- 1/15*y**6 + 0 + 0*y**4 - 2/3*y**3 + y**2. Factor z(t).
-2*(t - 1)**3*(t + 1)
Suppose -2*g - 2 = -o - 1, -o = 5*g - 15. Factor 12*t + 4*t**2 + 4*t**g - 5*t**2 + 12.
3*(t + 2)**2
Let 0 + 2/7*k**4 + 20/7*k**3 + 0*k + 18/7*k**2 = 0. Calculate k.
-9, -1, 0
Suppose -6*n + 15 = -n. Let m(l) be the second derivative of -1/90*l**6 + 1/60*l**5 + 0 + 1/36*l**4 + 0*l**2 + 2*l - 1/18*l**n. Factor m(d).
-d*(d - 1)**2*(d + 1)/3
Let i(c) be the third derivative of c**8/26880 + c**7/10080 - c**4/12 - 3*c**2. Let h(u) be the second derivative of i(u). Factor h(q).
q**2*(q + 1)/4
Suppose -11 = -4*t - 0*o - o, 2*t + 3*o - 3 = 0. Let f be (-12)/28*(-2)/t. Solve -2/7 - f*d**2 + 4/7*d = 0 for d.
1
Let s = 203/114 - -1/19. Let y(w) be the first derivative of -s*w**4 - 1/3*w**2 - 2/3*w + 8/15*w**5 + 2*w**3 + 1. Factor y(o).
2*(o - 1)**3*(4*o + 1)/3
Solve 0 + 0*h**2 + 0*h**4 + 32/13*h + 2/13*h**5 - 16/13*h**3 = 0.
-2, 0, 2
Let i(m) be the third derivative of m**7/5040 + m**6/270 + m**5/45 + 5*m**3/6 - 8*m**2. Let k(a) be the first derivative of i(a). Determine o so that k(o) = 0.
-4, 0
Let b = -7 + 10. Suppose 2*r = -2*o + 3*r + 5, -9 = -5*o - r. Find w, given that 2*w - 2 + 0*w**2 + 2*w**2 + 0*w - o*w**b = 0.
-1, 1
Let f = 11 - 6. Suppose 34*o**3 + 56*o + 16*o**3 + 0*o**3 + 2*o**f + 16*o**4 + 76*o**2 + 16 = 0. Calculate o.
-2, -1
Let o(q) be the third derivative of 1/100*q**5 + 0 + 2*q**2 - 1/120*q**4 + 0*q + 1/1050*q**7 + 0*q**3 - 1/200*q**6. Factor o(p).
p*(p - 1)**3/5
Let u(t) be the first derivative of -t**5/330 + t**4/66 - t**3/33 + 5*t**2/2 + 2. Let m(y) be the second derivative of u(y). Solve m(s) = 0 for s.
1
Let 3/2*q**3 - 7/2*q**2 + 1 - 3/2*q + 5/2*q**4 = 0. Calculate q.
-1, 2/5, 1
Suppose k - 1 = 0, k - 2 = 2*y - 9. Suppose -r**4 - y*r + 13/4*r**3 - 3/4*r**2 + 1 = 0. Calculate r.
-1, 1/4, 2
Let m(g) = -74*g**3 - 238*g**2 - 96*g + 38. Let r(v) = 25*v**3 + 79*v**2 + 32*v - 13. Let x(n) = -3*m(n) - 10*r(n). Determine t, given that x(t) = 0.
-2, -1, 2/7
Let k(o) be the first derivative of -1/3*o**3 - o + 1/6*o**4 - 2*o**2 + 3. Let t(p) be the first derivative of k(p). Suppose t(n) = 0. Calculate n.
-1, 2
Let n = 12853/5716 - -2/1429. Let -n*a - 1/2 - 7/4*a**2 = 0. What is a?
-1, -2/7
Let f = 204 - 201. Factor 2/11*i**f + 2/11*i**4 + 0 - 2/11*i**5 - 2/11*i**2 + 0*i.
-2*i**2*(i - 1)**2*(i + 1)/11
Let g(k) = -k**4 + 23*k**3 + 63*k**2 + 80*k + 32. Let a(m) = 4*m**4 - 70*m**3 - 188*m**2 - 240*m - 96. Let q(t) = 6*a(t) + 20*g(t). Solve q(c) = 0.
-4, -1
Let p(j) = 2*j**2 - 3*j - 2. Let x(o) = 4*o**2 - 7*o - 4. Let s(k) = 7*p(k) - 3*x(k). Factor s(z).
2*(z - 1)*(z + 1)
Solve 1/3*l**3 + 2/3 + 5/3*l + 4/3*l**2 = 0.
-2, -1
Let y(q) be the first derivative of 1/5*q**2 + 0*q - 2/15*q**3 - 1. Factor y(f).
