 1)
Determine m, given that -16/13*m**2 + 8/13*m**4 - 4/13*m**3 + 2/13*m + 2/13*m**5 + 8/13 = 0.
-4, -1, 1
Let p(d) be the second derivative of -1/20*d**4 + 1/30*d**3 + 0 + 0*d**2 + 8*d + 3/100*d**5 - 1/150*d**6. Let p(k) = 0. Calculate k.
0, 1
Let x(l) be the first derivative of -l**5/25 - l**4/10 - l**3/15 - 11. Find h such that x(h) = 0.
-1, 0
Let c(m) = -12*m**3 + 56*m**2 + 4*m - 48. Let t(w) = 8*w**3 - 37*w**2 - 3*w + 32. Let v(o) = -5*c(o) - 8*t(o). Solve v(i) = 0.
-1, 1, 4
Let a(r) = -r**3 - 31*r**2 - 16*r + 7. Let i(o) = 16*o**2 + 8*o - 4. Let g(w) = 4*a(w) + 7*i(w). Suppose g(p) = 0. Calculate p.
-2, -1, 0
Let n(z) = -2*z - 8. Let x be n(-11). Factor 2*v - 10*v + v - 18*v**3 + 3*v - x*v**2 - 2*v**5 - 10*v**4.
-2*v*(v + 1)**3*(v + 2)
Let m be (7 + 1010/(-80))*2/(-3). Determine t, given that -3/2 + 3/4*t**4 - 3/4*t**3 + m*t - 9/4*t**2 = 0.
-2, 1
Let h(f) be the second derivative of f**4/9 + 2*f**3/9 - 4*f**2/3 + 2*f. Determine x, given that h(x) = 0.
-2, 1
Let h(f) be the third derivative of -f**5/150 + 7*f**4/60 - 2*f**3/5 - 3*f**2 + 2*f. Factor h(w).
-2*(w - 6)*(w - 1)/5
Let z(j) be the third derivative of j**7/5040 + j**4/24 + 4*j**2. Let y(g) be the second derivative of z(g). Determine b, given that y(b) = 0.
0
Let z = 258 + -3348/13. Factor -z*j + 2/13*j**2 + 4/13.
2*(j - 2)*(j - 1)/13
Let u = 65 - 65. Find s such that u*s**3 - 2/9 + 4/9*s**2 + 0*s - 2/9*s**4 = 0.
-1, 1
Let b(c) be the second derivative of 1/18*c**4 - c - 4/9*c**2 + 2/45*c**5 + 1/135*c**6 - 4/27*c**3 + 0. Determine i so that b(i) = 0.
-2, -1, 1
Suppose -18 = -4*a + 7*a. Let j(q) = 3*q**3 - 15*q**2 + 15*q - 3. Let v(w) = w**2 - w. Let p(u) = a*v(u) - j(u). Factor p(s).
-3*(s - 1)**3
Let w(r) = 15*r**4 + 25*r**3 + 35*r**2 + 15*r. Let d(x) = 7*x**4 + 13*x**3 + 17*x**2 + 7*x. Let m(j) = 5*d(j) - 2*w(j). Determine z so that m(z) = 0.
-1, 0
Let g be (-4)/(-10) - 4/(-90). Let z be (-160)/(-76) - (-2)/(-19). Factor -g*m - 2/9 - 2/9*m**z.
-2*(m + 1)**2/9
Let j(z) be the first derivative of z**3 + 27*z**2 + 243*z + 31. Determine n so that j(n) = 0.
-9
Factor -5/6*j**3 - 5*j**2 + 0 - 25/6*j.
-5*j*(j + 1)*(j + 5)/6
Suppose -2*o + 15 + 32 = -5*k, -2*o - 4*k = -20. Factor -o*d**3 + 5*d + 10*d**3 + d - 3*d + 3*d**5.
3*d*(d - 1)**2*(d + 1)**2
Suppose 4*c = 4*n + 12, 5*n + 15 = 5*c + 2*n. Let m be 2 - 2*c/(-6). Let 0*b - 4/9*b**5 + 0 - 8/9*b**m + 2/9*b**2 + 10/9*b**4 = 0. What is b?
0, 1/2, 1
Suppose 0 = 2*d + 2*l - 15 + 3, 5*d - 2*l - 16 = 0. Suppose 2*f = 2, t - 4 = d*t - 4*f. Factor 2/7*p + 2/7*p**2 + t.
2*p*(p + 1)/7
Let a = 200/69 + -36/23. Factor -2*s + 2/3*s**2 + a.
2*(s - 2)*(s - 1)/3
Let c(f) be the first derivative of -1/5*f**4 + 0*f + 0*f**3 + 1/15*f**6 + 1/5*f**2 - 3 + 0*f**5. Let c(z) = 0. What is z?
