4)/6. Factor -a - 1/2 - d*a**2.
-(a + 1)**2/2
Suppose 0 + 0*a + 3/2*a**2 = 0. Calculate a.
0
Let j(i) = -i**2 - i + 1. Let z(o) = -11 - 8*o**2 + 16 - 2*o**3 + 4*o**3 + 2 - 7*o - o**4. Let k(d) = 21*j(d) - 3*z(d). What is n in k(n) = 0?
0, 1
Let p(k) = -k**3 + 3*k**2 + 5*k - 4. Let t be p(4). Suppose 0 = -t*l + l + v - 5, -3*v = 5*l - 19. Factor -s - 2*s**3 + 7*s**l - s - 3*s**2.
-2*s*(s - 1)**2
Factor -3*a - 137*a**2 + 6*a**4 - 129*a**2 + 3*a**5 + 260*a**2.
3*a*(a - 1)*(a + 1)**3
Let y = -26/37 - -848/259. Factor -y*j**2 + 10/7*j**3 - 2/7*j**4 - 4/7 + 2*j.
-2*(j - 2)*(j - 1)**3/7
Let f(x) be the third derivative of 0*x**5 + 3*x**2 + 0*x + 0 + 0*x**3 - 1/630*x**7 + 0*x**4 - 1/1008*x**8 + 0*x**6. Factor f(n).
-n**4*(n + 1)/3
Let c = 6847/630 + -76/7. Let b(x) be the third derivative of 0*x**3 + 0 + 0*x - c*x**5 - 1/72*x**4 - 1/360*x**6 + x**2. Determine a, given that b(a) = 0.
-1, 0
Let x = 8 - 4. Determine q so that 42*q**2 - 33*q + 6 + 4 + 21*q**5 + 16*q**3 - 48*q**x - 4 - 4*q**3 = 0.
-1, 2/7, 1
Let t(w) be the third derivative of -1/3*w**3 - 1/1440*w**6 - 1/24*w**4 + 0 + 0*w - 1/120*w**5 - w**2. Let i(u) be the first derivative of t(u). Factor i(x).
-(x + 2)**2/4
Solve -6/5*y - 4/5 - 2/5*y**2 = 0.
-2, -1
Suppose 19 = y - 4*a - 3, y + 5*a + 23 = 0. Let g(u) be the third derivative of u**y + 0 + 0*u + 1/60*u**5 - 1/6*u**3 + 0*u**4. Suppose g(z) = 0. What is z?
-1, 1
Suppose 0 = -0*b + 2*b - 6. Suppose -2*l + b*l - 3 = 0. Factor -3*w**3 + 2*w**5 + w**l + 0*w**5.
2*w**3*(w - 1)*(w + 1)
Let j = -5 - -10. Let d = j + -3. Let -1/3*v + 0 + v**d - v**3 + 1/3*v**4 = 0. Calculate v.
0, 1
Let z(o) be the first derivative of o**7/105 - o**5/25 + o**3/15 + 3*o - 2. Let v(i) be the first derivative of z(i). Determine u so that v(u) = 0.
-1, 0, 1
Let q(y) = y**4 + 3*y**2. Let h(p) = -p**4 - p**2. Suppose -6*v + 5*v = 3. Let f(m) = v*h(m) - q(m). Factor f(j).
2*j**4
Let i(u) be the third derivative of -2*u**7/15 + 8*u**6/15 + u**5/5 - 8*u**4/3 + 8*u**3/3 - 44*u**2. Solve i(j) = 0 for j.
-1, 2/7, 1, 2
Factor -4*t + 5*t - 5*t + t**3 + 0*t**3.
t*(t - 2)*(t + 2)
Let u = 1032/5 - 206. Factor -2/5*k**5 - 2/5*k + 4/5*k**2 + 4/5*k**3 - u - 2/5*k**4.
-2*(k - 1)**2*(k + 1)**3/5
Let c(w) be the first derivative of 4*w**3/3 + 2*w**2 + 5. Factor c(j).
4*j*(j + 1)
Let t(q) be the first derivative of 4*q**3/3 - 6*q**2 + 8*q - 44. What is f in t(f) = 0?
1, 2
Let t(p) = p**2 + 7*p - 11. Let z be t(-9). Find d, given that 7*d**4 + d**4 - z*d**4 - d**2 = 0.
-1, 0, 1
Let o = -1/1433 - -11473/12897. Let s(w) be the first derivative of 1 - 2/3*w - o*w**3 + 4/3*w**2. Solve s(a) = 0.
1/2
Let v(i) be the second derivative of 0 + 1/5*i**2 - 1/30*i**4 + 0*i**3 + 2*i. Factor v(g).
-2*(g - 1)*(g + 1)/5
Factor -t - 35/4*t**3 + 0 + 6*t**2.