-2*f*(f - 1)/5
Let s(d) be the second derivative of 3*d - 3/10*d**4 + 0 + 0*d**2 + 7/50*d**5 + 2/15*d**3. Factor s(b).
2*b*(b - 1)*(7*b - 2)/5
Let v(f) = f**3 + 5*f**2 + 3*f + 1. Let l be v(-4). Let s be (l + -5)/(-2 + 0). Determine t so that 4*t**4 + t**5 + 4*t**2 + 0*t**2 + t + s*t**4 + 6*t**3 = 0.
-1, 0
Let n(o) = -o**2 - 12*o + 2. Let j be n(-12). Let q(p) be the first derivative of 8/5*p**3 + 1/2*p**4 - j + 4/5*p + 9/5*p**2. Factor q(i).
2*(i + 1)**2*(5*i + 2)/5
Factor -2/13*x**4 + 0*x**3 + 6/13*x**2 + 0 - 4/13*x.
-2*x*(x - 1)**2*(x + 2)/13
What is v in -264*v**2 - 189*v**3 + 0 - 28*v**4 - 8 - 24 - 176*v + 41*v**3 = 0?
-2, -1, -2/7
Let s be (24/(-64))/(3 + (-30)/8). Factor 0 - s*f**4 - 1/2*f**3 + 0*f**2 + 0*f.
-f**3*(f + 1)/2
Let w(r) be the third derivative of 2/3*r**3 + 0 + 1/6*r**4 + 1/60*r**5 + 2*r**2 + 0*r. What is y in w(y) = 0?
-2
Let h = 59 + -57. Find x, given that 4/7 + h*x**2 + 18/7*x = 0.
-1, -2/7
Let r(w) = w**2 - 3. Let b(n) = -n + 2. Let q be b(5). Let u be (-6)/(-2*q/4). Let x(s) = 6*s**2 + s - 16. Let j(c) = u*x(c) + 22*r(c). Factor j(o).
-2*(o + 1)**2
Factor 1/2*i - 3/4*i**2 + 0.
-i*(3*i - 2)/4
Suppose 0 - 1/3*d**2 - 2/3*d = 0. Calculate d.
-2, 0
Let n(t) be the second derivative of 0*t**2 + 1/14*t**4 + 1/70*t**5 + 0 - 5*t + 0*t**3. Determine f, given that n(f) = 0.
-3, 0
Let l(a) = 5*a**3 + 6*a**2 + 5*a - 4. Let y(c) = -14*c + 6 + 5 + 10*c**3 - 17*c**2 - 24*c**3. Let z(s) = 11*l(s) + 4*y(s). Factor z(u).
-u*(u + 1)**2
Let q(l) = l + 6. Let t be q(-4). Suppose -6*z = -t*z. Factor 2/7*u**4 + 0 + 0*u + z*u**3 - 2/7*u**2.
2*u**2*(u - 1)*(u + 1)/7
Let y(k) be the second derivative of k**7/14 + 2*k**6/5 - 3*k**5/10 - 3*k**4 + 9*k**3/2 + 23*k. Factor y(c).
3*c*(c - 1)**2*(c + 3)**2
Let s(f) be the first derivative of 27*f**4/4 + 11*f**3 + 3*f**2 - 61. Solve s(o) = 0.
-1, -2/9, 0
Let p(k) be the first derivative of -k**4/4 + 16*k**3/9 - 5*k**2/2 - 6*k - 2. Factor p(t).
-(t - 3)**2*(3*t + 2)/3
Let d be (2/12)/(9/(-27))*-8. Solve 2/5 - 16/5*f**3 - 12/5*f**2 + 0*f - 6/5*f**d = 0 for f.
-1, 1/3
Determine q so that 289*q + 4*q**3 + 4*q**2 + 0*q**3 + 0*q**3 - 297*q = 0.
-2, 0, 1
Factor -2/11*f**2 + 0 - 2/11*f.
-2*f*(f + 1)/11
Let p(x) be the third derivative of x**7/1680 + x**6/480 + x**4/6 - 4*x**2. Let s(k) be the second derivative of p(k). Factor s(r).
3*r*(r + 1)/2
Let j(f) be the first derivative of 49*f**6/4 - 329*f**5/10 + 201*f**4/8 + f**3/6 - 6*f**2 + 2*f + 17. Let j(p) = 0. What is p?
-1/3, 2/7, 1
Let q(p) be the third derivative of -p**11/110880 + p**10/151200 + p**9/30240 + p**5/20 - 6*p**2. Let r(b) be the third derivative of q(b). Factor r(g).
-g**3*(g - 1)*(3*g + 2)
Let a(n) be the third derivative of -n**8/10080 - n**7/3780 - n**4/8 + 7*n**2. Let l(y) be the second derivative of a(y). Determine s so that l(s) = 0.