-1, 0, 1
Let l = -5 + 3. Let d be (l/4)/(15/(-48)). Find z such that d + 2/5*z**2 - 8/5*z = 0.
2
Let h = -10 - -8. Let v be (1 - 5/h) + -3. Factor v*c**2 - 3/2*c + 1.
(c - 2)*(c - 1)/2
Suppose 3*i + 36 = -3*h, -3*h - i + 12 = -4*h. Let q be ((-6)/4)/(9/h). Suppose 7/3*a**4 - 2/3*a + a**q + 4*a**3 + 0 = 0. Calculate a.
-1, 0, 2/7
Find y, given that 6/11*y**5 + 0 - 8/11*y**4 - 28/11*y**3 - 8/11*y**2 + 6/11*y = 0.
-1, 0, 1/3, 3
Let s(o) be the third derivative of o**8/560 + o**7/70 + o**6/20 + o**5/10 + o**4/8 + 2*o**3/3 + 6*o**2. Let r(j) be the first derivative of s(j). Factor r(u).
3*(u + 1)**4
Solve 8/3*t**2 + 0 + 1/3*t + 7/3*t**3 = 0.
-1, -1/7, 0
Let a = -24/7 + 83/14. Factor 0 + a*b**2 + 1/2*b + 2*b**3.
b*(b + 1)*(4*b + 1)/2
Let c(l) be the first derivative of 3*l**5/5 - 15*l**4/4 + 9*l**3 - 21*l**2/2 + 6*l - 9. Suppose c(w) = 0. Calculate w.
1, 2
Suppose -5*p - 4*v + 10 = 0, 3*v = 2*p + 8 + 11. Let d be -1 + 2/p - -5. Factor -3*b**5 + 2*b**4 - b**d + 3*b**4 + 4*b**4 + 3*b**2 - 8*b**3.
-3*b**2*(b - 1)**3
Let h be 1 + 3 + -2 + -5. Let g = -3 - h. Factor -2/7*d**5 + 2/7*d**2 + g*d + 2/7*d**3 - 2/7*d**4 + 0.
-2*d**2*(d - 1)*(d + 1)**2/7
Let f = -9 + 12. Let p(j) be the second derivative of 2*j + 1/12*j**4 + 0 + 1/6*j**f + 0*j**2. Factor p(y).
y*(y + 1)
Suppose l - 20 = -4*l. Solve -2*n - n**l + 2*n - 3*n**2 + 4*n**2 = 0.
-1, 0, 1
Let a(h) be the first derivative of 4*h**3/3 + 2*h**2 - 8*h - 4. Factor a(g).
4*(g - 1)*(g + 2)
Let s(b) = 4*b**5 - 9*b**4 - 8*b**3 + 31*b**2 - 29*b + 9. Let o(n) = n**4 + n**2 + n - 1. Let z(f) = -o(f) - s(f). Let z(k) = 0. Calculate k.
-2, 1
Let b(p) be the first derivative of -18*p**4/5 + 8*p**3/5 - p**2/5 + 11. Factor b(a).
-2*a*(6*a - 1)**2/5
Let h be (-1)/(-1) - (3 + (-17)/3). Determine y so that h*y**2 + 16/3*y**3 + 7/3*y**4 + 2/3*y + 0 = 0.
-1, -2/7, 0
Suppose 2*d = -0*d - 0*d. Let s(r) be the third derivative of 3*r**2 + 0*r**3 + 1/180*r**5 - 1/360*r**6 + d*r + 0*r**4 + 0. Find k such that s(k) = 0.
0, 1
Let f = -16 - -18. Factor 3*v + 2 - v**3 + 3*v**2 - 3*v**f.
-(v - 2)*(v + 1)**2
Let u(p) be the third derivative of p**6/120 - p**5/15 + p**4/8 + 18*p**2. Let u(w) = 0. What is w?
0, 1, 3
Let h(v) be the second derivative of v**4/36 - 5*v**3/18 - 5*v - 1. Factor h(c).
c*(c - 5)/3
Let f be 8*(4/16 - 0). Let 0*o**f + 0*o**3 + 1/4*o**4 + 0*o + 1/4*o**5 + 0 = 0. What is o?
-1, 0
Let w(c) be the third derivative of -c**8/11520 + c**7/1260 - c**6/720 + 7*c**5/60 + 7*c**2. Let o(a) be the third derivative of w(a). What is d in o(d) = 0?
2/7, 2
Let j(g) be the first derivative of -g**4/16 - g**3/4 - g**2/4 - 21. What is q in j(q) = 0?
-2, -1, 0
Let b(t) be the second derivative of -t**6/150 + t**5/50 - t**3/15 + t**2/10 - 13*t. Let b(y) = 0. What is y?
