1)
Let f(d) be the second derivative of d**5/70 - d**4/42 + 4*d. Factor f(j).
2*j**2*(j - 1)/7
Let s(d) be the first derivative of d**4/7 + 4*d**3/7 - 2*d**2/7 - 12*d/7 + 54. Let s(x) = 0. What is x?
-3, -1, 1
Let j = 196232831/345 - 568790. Let s = -1/69 + j. Factor -2/5*z + 2/5*z**5 + 0 + 0*z**3 - 4/5*z**4 + s*z**2.
2*z*(z - 1)**3*(z + 1)/5
Let g(a) = -654*a**3 + 356*a**2 - 62*a + 8. Let p(m) = -m**3 - m**2 + m + 1. Let i(t) = g(t) - 4*p(t). Determine v, given that i(v) = 0.
2/13, 1/5
Let q be (-12 - -9)*2/(-24). Solve q*n + 0 - 1/4*n**2 = 0.
0, 1
Suppose -5*o + 15 = 0, -3*p - 4*o + 15 = o. Let h = 146/21 + -44/7. Solve 0*d**3 + p + 1/3*d**4 - h*d - d**2 = 0.
-1, 0, 2
Let i be (-3)/2 - 15/(-75)*15. Find m, given that 1 - i*m**2 - 1/2*m = 0.
-1, 2/3
Let q = -2 + 6. Let l(x) be the first derivative of -1/2*x**q - 8*x + 2*x**3 + 0*x**2 + 1. Factor l(y).
-2*(y - 2)**2*(y + 1)
Let p(r) be the third derivative of -r**9/60480 + r**8/20160 + r**7/5040 - r**6/720 - r**5/20 + 2*r**2. Let z(m) be the third derivative of p(m). Factor z(g).
-(g - 1)**2*(g + 1)
Factor 13*u - 30 - 2*u**2 + 8*u - 53*u.
-2*(u + 1)*(u + 15)
Let q(i) be the third derivative of -i**7/504 + i**6/240 + i**5/60 - i**4/24 - i**2. Let b(n) be the second derivative of q(n). Find h, given that b(h) = 0.
-2/5, 1
Let i(n) be the third derivative of -n**11/498960 - n**10/113400 - n**9/90720 - n**5/60 + 3*n**2. Let a(w) be the third derivative of i(w). Factor a(y).
-2*y**3*(y + 1)**2/3
Let y be (0 + 1)*(3 - 7). Let a(z) = -z**3 - 4*z**2 - 2*z - 6. Let g be a(y). Factor -2*t + 3*t + t**3 + 0*t**3 - g*t**2.
t*(t - 1)**2
Let v(o) be the second derivative of 2*o**6/5 + o**5/10 - o**4/3 + 16*o. Determine n, given that v(n) = 0.
-2/3, 0, 1/2
Let z(c) be the third derivative of -c**8/112 - c**7/70 + c**6/40 + c**5/20 + 16*c**2. Factor z(s).
-3*s**2*(s - 1)*(s + 1)**2
Let b be 0 + 0 + 2/(-63). Let m = b - -136/315. Factor -2/5*l**3 + 0*l + m*l**2 + 0.
-2*l**2*(l - 1)/5
Let b(g) be the first derivative of g**3 + 6*g**2 + 12*g + 2. Factor b(r).
3*(r + 2)**2
Suppose 0 - 11 = -3*x + f, 2*x - 5*f - 29 = 0. Factor 0*n + 0 + 2/9*n**3 - 4/9*n**4 + 2/9*n**x.
-2*n**2*(n - 1)*(2*n + 1)/9
Let b(r) be the third derivative of -r**8/112 + r**6/10 - r**5/10 - 3*r**4/8 + r**3 + 19*r**2. Determine d so that b(d) = 0.
-2, -1, 1
Factor -8 - u**2 + 10*u**2 - 8*u + 2*u**3 - 7*u**2.
2*(u - 2)*(u + 1)*(u + 2)
Let w = -862/9 - -96. Factor 0*n**2 - w*n + 2/9*n**3 + 0.
2*n*(n - 1)*(n + 1)/9
Suppose 0 = 3*r - 9. Determine u so that 3 - 3*u + r*u**2 - 5*u + 2*u = 0.
1
Find l such that 0*l + 2/9*l**4 - 2/9*l**2 + 0 + 0*l**3 = 0.
-1, 0, 1
Let x = 114/7 - 6833/420. Let d(o) be the second derivative of 0 - o + x*o**6 + 1/40*o**5 - 1/12*o**3 + 1/2*o**2 - 1/8*o**4. Factor d(n).
