*5/25 + 2*y**4/5 - 3*y**3/5 + 3*y. Factor m(s).
-2*s*(s - 1)**2*(s + 3)**2/5
Let v(q) = -19*q**3 - 2*q - 1. Let r be v(-1). Let t be 207/30 - (-12)/r. Determine c, given that -t*c**2 - 3/2*c + 3/2*c**3 + 9/2*c**4 + 3 = 0.
-1, 2/3, 1
Find d such that 0*d + 0 + 1/5*d**3 + 0*d**2 = 0.
0
Factor -3*f**2 - 18*f**3 + 0*f**5 - 3*f**5 - 9*f**2 - 3*f - 12*f**4.
-3*f*(f + 1)**4
Let z(c) be the second derivative of -c**8/168 - 2*c**7/105 + c**5/15 + c**4/12 + 3*c**2/2 + 2*c. Let j(m) be the first derivative of z(m). Factor j(v).
-2*v*(v - 1)*(v + 1)**3
Let k(f) be the first derivative of f**6/5 + 38*f**5/25 + 4*f**4 + 16*f**3/5 - 16*f**2/5 - 32*f/5 - 39. Let k(y) = 0. What is y?
-2, -1, 2/3
Let w(h) be the second derivative of h**7/14 - 3*h**5/20 - 5*h. Factor w(s).
3*s**3*(s - 1)*(s + 1)
Let u(d) be the third derivative of 1/45*d**5 - 1/144*d**8 + 0 + d**2 - 1/18*d**6 + 0*d**4 + 23/630*d**7 + 0*d + 0*d**3. Find z, given that u(z) = 0.
0, 2/7, 1, 2
Let g(i) = 16*i**2 + 7*i - 11. Let h(k) = -2*k + 4*k**2 + 2 + 4*k - 5. Let v(y) = 6*g(y) - 22*h(y). Let v(q) = 0. What is q?
0, 1/4
Let h(i) be the second derivative of 11*i**4/78 - i**3/3 + 2*i**2/13 + i. Let h(s) = 0. What is s?
2/11, 1
Factor 27/2*c**2 - 24 + 3/2*c**3 + 9*c.
3*(c - 1)*(c + 2)*(c + 8)/2
Solve -3/7*k**2 + 0 - 1/7*k**3 - 2/7*k = 0.
-2, -1, 0
Suppose 3*d + 0*d = 6. Suppose 0*o**3 + 0*o**d + 3*o**3 - o**2 - 2*o**3 = 0. Calculate o.
0, 1
Solve 6*j**2 + 22*j**3 + 6*j**3 - 16*j**4 + 2*j**2 = 0.
-1/4, 0, 2
Suppose 0 = 3*v - 4 - 5. Factor -8*k + 24*k**2 - 7*k**3 + 0*k - 11*k**v + 0*k.
-2*k*(3*k - 2)**2
Let y(w) = 49*w**2 + 28*w + 10. Let h(o) = 1. Let d = 12 - 8. Let n(l) = 1. Let i(f) = d*n(f) - 5*h(f). Let p(s) = 6*i(s) + y(s). Factor p(z).
(7*z + 2)**2
Suppose 10 = 4*m + 2. Let u be ((-2)/4)/((-2)/16). Determine s so that -s**u + s**2 - 2*s + m*s = 0.
-1, 0, 1
Let i(k) be the second derivative of -9/40*k**5 + 3/4*k**4 + 1/40*k**6 - k**3 - 3*k + 0*k**2 + 0. Factor i(w).
3*w*(w - 2)**3/4
Let g(x) be the third derivative of x**5/15 + 2*x**2. Let t be g(-1). Find d, given that -2/5*d**t - 2/5 + 8/5*d + 8/5*d**3 - 12/5*d**2 = 0.
1
Let 2/7*x**2 - 10/7*x**4 + 2/7*x**5 - 16/7*x + 8/7 + 2*x**3 = 0. Calculate x.
-1, 1, 2
Let z = -8 + 16. Suppose -3*x = 5*f - 2 - 4, -2*f - 4*x + z = 0. Factor 2*l**2 - 2*l**3 + 0*l + f*l.
-2*l**2*(l - 1)
Let o = 292/57 - 72/19. Solve -8/3 + 2*l**2 + 5/3*l**3 - o*l + 1/3*l**4 = 0 for l.
-2, 1
Let a = 380 + -759/2. Factor 0*c - 9/4*c**2 + 1 + a*c**3 + 3/4*c**4.
(c - 1)**2*(c + 2)*(3*c + 2)/4
Let a be 2*(-2)/(-8)*12/2. Factor -1/4*d**a + 1/4*d**2 + 0*d + 0.
-d**2*(d - 1)/4
Let m(v) be the second derivative of 1/15*v**5 + 4*v - 1/18*v**4 - 2/9*v**3 + 0*v**2 + 0 + 1/45*v**6. Let m(k) = 0. Calculate k.
