- 1)
Let y(h) be the third derivative of 0*h + 8*h**2 + 1/12*h**3 + 0 + 1/240*h**6 - 1/48*h**4 - 1/120*h**5. Determine v so that y(v) = 0.
-1, 1
Let m(c) = c - 3*c**2 + 11*c**3 - 10*c**3 - 3 + c. Let q be m(3). Factor -7*b**3 + b**3 - 2*b**2 - 6*b**2 - q*b + b.
-2*b*(b + 1)*(3*b + 1)
Let c(h) be the second derivative of h**5/90 - h**4/18 + 2*h**3/27 - 6*h. Factor c(q).
2*q*(q - 2)*(q - 1)/9
Let v = 30 + -28. Solve 2 - 3/2*i**v + 0*i + 1/2*i**3 = 0.
-1, 2
Factor -4*f + 58*f**3 + 4*f - 62*f**3.
-4*f**3
Solve 16*b - 36*b**2 - 24*b - 50*b**3 + 22*b**3 = 0 for b.
-1, -2/7, 0
Let t(m) be the first derivative of 4 + 0*m**2 + 1/6*m - 1/18*m**3. Factor t(j).
-(j - 1)*(j + 1)/6
Let z(i) be the second derivative of -i**4/24 + i**3/6 - 6*i. Solve z(y) = 0.
0, 2
Let b be (15/105)/((-1)/(-4)). Factor 2/7*m**5 + b*m**2 + 0*m**3 - 4/7*m**4 + 0 - 2/7*m.
2*m*(m - 1)**3*(m + 1)/7
Let x(d) be the first derivative of -5*d**3/3 + 35*d**2 - 245*d - 42. Solve x(r) = 0 for r.
7
Let j(i) be the third derivative of 0*i**3 - 1/70*i**7 + 11/60*i**6 + 1/20*i**5 - 5/84*i**8 + 0 + 0*i - 7*i**2 - 1/12*i**4. Find t, given that j(t) = 0.
-1, -2/5, 0, 1/4, 1
Let v(r) be the third derivative of -r**8/6720 - r**7/1680 + r**5/60 + 6*r**2. Let n(a) be the third derivative of v(a). Factor n(x).
-3*x*(x + 1)
Let i(s) be the second derivative of s**9/52920 - s**8/7840 + s**7/4410 - s**4/2 + s. Let h(b) be the third derivative of i(b). Solve h(q) = 0 for q.
0, 1, 2
Determine i, given that 12/13*i**3 - 8/13*i**4 - 8/13*i**2 + 0 + 2/13*i + 2/13*i**5 = 0.
0, 1
Let z(t) be the first derivative of 11/25*t**5 - 1/10*t**6 - t**3 - 1/4*t**4 + 4/5*t**2 + 4/5*t - 3. Let z(o) = 0. Calculate o.
-1, -1/3, 1, 2
Let h**3 + 2 + h**4 - 2 - 2*h - h**2 + h = 0. Calculate h.
-1, 0, 1
Let n(j) = -j**2 + 8*j - 1. Let z be n(10). Let q be (-4)/(-14) - 78/z. Find t, given that 0*t**2 - 2*t**2 + 5*t**2 - t**3 - t**q - t**2 = 0.
-2, 0, 1
Let d(i) be the second derivative of i**7/112 + i**6/80 - 3*i**5/80 - i**4/16 + i**3/16 + 3*i**2/16 + 4*i. Solve d(m) = 0 for m.
-1, 1
Let g be ((7 - 3)*-1)/(-2). Let h(k) = -k - 1. Let s be h(-4). Determine d so that -4*d + 2 - 12*d**g - 7*d**s + 0*d**2 + d = 0.
-1, 2/7
Suppose -2*b - 5*a + 0*a + 211 = 0, -5*b + 511 = -4*a. Let d = b + -925/9. Determine o, given that 0 + d*o**2 + 2/9*o = 0.
-1, 0
Suppose 4*l + 0*a - 3 = -5*a, 2*a + 2 = 0. Let v(i) be the second derivative of 2/21*i**3 + 0 - l*i - 1/7*i**2 - 1/42*i**4. Determine k so that v(k) = 0.
1
Let z(i) be the second derivative of i**4/90 - i**3/9 + 4*i**2/15 - 4*i. Factor z(g).
2*(g - 4)*(g - 1)/15
Let w(k) be the first derivative of -3 - 1/20*k**5 + 0*k + 3/2*k**2 - 9/2*k**3 - 3/4*k**4. Let t(u) be the second derivative of w(u). Solve t(n) = 0 for n.
-3
Suppose 22*y + 2 = 23*y. Suppose 0 + 0*u + 1/3*u**3 + 0*u**y + 1/3*u**5 + 2/3*u**4 = 0. What is u?