(n - 1)**2*(n + 1)*(n + 2)/2
Let r(w) be the second derivative of -w**7/420 - w**6/180 + w**5/60 + w**4/12 - 5*w**3/6 + 6*w. Let k(h) be the second derivative of r(h). Factor k(z).
-2*(z - 1)*(z + 1)**2
Let o be 2 + (2 + 0 - 2). Factor 3*f**3 + 3*f**3 + 2 + 4*f**o + 5*f - 5*f**3.
(f + 1)**2*(f + 2)
Let z = -38 + 43. Let l(x) be the third derivative of 0 + 1/120*x**6 + 0*x**3 + 0*x + 0*x**4 + 2*x**2 + 1/60*x**z. Find u such that l(u) = 0.
-1, 0
Let n(p) = p**2 + 25*p + 86. Let s be n(-4). What is c in 1/2*c**2 - s*c + 3/2 = 0?
1, 3
Factor 0*b - 2/5*b**4 - 4/5*b**3 + 0 + 6/5*b**2.
-2*b**2*(b - 1)*(b + 3)/5
Let u(d) be the first derivative of d**7/840 + d**6/360 + 2*d**3/3 + 2. Let z(a) be the third derivative of u(a). Let z(o) = 0. Calculate o.
-1, 0
Let q(p) = -7*p**2 - p + 11. Let l(z) = -8*z**2 - 2*z + 12. Let m = 7 + -2. Let u(j) = m*l(j) - 6*q(j). Find f such that u(f) = 0.
-1, 3
Let b = 97 - 95. Factor 2/9*m - 2/9*m**b + 0.
-2*m*(m - 1)/9
Suppose p + 2*p = 9. Let r(g) = 9*g**3 + 17*g**2 + 19*g + 7. Let k(h) = -9*h**3 - 18*h**2 - 18*h - 6. Let v(n) = p*r(n) + 4*k(n). Solve v(m) = 0 for m.
-1, -1/3
Let t = -1 - -6. Let u be 52/14 - 26/(-91). Suppose 6*j**u - 4*j**5 + 0*j**2 - j + 7*j**t - 2*j - 6*j**2 = 0. What is j?
-1, 0, 1
Let t(z) be the first derivative of 3*z**5/35 + z**4/7 - z**3/21 - z**2/7 + 14. Factor t(m).
m*(m + 1)**2*(3*m - 2)/7
Let a(d) be the third derivative of 0*d**4 + 0 + 0*d**5 + 0*d + d**2 + 0*d**3 + 0*d**7 - 1/1008*d**8 + 1/360*d**6. Factor a(c).
-c**3*(c - 1)*(c + 1)/3
Suppose -3*w = -8*w - 25. Let k(r) = -7*r**4 + 3*r**3 - 3*r**2 + 7*r + 5. Let o(j) = j**4 - j**3 + j**2 - j - 1. Let l(b) = w*o(b) - k(b). Factor l(i).
2*i*(i - 1)*(i + 1)**2
Factor 12*r - 15*r**2 - 12 + 12*r**2 + 0*r**2.
-3*(r - 2)**2
Let t(g) = -g**3 - 8*g**2 - 6*g + 9. Let k be t(-7). Suppose 2 = -l + k*l. Let 2/3*y + 0 + 2/3*y**l = 0. What is y?
-1, 0
What is l in -1/3*l**4 + l**2 + 1/3*l**3 + 2/3 - 5/3*l = 0?
-2, 1
Let l(f) = -2*f**2 - 7*f + 9. Let a(q) = -10*q**2 - 34*q + 44. Let u(h) = 6*a(h) - 28*l(h). Factor u(r).
-4*(r - 1)*(r + 3)
Let m = -114 + 114. Let f(t) be the first derivative of m*t + 2/11*t**2 + 4 - 2/33*t**3. Factor f(q).
-2*q*(q - 2)/11
Solve 6/5*z**3 + 0 - 1/5*z**4 + 0*z - 9/5*z**2 = 0 for z.
0, 3
Let t(i) be the first derivative of -2*i**6/3 - 16*i**5/5 - 6*i**4 - 16*i**3/3 - 2*i**2 + 4. Determine q, given that t(q) = 0.
-1, 0
Let p(h) be the first derivative of 5*h**4/4 - 10*h**3/3 - 15*h**2/2 - 2. What is z in p(z) = 0?
-1, 0, 3
Let c(v) = -v + 1. Let j(h) = -3*h**2 + 24*h - 21. Let g(i) = 12*c(i) + j(i). Solve g(f) = 0.
1, 3
Factor -10*u**3 + 2*u - 2*u + 15*u**5 - 10*u**5 + 5*u.