-t*(5*t - 2)*(7*t - 2)/4
Let b(x) be the second derivative of -1/84*x**7 + 1/10*x**6 + x - 7/20*x**5 + 2/3*x**4 - 3/4*x**3 + 1/2*x**2 + 0. What is o in b(o) = 0?
1, 2
Suppose -4*v = -3*v - 3. Let y be 0/((v - 0) + -1). Factor 4/3*z**2 + 0*z - 2/3*z**3 + y.
-2*z**2*(z - 2)/3
Suppose 0 = -2*u - 6*r + 2*r - 12, -3*u - 5*r - 15 = 0. Let a be ((-2)/(-7) + u)*1. Suppose -a + 4/7*y**2 + 0*y - 2/7*y**4 + 0*y**3 = 0. What is y?
-1, 1
Let y(i) = 5*i**3 - 13*i**2 + 24*i - 3. Let g(p) = p**3 - 3*p**2 + 6*p - 1. Let d(q) = 26*g(q) - 6*y(q). Factor d(k).
-4*(k - 1)**2*(k + 2)
Let r(z) = -13*z**5 - 55*z**4 - 73*z**3 - 45*z**2 - 8*z. Let n(d) = d**5 + d**3 + d. Let c(u) = 2*n(u) - r(u). Factor c(p).
5*p*(p + 1)**3*(3*p + 2)
Let a(x) = 15*x**4 + 41*x**3 + 4*x**2 + 11. Let r(g) = 3*g**4 + 8*g**3 + g**2 + 2. Let y(n) = -2*a(n) + 11*r(n). Factor y(m).
3*m**2*(m + 1)**2
Let -1/7*t - 1/7*t**2 + 0 = 0. Calculate t.
-1, 0
Let i = -16 + 19. Solve 0*u**3 + 5*u - 5*u - 2*u**i + 2*u - 4 + 4*u**2 = 0.
-1, 1, 2
Let d = -157 + 15. Let k = -708/5 - d. Factor -8/5*v**2 + 8/5*v - k.
-2*(2*v - 1)**2/5
Let d(g) = -3*g**3 - g**2 - 2*g - 2. Let k(i) = 3*i**3 + 3*i + 3. Let c(y) = -y**2 - 4*y - 5. Let p be c(-3). Let h(r) = p*k(r) - 3*d(r). Factor h(u).
3*u**2*(u + 1)
Let d(j) be the second derivative of j**4/6 - 5*j**3/12 + j**2/4 + 45*j. Factor d(y).
(y - 1)*(4*y - 1)/2
Let p(c) = -c + 1. Let o(a) = a**2 - 8*a + 13. Let h(r) = 2*o(r) - 22*p(r). Factor h(t).
2*(t + 1)*(t + 2)
Let t(h) be the second derivative of h**4/24 - 5*h**3/6 + 25*h**2/4 + h. Factor t(j).
(j - 5)**2/2
Let a(g) = -g**3 - 6*g**2 + 7*g + 2. Let x be a(-7). Let q(s) be the first derivative of s**2 + 6*s**3 - 7*s**x + 5 - 1 + 3*s - s. Factor q(u).
2*(3*u - 1)**2
Let v be 68/(-12)*-3 - -3. Let i be 1 - (-1)/1 - -2. Find q such that -28*q**3 - v*q**2 - 5*q**3 - 30*q**4 - i*q - 9*q**5 - 4*q**3 = 0.
-1, -2/3, 0
Factor y**3 + 0 - y + 122*y**2 + 2 - 124*y**2.
(y - 2)*(y - 1)*(y + 1)
Let a = 157/2 - 78. Determine u so that a*u**3 + 1/2*u + 0 + u**2 = 0.
-1, 0
Let v(m) be the first derivative of m**6/360 - m**5/90 - m**4/72 + m**3/9 - 2*m**2 - 1. Let u(f) be the second derivative of v(f). Factor u(o).
(o - 2)*(o - 1)*(o + 1)/3
Let n(p) be the first derivative of p**2 + 1/6*p**4 + 2 - 2/3*p**3 + 2*p. Let a(o) be the first derivative of n(o). Factor a(w).
2*(w - 1)**2
Let d(q) = -7*q**2 - 3*q. Let m(k) = 3*k**2 + k. Let n(z) = 2*d(z) + 5*m(z). Solve n(u) = 0.
0, 1
Let j be (-84)/32 - -3 - (-3)/(-9). Let m(o) be the third derivative of -o**2 + 0*o**4 + 0*o + 1/240*o**5 - j*o**3 + 0. Let m(c) = 0. What is c?
-1, 1
Let s = 53 + -953/18. Let j(z) be the first derivative of 0*z - 1 - 4/27*z**3 + s*z**4 + 1/9*z**2. Factor j(r).