-1, 0
Let y(s) = 6*s**2 - 3*s - 6. Let l(i) = -7*i**2 + 4*i + 7. Let m(j) = -3*l(j) - 4*y(j). Factor m(k).
-3*(k - 1)*(k + 1)
Let t = 8 + -6. Let d be 3 - (35/(-25) + 4). Factor 0 - 2/5*s + 2/5*s**3 - d*s**4 + 2/5*s**t.
-2*s*(s - 1)**2*(s + 1)/5
Let i(d) be the first derivative of d**2 + 3/2*d**4 + 0*d + 4 - 8/3*d**3. Let p(k) = -6*k**3 + 7*k**2 - k. Let s(j) = -5*i(j) - 6*p(j). What is w in s(w) = 0?
-2/3, 0, 1
Factor 293*a**3 + 75*a + 35*a**5 - 3 - 43*a**3 + 200*a**2 + 150*a**4 + 13.
5*(a + 1)**4*(7*a + 2)
Let h(f) be the second derivative of 0 - 1/2*f**2 + 1/12*f**3 + 1/24*f**4 + 2*f. Factor h(k).
(k - 1)*(k + 2)/2
Let z(v) be the second derivative of 0*v**2 - 5*v + 0 + 2/21*v**3 - 1/42*v**4. Factor z(x).
-2*x*(x - 2)/7
Factor -1/6*w + 11/6*w**2 - 1/2 - 7/6*w**3.
-(w - 1)**2*(7*w + 3)/6
Let f(i) be the second derivative of 0*i**3 + 0*i**2 + 0*i**4 + 2*i + 0 + 1/165*i**6 + 1/110*i**5. Factor f(q).
2*q**3*(q + 1)/11
Let i(n) be the first derivative of -n**3/3 - 2*n**2 - 4*n + 6. Factor i(h).
-(h + 2)**2
Let b(n) be the second derivative of n**4/12 + n**3/3 - 8*n. Factor b(k).
k*(k + 2)
Suppose -28 = -2*m + 4*s, -7 = 5*m + s - 33. Suppose -20 = q - m*q. Factor 2/7*d**5 + 2/7*d**q - 4/7*d**3 - 4/7*d**2 + 2/7*d + 2/7.
2*(d - 1)**2*(d + 1)**3/7
Let d(b) = 0*b + 6*b - 4*b + 2*b**2. Let n(z) be the second derivative of -z**4/6 - z**3/2 - z**2/2 - 8*z. Let q(m) = 3*d(m) + 2*n(m). Factor q(o).
2*(o - 1)*(o + 1)
Let f(j) be the second derivative of -j**4/4 - 2*j**3 - 6*j**2 - 17*j. Determine i so that f(i) = 0.
-2
Let t(x) = 3*x**2 - 4*x + 4. Let a(h) = 4*h**2 - 4*h + 5. Let p(j) = 4*a(j) - 5*t(j). Determine y so that p(y) = 0.
-4, 0
Let l(u) be the third derivative of -u**6/300 - 18*u**2. Factor l(d).
-2*d**3/5
Factor 392 + 5*z**2 + 17*z - 3*z**2 + 0*z**2 + 39*z.
2*(z + 14)**2
Let w(d) be the third derivative of 0*d**3 - 1/360*d**6 + 0 + 0*d**4 - 1/630*d**7 - 2*d**2 + 1/180*d**5 + 1/1008*d**8 + 0*d. Factor w(z).
z**2*(z - 1)**2*(z + 1)/3
Suppose 0 = -5*x - 4*d + 22, -3*x - 3*d - d = -18. Let h be 3/(3/x) + 0. Determine w so that 4*w**2 - 4*w**3 + h*w + 2*w**3 - 12*w**3 + 8*w**4 = 0.
-1/4, 0, 1
Let u be 1*(-1)/3*-3. Let t = u + -2. Let v(g) = g**3 - g**2 + g - 1. Let a(j) = -j**4 + 3*j**3 - j**2 + j - 2. Let x(q) = t*a(q) + 2*v(q). Factor x(b).
b*(b - 1)**2*(b + 1)
Let l be 4 - ((-46761)/(-900))/13. Let f(t) be the third derivative of 0 - 1/525*t**7 + 0*t**3 + t**2 + 0*t + 1/150*t**5 - l*t**6 + 1/60*t**4. Factor f(y).
-2*y*(y - 1)*(y + 1)**2/5
Let p(h) = h**2. Let c be p(0). Let f(a) be the second derivative of 0*a**3 + 0*a**6 - 3*a + c*a**2 + 0*a**5 - 1/126*a**7 + 0*a**4 + 0. Factor f(d).