-1, 1
Suppose 0 = 5*j - 19 - 16. Let g(h) be the third derivative of 0*h**3 + 0 + 0*h + 0*h**4 + h**2 + 1/300*h**5 + 1/300*h**6 + 1/1050*h**j. Factor g(i).
i**2*(i + 1)**2/5
Let h(a) = 14*a + 268. Let i be h(-19). Factor 2/5 + 2/5*r**i - 4/5*r.
2*(r - 1)**2/5
Suppose l + 0 - 3 = 0. Factor 12 + 7*x**2 + 45*x**2 - 47*x + 3*x - 30*x**l + 10*x**3.
-4*(x - 1)**2*(5*x - 3)
Let y = -7269/5 - -1425. Let a = y + 467/15. Factor -2/3*o**3 + 4/3*o**5 - 2/3*o + a*o**4 + 1/3 - 8/3*o**2.
(o - 1)*(o + 1)**3*(4*o - 1)/3
Let h(a) = -4*a**3 + 6*a**2 + 14*a - 2. Let u(q) = -4*q**3 + 5*q**2 + 15*q - 3. Let c(t) = 3*h(t) - 2*u(t). Find y, given that c(y) = 0.
-1, 0, 3
Let d be (-76)/(-70) + 10/(-35). Factor d*c + 2/5*c**2 + 2/5.
2*(c + 1)**2/5
Let q = -4 + 7. Factor -18*u**3 - 8*u - 5*u**2 + 9*u**3 - 4 + 6*u**q + 2*u**3.
-(u + 1)*(u + 2)**2
Determine a, given that 12*a - 12*a**2 - 7*a**3 + 13*a**5 - 6*a**3 - 16*a**5 + 12*a**4 + 4*a**3 = 0.
-1, 0, 1, 2
Let q(m) be the first derivative of -m**6/120 - m**5/80 + m**4/48 + m**3/24 + 4*m - 1. Let k(a) be the first derivative of q(a). Determine n so that k(n) = 0.
-1, 0, 1
Let o(x) be the first derivative of -x**6/39 - 4*x**5/65 - x**4/26 - 10. Determine i, given that o(i) = 0.
-1, 0
Let t**2 - 2*t**2 - 1 + 2*t**2 - 2*t**2 - 2*t = 0. Calculate t.
-1
Let y(j) be the third derivative of -j**6/24 - j**5/4 + 28*j**2. Solve y(p) = 0 for p.
-3, 0
Let f(p) be the first derivative of -p**6/165 + p**5/110 + p**4/22 - 5*p**3/33 + 2*p**2/11 - 2*p + 7. Let o(g) be the first derivative of f(g). Factor o(j).
-2*(j - 1)**3*(j + 2)/11
Let k(z) = z + 2. Let l be k(-2). Suppose l = -5*h + 4*b - 8*b + 22, -20 = -4*h - 4*b. Suppose 0 - 1/3*t**h + 1/3*t**3 + 0*t = 0. Calculate t.
0, 1
Let b be (-6)/5*(40/36)/(-1). Factor 2/3*s + 2/3*s**3 + 0 + b*s**2.
2*s*(s + 1)**2/3
Let c(t) = -6*t**2 - 2*t. Let w(q) be the second derivative of 11*q**4/12 + 2*q**3/3 - q. Let m(z) = -7*c(z) - 4*w(z). Factor m(a).
-2*a*(a + 1)
Factor -v**3 + 26*v**2 + 0*v**3 - 16*v - 71*v**2 + 37*v**2.
-v*(v + 4)**2
Let i be -3 + 4 - 6/10. Factor 1/5*k**2 + i*k + 1/5.
(k + 1)**2/5
Solve 1/2*v + 0 - 2*v**4 - 2*v**2 + 1/2*v**5 + 3*v**3 = 0.
0, 1
Factor o**3 + 0 + 1/4*o**2 + 0*o.
o**2*(4*o + 1)/4
Suppose -2*x - 8 = 4*o, x + 4 = 5*x - 2*o. Let r(n) be the second derivative of -1/20*n**5 + 2*n + 1/3*n**2 + x - 1/9*n**4 + 1/18*n**3. Solve r(c) = 0 for c.
-1, 2/3
Let t = 1 - -3. Suppose -4*r - 8 = -2*o, -2*o = -r - t*r - 9. Suppose 2*i**o + 22*i**4 - 3*i**3 + 7*i**3 + 14*i**3 - 2*i + 8*i**5 = 0. Calculate i.
-1, 0, 1/4
Let x(u) be the third derivative of -7/2*u**5 - 4*u**3 + 49/40*u**6 - 13/2*u**4 + 0 + 0*u + 6*u**2. Factor x(l).
3*(l - 2)*(7*l + 2)**2
Let g(r) be the second derivative of r**7/42 + r**6/30 - 3*r**5/20 - r**4/12 + r*