + m*q**3.
2*q**2*(q + 1)**2
Let w(c) = c**2 - 6*c + 7. Let i be w(5). Let b = 0 - -2. Factor i*h**2 - h**3 - 3*h**2 + b*h**3.
h**2*(h - 1)
Let i(x) be the third derivative of 0*x - 1/480*x**6 + 0*x**3 + 0*x**5 + 1/96*x**4 + 0 + 3*x**2. Suppose i(p) = 0. Calculate p.
-1, 0, 1
Let z be (6/(-2))/(8 - 9). Let 0 + m**5 + 0*m - m**z + 1/2*m**2 - 1/2*m**4 = 0. What is m?
-1, 0, 1/2, 1
Let v(d) be the first derivative of d**5/30 + d**4/12 + 3*d**2 - 6. Let c(g) be the second derivative of v(g). Factor c(i).
2*i*(i + 1)
Let b = -5 - -9. Suppose b = -2*v + 8. Factor k**4 - 3 - 29*k**v - 4*k**4 + 35*k**2.
-3*(k - 1)**2*(k + 1)**2
Let m(b) be the third derivative of -2/105*b**7 - 1/336*b**8 - 1/40*b**6 + 0 + 0*b**3 + 1/15*b**5 + 1/6*b**4 + 0*b - 5*b**2. Factor m(d).
-d*(d - 1)*(d + 1)*(d + 2)**2
Let q = -13 + 67/5. Let b = q - 3/20. Factor 0*u**2 + 1/4*u**4 + 0 + b*u**3 + 0*u.
u**3*(u + 1)/4
Let t(a) be the first derivative of -1/3*a - 1/6*a**2 + 1/9*a**3 + 1/12*a**4 - 1. Suppose t(b) = 0. Calculate b.
-1, 1
Let b(s) = s**2 - s + 3. Let t be b(-2). Factor 2*k - t*k**3 + 0*k - 3*k**4 - 8*k**2 - k**2 - 5*k.
-3*k*(k + 1)**3
Let v be ((-129)/48)/((-6)/(-8)). Let h = -10/3 - v. Solve 1/4*r**2 - h*r + 0 = 0.
0, 1
Let f(k) be the first derivative of -k**5/20 + k**4/16 + 5. Solve f(z) = 0 for z.
0, 1
Let r(c) be the first derivative of -2 + 1/72*c**4 - 1/360*c**6 + 0*c - 1/180*c**5 + 1/18*c**3 + 2*c**2. Let b(x) be the second derivative of r(x). Factor b(n).
-(n - 1)*(n + 1)**2/3
Let z(m) be the second derivative of -2*m**4/27 - 13*m**3/27 - m**2/3 + 11*m. Suppose z(k) = 0. Calculate k.
-3, -1/4
Let j(k) be the first derivative of -k**6/33 - 14*k**5/55 - 8*k**4/11 - 16*k**3/33 + 16*k**2/11 + 32*k/11 - 2. Solve j(h) = 0 for h.
-2, 1
Let s = -105 + 211/2. Let x = 139/90 + -2/45. Determine z, given that s*z + x*z**2 + 0 = 0.
-1/3, 0
Determine w, given that 1/5*w + 3/5*w**2 + 3/5*w**3 + 0 + 1/5*w**4 = 0.
-1, 0
Let x = 35 + -28. Suppose 0 = d - x*d + 18. Factor -1/3*c**d + 0*c + 0 + 2/3*c**4 - 1/3*c**2.
c**2*(c - 1)*(2*c + 1)/3
Suppose -s = 5*x + 22, -x = 4*s - 0 - 7. Suppose c + 2*w + 5 = -5, 15 = -s*w. Factor q**2 + c*q**2 - 5 - q + 3.
(q - 2)*(q + 1)
Let t(n) be the second derivative of n**4/66 + n**3/11 + 2*n**2/11 + n - 21. Factor t(w).
2*(w + 1)*(w + 2)/11
Let u(j) be the second derivative of j**6/1260 + j**5/420 - j**4/42 + 2*j**3/3 - 3*j. Let i(m) be the second derivative of u(m). Find z such that i(z) = 0.
-2, 1
Suppose -a - 2*h - 5 = 0, 5*a - 5*h - 1 = -2*h. Let w be a/(-21) + (-8)/(-28). Find z, given that -w*z**3 + 0*z**2 + 1/3*z + 0 = 0.