-1, 0
Let c(l) = -9*l**2 + l. Let t be c(-1). Let d be (t - -8) + 8/3. Factor 2*s**2 - 4/3*s - d*s**3 + 0.
-2*s*(s - 2)*(s - 1)/3
Let t(q) = -q + 20. Let k be t(14). Let w(d) be the second derivative of 0*d**5 - d + 0*d**2 + 1/15*d**k + 0*d**3 + 0 - 1/6*d**4. Factor w(a).
2*a**2*(a - 1)*(a + 1)
Let d(j) be the second derivative of 0 - 2*j - 1/60*j**4 + 1/100*j**5 + 1/10*j**2 - 1/30*j**3. Find v, given that d(v) = 0.
-1, 1
Let j(f) be the first derivative of -f**4/24 + f**3/4 - f**2/2 + 3*f + 1. Let y(p) be the first derivative of j(p). Factor y(a).
-(a - 2)*(a - 1)/2
Suppose -28*f + 20*f + 32 = 0. Factor -1/2*a**3 + 0 + 0*a**f + 1/4*a + 1/4*a**5 + 0*a**2.
a*(a - 1)**2*(a + 1)**2/4
Let p(m) be the second derivative of 0*m**4 - 1/3*m**3 + 0*m**6 + 0*m**2 + 1/420*m**7 - m + 0 + 0*m**5. Let l(u) be the second derivative of p(u). Factor l(q).
2*q**3
Suppose 2*b**2 + 6 - 3 + 20*b - 4*b + 29 = 0. What is b?
-4
Let w(o) be the second derivative of o**5/90 + 3*o**2 - 5*o. Let p(u) be the first derivative of w(u). Factor p(v).
2*v**2/3
Suppose 2*u + u + 9 = 3*f, 0 = -5*f - u + 15. Let c(x) be the first derivative of 4*x**f - 4*x**5 - 4*x - 5*x**2 + 2 + 11/2*x**4. Find b such that c(b) = 0.
-1/2, -2/5, 1
Determine d so that -16/5*d + 2*d**2 - 2/5*d**3 + 8/5 = 0.
1, 2
Let r(h) be the second derivative of h**6/120 - h**4/24 - h**2/2 + h. Let l(x) be the first derivative of r(x). Factor l(v).
v*(v - 1)*(v + 1)
Let w be ((-1)/3)/((-2)/24). Let p be (-4 - 18/(-7)) + w. Factor 8/7 + p*u**4 - 60/7*u**3 + 40/7*u + 26/7*u**2.
2*(u - 2)**2*(3*u + 1)**2/7
Let a(y) = -11*y**3 - 7*y**2 + 2*y + 7. Let q(c) = 5*c**3 + 3*c**2 - c - 3. Let m = -2 + -2. Let r(j) = m*a(j) - 9*q(j). Factor r(u).
-(u - 1)**2*(u + 1)
Let z = -18 - -22. Let v(y) = -3*y**3 - y**2 + 11*y + 7. Let g(f) = -2*f**3 + 6*f + 4. Suppose -5*l = -4*l + 7. Let q(n) = l*g(n) + z*v(n). Factor q(c).
2*c*(c - 1)**2
Let a = 13 + -6. Let 4*m**5 - 11*m**3 + 2*m**4 + a*m**5 - 7*m**2 + m**5 - m + 5*m**4 = 0. What is m?
-1, -1/3, -1/4, 0, 1
Let z(s) = 10*s + 18. Let a(r) = r. Let j(x) = 8*a(x) - z(x). Let y be j(-9). Factor 9/4*b**3 + y*b - 3 + 21/4*b**2.
3*(b + 1)*(b + 2)*(3*b - 2)/4
Determine u so that -6*u**2 + 6*u**2 + 6 + 2*u + 3*u**2 + 7*u = 0.
-2, -1
Suppose 2*n - 2*g = -g + 9, 3*g - 33 = -4*n. Factor 19*t**2 + 2 - n - 5*t**2 + 10*t.
2*(t + 1)*(7*t - 2)
Suppose 5*x - 32 = -22. Factor 5/4*j**x + 7/4*j + 1/2.
(j + 1)*(5*j + 2)/4
Let j(c) = c**2 + 8*c**3 + 2 - 5 + 2*c - 12*c**3. Let u(s) = -7*s**3 + 2*s**2 + 4*s - 5. Let y(l) = -10*j(l) + 6*u(l). Solve y(p) = 0 for p.
-1, 0, 2
Let s(t) = -t**3 + t**2. Let y(w) = -25*w**4 + 63*w**3 - 37*w**2 + 8*w. Let g(v) = -21*s(v) + 3*y(v). Let g(o) = 0. Calculat