-2, -1, 0, 1
Let f(z) be the first derivative of -1/1260*z**6 + 0*z**2 + z**3 - 1/84*z**4 + 0*z + 3 + 1/210*z**5. Let g(w) be the third derivative of f(w). Factor g(q).
-2*(q - 1)**2/7
Suppose -5*x**3 + 0*x**4 + 0 + 5/6*x**5 - 20/3*x**2 - 5/2*x = 0. What is x?
-1, 0, 3
Let n be 1600/760 - (-2 - 80/(-38)). Solve -2/9*p**n + 0 + 4/9*p = 0.
0, 2
Solve 0*x**3 - 39*x + 4 - 2*x**3 + 45*x = 0 for x.
-1, 2
Factor 8*b**4 + 8*b**4 - 20*b**4 + 8*b**3.
-4*b**3*(b - 2)
Let x(s) be the third derivative of s**5/15 - s**4/3 + 2*s**2 - 11*s. Factor x(u).
4*u*(u - 2)
Let i be 4/8 - 3/6*-3. Factor 1/3*m**i + 0 + 1/3*m**3 + 0*m.
m**2*(m + 1)/3
Let a = 97/4 + -481/20. Factor -a*i**3 + 0*i + 1/5*i**5 + 0*i**4 + 0*i**2 + 0.
i**3*(i - 1)*(i + 1)/5
Let g(a) be the third derivative of -3/20*a**5 + 0*a + 0 + 1/12*a**4 + 5*a**2 - 1/120*a**7 + 0*a**3 + 1/16*a**6. Factor g(s).
-s*(s - 2)**2*(7*s - 2)/4
Let h(y) be the second derivative of -y**7/147 + 2*y**6/105 + y**5/70 - y**4/21 - 8*y. Suppose h(d) = 0. What is d?
-1, 0, 1, 2
Let b be 16/72 - 50/(-18). Factor 0*k**4 - k**4 + 4 + 0*k**4 - 2 + 3*k - b*k**3 - k**2.
-(k - 1)*(k + 1)**2*(k + 2)
Let q(p) = p**2 + 18*p + 3. Let y be q(-18). Let r(z) be the first derivative of 0*z + 0*z**2 - 1/15*z**3 + 3/25*z**5 - y + 1/10*z**4. Solve r(w) = 0 for w.
-1, 0, 1/3
Let f(n) = n**3 - 4*n**2 - 3*n - 4. Let r be f(5). Suppose g - r*g = -10. Factor -2/7 + 4/7*h - 2/7*h**g.
-2*(h - 1)**2/7
Let n be 2/(-11) - 24/(-11). Let q(g) = -2*g**2 - 1 + 0 + 3*g**n + 0. Let h(b) = -2*b**3 + 6*b**2 - 4. Let c(t) = -h(t) + 4*q(t). Factor c(x).
2*x**2*(x - 1)
Let h(d) = 2*d - 5*d + 1 + 5*d. Let r be h(2). Find w such that 2*w**4 - 3*w**4 - w - 4*w**2 + r*w**2 + w**3 = 0.
-1, 0, 1
Let z(s) = -8*s**4 + 27*s**3 - 65*s**2 + 63*s - 17. Let t(r) = 23*r**4 - 82*r**3 + 195*r**2 - 188*r + 52. Let w(v) = -3*t(v) - 8*z(v). Factor w(d).
-5*(d - 2)**2*(d - 1)**2
Suppose 2*t = -5*p + 8, 0 = p - 2*p + 2*t - 8. Factor 0 + 3*l**4 - 5/4*l**5 + p*l + 1/2*l**2 - 9/4*l**3.
-l**2*(l - 1)**2*(5*l - 2)/4
Let x(l) = -l**2 + 7*l - 10. Let k be x(5). Let b(a) be the first derivative of a**2 - 3 + k*a - 1/3*a**3. Let b(c) = 0. Calculate c.
0, 2
Factor 2/3*o**2 + 0 + 0*o + 2/3*o**3.
2*o**2*(o + 1)/3
Let f(y) be the third derivative of -y**8/8400 + y**7/4200 + y**6/3600 - y**4/12 + 3*y**2. Let q(w) be the second derivative of f(w). Factor q(c).
-c*(c - 1)*(4*c + 1)/5
Let k(d) = 2*d. Let g be k(-5). Let c = 10 + g. Determine y, given that -1 + 4*y**2 + 0*y**4 + c - 2*y**4 - 1 = 0.
-1, 1
Suppose 9*k = -r + 4*k + 8, 0 = -2*r - 4*k + 10. Suppose -2 = 2*x - r*x. Let -x*j**4 - 2*j**4 + 5*j**4 - 2*j**3 - j**2 + 2*j = 0. What is j?