2*r*(r - 1)**2/9
Let h(i) be the second derivative of -i**8/5040 - i**7/1260 + i**5/180 + i**4/72 + 2*i**3/3 + 3*i. Let q(n) be the second derivative of h(n). Solve q(a) = 0.
-1, 1
Let a be 8/32 - (-647)/4. Let x be (-4)/18 + 279/a. Find z, given that 3/2*z**2 + 1/2*z**4 + 0 - 1/2*z - x*z**3 = 0.
0, 1
Let f(p) be the third derivative of 1/240*p**5 + 0 + 0*p - p**2 + 0*p**4 + 0*p**3. Factor f(t).
t**2/4
Suppose z + 2*k - 2 = 0, 6*z = z - k + 1. Solve 0*w - 1/5*w**5 + z + 0*w**3 + 2/5*w**4 + 0*w**2 = 0 for w.
0, 2
Let d(c) = c**3 + 11*c**2 + 14*c - 36. Let j be d(-9). Let f = -59/2 + 30. Factor j*h - f*h**2 + 1/2.
-(h - 1)*(h + 1)/2
Let n(k) be the second derivative of -k**4/42 + 6*k**3/7 - 81*k**2/7 - 9*k + 3. Factor n(t).
-2*(t - 9)**2/7
Let c(w) be the first derivative of 9*w**4/16 - 5*w**3/4 + 3*w**2/8 + 3*w/4 - 15. Factor c(f).
3*(f - 1)**2*(3*f + 1)/4
Suppose -281 = -r - 278. Let u(k) be the second derivative of 0*k**4 + 4*k - 1/20*k**5 + 0 + 0*k**2 + 0*k**r. Let u(v) = 0. Calculate v.
0
Let j(l) = -l**3 + 6*l**2 + l - 1. Let t be j(6). Factor -5*i**2 - 9*i**2 - 3*i + 6*i**4 - 18*i**3 - i - 2*i**t - 16*i**4.
-2*i*(i + 1)**3*(i + 2)
Let i(k) be the second derivative of k**6/4 - 59*k**5/60 + 35*k**4/24 - k**3 + k**2/3 + 10*k. Determine g so that i(g) = 0.
2/9, 2/5, 1
Factor 2*s + 33*s**2 - 21*s**2 - 7*s - 7*s**2.
5*s*(s - 1)
Suppose 3*f - 3*h - 15 = 3, 2*f = -5*h + 5. Let c(x) = -x**3 + x**2 + x - 1. Let u(t) = 3*t**3 - 3*t**2 + 5*t + 11. Let s(l) = f*c(l) + u(l). Solve s(q) = 0.
-1, 3
Let x(z) be the first derivative of 0*z**4 - 1/35*z**5 + 0*z + 0*z**2 + 1/21*z**3 + 8. Factor x(n).
-n**2*(n - 1)*(n + 1)/7
Let g(r) = 2*r**5 - 2*r**4 + r**2 - r. Let y = 4 - 7. Let n(m) = 2*m**5 - 3*m**4 + m**3 + m**2 - m. Let b(k) = y*n(k) + 2*g(k). Factor b(c).
-c*(c - 1)**3*(2*c + 1)
Solve -8/5 - 4/5*q**3 - 6/5*q**4 + 18/5*q**2 + 0*q = 0 for q.
-2, -2/3, 1
Suppose g + h = 4, -12 = -5*g - 3*h - 0*h. Suppose 2/3*k**2 + g + 2/3*k = 0. What is k?
-1, 0
Let v = 22 - 28. Let d(b) = -10*b**2 + 14*b - 14. Let l(s) = -2*s**2 + 3*s - 3. Let c(z) = v*d(z) + 28*l(z). Factor c(y).
4*y**2
Suppose -u = -4*u, d = -4*u. Let k(t) be the second derivative of 0*t**2 + 0*t**3 + 1/60*t**5 + d + 0*t**4 + t. Solve k(o) = 0 for o.
0
Let y = 29 - 23. Suppose 9 = 5*j - y. Suppose -2/3*o**2 + 2/3*o**j + 2/3*o**4 + 0 - 2/3*o = 0. What is o?
-1, 0, 1
Let r(v) be the first derivative of 0*v**2 + 2*v - 2 + 0*v**3 + 1/30*v**4. Let g(d) be the first derivative of r(d). Find a such that g(a) = 0.
0
Determine w, given that 4/3 + 1/6*w**2 - w = 0.
2, 4
Let c(i) = i**3 + 4*i**2 - 5*i + 1. Let l be c(-5). Suppose -3*v - l + 4 = 0. Factor -2 + r**3 - r**2 + 3*r - v + 4*r**2 + 4.
(r + 1)**3
Let n be 1/(2/28*2). Let -n*v - 8*v - 6 + 5*v**2 + 10*v**2 + 6*v**2 = 0. Wh