5*u*(u - 1)**2*(u + 1)**2
Let z(x) = -4*x**3 + 3*x. Let a(q) = -3*q**2 + q. Let b(k) = k**3 - 2*k**2. Let l(h) = -2*a(h) + 3*b(h). Let n(f) = 3*l(f) + 2*z(f). Let n(p) = 0. Calculate p.
0
Let j(v) be the third derivative of -1/144*v**4 - 1/240*v**6 + 0 + 0*v - 1/120*v**5 + 2*v**2 + 0*v**3 - 1/1260*v**7. Find m such that j(m) = 0.
-1, 0
Let g(q) = -q**2 - 15*q + 10. Let f(t) = -10*t**2 - 135*t + 90. Let n(u) = 6*f(u) - 55*g(u). Factor n(d).
-5*(d - 2)*(d - 1)
Let y(v) be the second derivative of v**6/660 + v**5/110 + v**4/66 - 2*v**2 - 3*v. Let j(a) be the first derivative of y(a). Factor j(w).
2*w*(w + 1)*(w + 2)/11
Let v(o) be the second derivative of -o**4/24 - o**3/4 - o**2/2 - 15*o. Let v(r) = 0. Calculate r.
-2, -1
Determine d, given that -d**2 + d**4 + 0*d + 0 + 7/2*d**5 - 7/2*d**3 = 0.
-1, -2/7, 0, 1
Let m(a) be the third derivative of a**7/2520 + a**6/540 + a**5/360 + 2*a**3/3 + a**2. Let f(k) be the first derivative of m(k). Find x such that f(x) = 0.
-1, 0
Determine q so that 13 + 2*q**2 - q**3 - 3 + 7*q - 6 = 0.
-1, 4
Let r(h) be the first derivative of -h**3/21 - h**2/7 + 8*h/7 + 22. Factor r(k).
-(k - 2)*(k + 4)/7
Suppose -110*g**3 + 20*g**3 - 70*g**2 - 28*g**4 + 5*g + 8 - 5*g = 0. What is g?
-2, -1, -1/2, 2/7
Suppose 2*j + 1 = m, -4*m + 8 = -j - 10. Factor -5*q + 21*q**3 - 60*q**j + 17*q**4 + 10*q**4 + 17*q.
3*q*(q - 1)*(q + 2)*(9*q - 2)
Let c be 5 + -2 - 3 - 0. Suppose q + q = c. Factor 0*j + 2/5*j**2 + 0*j**3 + q - 2/5*j**4.
-2*j**2*(j - 1)*(j + 1)/5
Let l(s) = 18*s**2 + 6*s - 12. Let d(f) = f**3 - 17*f**2 - 5*f + 13. Let g(i) = -3*d(i) - 2*l(i). Factor g(z).
-3*(z - 5)*(z - 1)*(z + 1)
Let v(j) be the second derivative of -j**4/28 + j**3/7 + 9*j**2/14 + 28*j. Determine n, given that v(n) = 0.
-1, 3
Let m(b) be the second derivative of -b**8/7560 - b**7/1890 - b**6/1620 + b**3/6 - 2*b. Let l(a) be the second derivative of m(a). Factor l(r).
-2*r**2*(r + 1)**2/9
Suppose -o = -2*o + 2. Suppose -5*f + 14 = -o*q, 3 = 2*q + 7. Factor -2/3*r - r**f + 5/3*r**3 + 0.
r*(r - 1)*(5*r + 2)/3
Let k = 241/4 + -60. Let r(u) be the second derivative of u - k*u**2 + 1/4*u**3 - 1/8*u**4 + 0 + 1/40*u**5. Solve r(a) = 0 for a.
1
Let m(h) = 14*h**3 - 17*h**2 - 8*h - 11. Let i(w) = -5*w**3 + 6*w**2 + 3*w + 4. Let y(u) = -11*i(u) - 4*m(u). Let y(n) = 0. What is n?
0, 1
Let u(w) be the first derivative of 3*w**5/5 - 15*w**4/2 + 33*w**3 - 66*w**2 + 60*w - 3. Solve u(a) = 0 for a.
1, 2, 5
Let p = -13 + 15. Let f(c) be the first derivative of -c**4 - 10/3*c**3 + 12/5*c**5 + 1 - p*c - 5/6*c**6 + 9/2*c**2. Find g, given that f(g) = 0.
-1, 2/5, 1
Let c(p) = -4*p + 24 - 11 + 3*p. Let b be c(10). Factor -4/3*i**2 + 2/3*i**b + 2/3*i + 0.
2*i*(i - 1)**2/3
Factor 29*q + 5*q**5 + 45*q**4 + 230*q**2 - 150*q**3 - 194*q - 10*q**5 + 45.
-5*(q - 3)**2*(q - 1)**3
Let n = 1/163 + 321/815. Fa