-d**5/3
Let r be 3/(3 + 21/(-6)). Let i be -30*(-5)/((-135)/r). Determine v, given that -8/3 - 7/3*v**3 - 1/3*v**4 - 6*v**2 - i*v = 0.
-2, -1
Factor -8/5*i**4 - 12*i - 18/5 - 74/5*i**2 - 8*i**3.
-2*(i + 1)**2*(2*i + 3)**2/5
Let i(h) be the third derivative of h**5/40 - 3*h**4/8 + 9*h**3/4 + 16*h**2. Factor i(l).
3*(l - 3)**2/2
Suppose -o + 4*o - 14 = 5*u, 0 = 4*o - 5*u - 17. Find x such that -6*x**2 + 6*x**2 - 4*x**o + 4*x + 2*x**2 - 2 = 0.
-1, 1/2, 1
Let f(z) = -z**5 + 4*z**3 + z. Let o(n) = 6*n**5 - 25*n**3 - 7*n. Let v(a) = 39*f(a) + 6*o(a). Factor v(w).
-3*w*(w - 1)**2*(w + 1)**2
Let j(f) be the second derivative of f**6/720 - f**4/48 + f**3/2 + 3*f. Let y(u) be the second derivative of j(u). Factor y(z).
(z - 1)*(z + 1)/2
Let f(s) = 2*s**2 - 6*s + 7. Let v be f(2). Let 0 + 2/5*t + 4/5*t**2 + 2/5*t**v = 0. Calculate t.
-1, 0
Let v(d) be the third derivative of -d**10/302400 + d**9/120960 + d**5/30 - 4*d**2. Let r(n) be the third derivative of v(n). Find o such that r(o) = 0.
0, 1
Factor -26*i - 4*i**2 - 33*i - i**3 + 55*i.
-i*(i + 2)**2
Let s(p) = -p**2 - 14*p - 11. Let n be s(-14). Let t = n - -15. Factor -6/5*j**t + 0*j + 2/5*j**2 - 4/5*j**3 + 0.
-2*j**2*(j + 1)*(3*j - 1)/5
Let t(w) = -3*w**3 - 12*w**2 + 15*w - 9. Let m(v) = v**3 + 3*v**2 - 4*v + 2. Let j(d) = -9*m(d) - 2*t(d). Factor j(x).
-3*x*(x - 1)*(x + 2)
Let g(t) be the third derivative of -t**6/120 + t**5/60 + t**4/12 + 9*t**2. Factor g(q).
-q*(q - 2)*(q + 1)
Let c(w) be the third derivative of -w**9/60480 + w**7/5040 + w**5/30 + w**2. Let u(q) be the third derivative of c(q). Factor u(t).
-t*(t - 1)*(t + 1)
Let j(w) = 8*w**2 + 17*w - 9. Let o(i) = 2*i**2 + 4*i - 2. Suppose 0 = -3*s - 11 + 5. Let l(z) = s*j(z) + 9*o(z). Suppose l(q) = 0. What is q?
-1, 0
Factor -2/15*o**2 + 0 + 2/5*o.
-2*o*(o - 3)/15
Factor -14*b**3 + 9*b**3 - 5*b**4 - 2*b**2 + 4*b**2 + 3*b**2 + 5*b**5.
5*b**2*(b - 1)**2*(b + 1)
Let u(f) be the first derivative of -12/35*f**5 + 0*f - 15/28*f**4 + 0*f**2 - 2/7*f**3 - 1/14*f**6 - 2. Determine t, given that u(t) = 0.
-2, -1, 0
Suppose -33*m - 8 = -8. Factor -1/4*t + m - 1/4*t**5 + t**2 + t**4 - 3/2*t**3.
-t*(t - 1)**4/4
Determine p, given that -20/3*p**2 - 32/3*p + 0 = 0.
-8/5, 0
Let t(d) = -d - 7. Let g be t(-8). Let k(j) = -1 - j**2 + 0*j**2 + 0. Let h(v) = 2*v**2 - 2*v + 2. Let x(a) = g*h(a) + 3*k(a). Let x(p) = 0. Calculate p.
-1
Let o be (0 + 3801/(-27))*1. Let m = o - -141. Factor -m*s**5 + 2/3*s**4 + 0 + 2/9*s**2 - 2/3*s**3 + 0*s.
-2*s**2*(s - 1)**3/9
Suppose -3*o**3 + 3/5*o**5 + 12/5*o + 3/5*o**4 - 3*o**2 + 12/5 = 0. What is o?
-2, -1, 1, 2
Let l be (2 + -3)*-1*(-5)/(-35). Factor 0 - l*a - 1/7*a**2.
-a*(a + 1)/7
Let w = -127 - -1145/9. Suppose -w*p**2 + 4/9*p - 2/9 = 0. Calculate p.
1
Let i(a) = -12*a**3 + 