-1, 0, 1
Suppose 5*a - 40 = -4*f, 0 = 2*f - a - 6. Solve 2/5*i**2 + 0 - 1/5*i - 2/5*i**4 + 1/5*i**f + 0*i**3 = 0 for i.
-1, 0, 1
Let g(h) be the third derivative of h**5/12 - 31*h**2. Let g(t) = 0. Calculate t.
0
Let p(u) = -u**2 - 4*u + 7. Let j be p(-6). Let i = -3 - j. Solve -3*z**3 + i*z**5 + 0*z**4 - 2*z**4 + 2*z**2 + z**3 = 0.
-1, 0, 1
Suppose 3*o - 5 = -5*w + 4*o, 5*w + 4*o = 30. Let l(j) be the first derivative of 2*j**2 + 1/4*j**4 + 0*j - w + 4/3*j**3. Solve l(r) = 0.
-2, 0
Let u = 3 - 1. Let h be (-2 + 1)/(2/(-8)). Factor 0*y - 5*y - h - u*y + y + 2*y**3.
2*(y - 2)*(y + 1)**2
Let d be ((-4)/7)/(75/(-175)). Factor d*p - 2/3 - 2/3*p**2.
-2*(p - 1)**2/3
Let t(u) = -u - 13. Let y be t(-18). Let a(o) be the first derivative of 0*o**2 - 2 + 1/10*o**y + 0*o + 1/4*o**4 + 1/6*o**3. Find m such that a(m) = 0.
-1, 0
Suppose 0 = u + k - 7, u + 4*k - 18 = 2*u. Solve 3/4*t**3 + 9/4*t - 3/4 - 9/4*t**u = 0.
1
Let 0 + 2/9*f**3 + 0*f**2 - 2/9*f = 0. What is f?
-1, 0, 1
Let v(u) be the third derivative of 5*u**2 + 1/8*u**3 - 1/48*u**4 + 0*u - 1/240*u**5 + 0. Solve v(m) = 0.
-3, 1
Suppose -1/3*d**2 + 4/3*d - 4/3 = 0. Calculate d.
2
Let x(z) be the third derivative of z**8/112 - 3*z**7/70 + z**6/20 + z**5/10 - 3*z**4/8 + z**3/2 - 4*z**2. Factor x(y).
3*(y - 1)**4*(y + 1)
Let i(k) be the first derivative of -5/48*k**4 + 0*k**2 - 7/80*k**5 + 1/12*k**3 + k + 1. Let g(y) be the first derivative of i(y). Let g(s) = 0. What is s?
-1, 0, 2/7
Factor 0*m**5 - 2*m**5 + 12*m**4 - 4*m**5 - 6*m**2 - 6 + 3*m**5 - 12*m**3 + 15*m.
-3*(m - 2)*(m - 1)**3*(m + 1)
Suppose -2*v - j + 10 = -6*j, 2*v - 10 = 3*j. Let h be (-22)/55*v/(-6). Factor s**2 - s + 1/3 - h*s**3.
-(s - 1)**3/3
Factor x**3 - x**3 - 14*x**4 - 10*x**3 + 19*x**4.
5*x**3*(x - 2)
Let t(i) be the third derivative of i**8/4200 - i**6/450 + i**4/60 - 5*i**3/6 - 7*i**2. Let o(n) be the first derivative of t(n). Find q, given that o(q) = 0.
-1, 1
Let g(c) be the second derivative of c**7/252 - c**5/30 + c**4/36 + c**3/12 - c**2/6 + 3*c - 9. Let g(z) = 0. What is z?
-2, -1, 1
Let i = 16 + 0. Let z be i/72 + (-5)/(-18). Factor 0 - z*r**3 + 1/2*r**2 + 0*r.
-r**2*(r - 1)/2
Let q(s) be the second derivative of 2*s**6/15 - 2*s**5 + 25*s**4/3 - 4*s. Determine w so that q(w) = 0.
0, 5
Let j(z) be the third derivative of z**8/840 - 2*z**7/175 + 7*z**6/150 - 8*z**5/75 + 3*z**4/20 - 2*z**3/15 - z**2 - 28. Factor j(r).
2*(r - 2)*(r - 1)**4/5
Let o(c) be the third derivative of -c**6/180 - c**5/15 - c**4/4 - 4*c**3/9 + 8*c**2. Suppose o(a) = 0. What is a?
-4, -1
Let k(v) = -1. Let j(u) = -14*u**2 + 4*u + 10. Let h(t) = 2*j(t) + 20*k(t). Factor h(a).
-4*a*(7*a - 2)
Let s be ((-441)/15)/(-7) - (-1 + 5). Factor 2/5*o**3 - 1/5*o**5 - 1/5*o - 1/5 - s*o**4 + 2/5*o**2.
-(o - 1)**2*(o + 1)**3/5
Let r = 109/321 + -2/321. Factor 2/3*v**3 + 0*v**4 - r*v**5 + 0 + 0*v**2 - 1/3*v.
-v*(v - 1)**2*(v + 1)**2/3
Let l = -13/75 - -11/25. Let o(v) be the first derivative of 0*v + 2 - l*v**5 - 1/3*v**2 + 4/9*v**3 + 1/9*v**6 + 0*v**4. Solve o(y) = 0 for y.
-1, 0, 1
Let q(k) = k + 22. Let d be q(-16). Let h(p) be the second derivative of 1/45*p**d + 0 - 1/3*p**2 - p + 0*p**4 - 1/15*p**5 + 2/9*p**3. Factor h(r).
2*(r - 1)**3*(r + 1)/3
Let y(g) = -g**3 + 5*g**2 + 4*g + 1. Let f(t) = -t**3 + 4*t**2 + 3*t. Let d(j) = 6*f(j) - 4*y(j). Suppose d(o) = 0. What is o?
-1, 1, 2
Suppose 0 = -k - 0 + 2. Suppose -q + 2*a = -8, -k*a = q - 3*q + 12. Factor 0 + 2/9*v**q + 0*v**3 - 2/9*v**2 + 0*v.
2*v**2*(v - 1)*(v + 1)/9
Factor -n**2 + 0*n**2 - 8 - n**2 + n**2 + 9*n.
-(n - 8)*(n - 1)
Let h(r) be the third derivative of 7*r**2 - 1/27*r**4 + 0 + 0*r - 1/540*r**5 - 8/27*r**3. Let h(y) = 0. What is y?
-4
Let q be (12/(-72))/((-1)/3). Let p be (-1 - -4) + (-1 - -1). Find l such that -1/2*l**p + 1/2*l + q*l**2 - 1/2 = 0.
-1, 1
Suppose -17 = -q - 3*g, -q = 3*q + g - 13. Suppose q*l + 1 = 7. What is o in 1/2*o - 7/4*o**2 + o**l + 1/4 = 0?
-1/4, 1
Let r(a) be the first derivative of 0*a**4 - 1/8*a**2 + 1/6*a**3 + 0*a + 1/24*a**6 - 3 - 1/10*a**5. Let r(f) = 0. What is f?
-1, 0, 1
Let i(t) be the second derivative of -t**6/150 + 4*t**5/25 - 8*t**4/5 + 128*t**3/15 - 128*t**2/5 + 16*t. Factor i(z).
-(z - 4)**4/5
Solve -2/9*x + 2/9*x**2 - 4/9 = 0.
-1, 2
Let -12*y - 4 - 11*y**3 + 32*y**3 + 3*y**2 + 2*y**2 - 10*y**4 = 0. Calculate y.
-1/2, -2/5, 1, 2
Let x(b) be the third derivative of b**6/160 - b**5/80 - 11*b**2. Factor x(p).
3*p**2*(p - 1)/4
Let v be 0 + 0*5/(-25). Let t(s) be the second derivative of v - 2*s - 1/10*s**5 + 2/5*s**2 - 1/15*s**3 - 4/15*s**4. Solve t(u) = 0 for u.
-1, 2/5
Let r(m) = m**3 + 4*m**2 + 3. Let c(z) = -2*z**3 - 4*z**2 - 4. Let q(l) = 3*c(l) + 4*r(l). Determine w so that q(w) = 0.
0, 2
Let o be (2 - 0) + 0 + 4. Suppose -5*u - 6*n + 2*n = -o, -u - 5*n - 3 = 0. Factor 8 - 2*i**3 - u*i**2 + 0*i**2 - 4*i**2.
-2