-1, 0, 1, 2
Let k(r) be the first derivative of r**7/840 - r**5/120 - 4*r**3/3 - 4. Let s(q) be the third derivative of k(q). Factor s(h).
h*(h - 1)*(h + 1)
Let -57/5*m**4 + 9*m**3 - 3/5*m**2 - 6/5*m + 21/5*m**5 + 0 = 0. Calculate m.
-2/7, 0, 1
Let o = -445/6 - -224/3. Let -1/4*u**5 - o*u**2 + 0*u**3 + 1/2*u**4 + 1/4*u + 0 = 0. Calculate u.
-1, 0, 1
Let t(s) be the first derivative of -s**4/20 + 2*s**3/15 - s**2/10 - 2. Find q, given that t(q) = 0.
0, 1
Let m(d) = -d**2 - d. Let g(o) = -4*o**2 + o - 5. Let c(i) = -g(i) + 5*m(i). Let p be c(-6). Factor -2*u**4 + u - 3*u**2 - 5*u**5 + u**2 + 4*u**4 + 4*u**p.
-u*(u - 1)**3*(u + 1)
Let j(g) = g**2 + 3*g + 4. Let d be j(-4). Solve -4 + 6*n + 8*n**4 - 6*n**2 - d*n**3 - 5*n - 2*n**5 + 2*n**2 + 9*n = 0 for n.
-1, 1, 2
Let h = 6 - 6. Solve 6 - 4*x**2 - 4 + h*x**4 + 6*x**4 - 4*x**4 = 0 for x.
-1, 1
Let t(f) be the first derivative of f**5/15 - f**4/12 - f**3/3 + 5*f**2/6 - 2*f/3 - 7. Factor t(r).
(r - 1)**3*(r + 2)/3
Determine q, given that 9/2*q + 9/4*q**2 + 5/4 = 0.
-5/3, -1/3
Let n(p) be the first derivative of p**6/2 - 21*p**5/5 + 45*p**4/4 - 13*p**3 + 6*p**2 - 11. Factor n(t).
3*t*(t - 4)*(t - 1)**3
Let t(d) be the third derivative of 1/420*d**7 + 0*d + 0*d**4 - 1/120*d**5 + 2*d**2 + 0 + 0*d**3 - 1/240*d**6 + 1/672*d**8. Factor t(o).
o**2*(o - 1)*(o + 1)**2/2
Suppose 0 = 28*h - 26*h - 6. Let n(j) be the second derivative of 0*j**h - 2/15*j**6 + 1/10*j**5 + 2*j + 1/21*j**7 + 0*j**4 + 0 + 0*j**2. Factor n(z).
2*z**3*(z - 1)**2
Let y(a) be the first derivative of -a**6/2 + 21*a**5/10 - 27*a**4/8 + 5*a**3/2 - 3*a**2/4 + 21. Factor y(k).
-3*k*(k - 1)**3*(2*k - 1)/2
Let o = -76 - -534/7. Solve -2/7*b**2 - o*b + 0 = 0.
-1, 0
Let q(j) be the second derivative of -j**7/105 + 2*j**6/75 - j**4/15 + j**3/15 + j. Solve q(y) = 0 for y.
-1, 0, 1
Let o(s) = s**2 - s. Let v = 13 + -7. Let b = v - 4. Let d(w) = -w**2 + 2*w - 1. Let h(z) = b*d(z) + 3*o(z). Factor h(g).
(g - 1)*(g + 2)
Determine s so that 13*s - 9*s + 4*s**3 - 8*s**3 = 0.
-1, 0, 1
Solve 4/7*b**4 + 0*b**3 + 2/7*b**5 - 4/7*b**2 - 2/7*b + 0 = 0.
-1, 0, 1
Solve 3*c**3 - c**2 - 2*c**3 + 2*c**2 = 0.
-1, 0
Suppose 9/4*h**2 - h**3 + 1/4 - 3/2*h = 0. What is h?
1/4, 1
Let p(x) be the third derivative of -2*x**2 + 0*x + 0 + 1/90*x**5 - 1/9*x**3 + 1/24*x**4. Factor p(u).
(u + 2)*(2*u - 1)/3
Let c = 86 - 859/10. Let x(l) be the third derivative of 3*l**2 + 1/3*l**4 + 0 + c*l**5 + 0*l + 1/3*l**3. Factor x(r).
2*(r + 1)*(3*r + 1)
Let y = -2/421 + 3799/2105. Solve 0 + 3/5*o**3 + y*o**2 + 6/5*o = 0 for o.
-2, -1, 0
Let i = 1013/80 + -63/5. Let w(m) be the first derivative of -1 + 1/8*m**2 - i*m**4 - 1/12*m**3 + 1/4*m. Find g such that w(g) = 0.
-1, 1
Find q such that 2/11*q**2 - 2/11*q + 2/11*q**3 - 2/11 = 0.
-1, 1
Let n(l) be the first derivative of -l + 2 - 3/4*l**2 - 1/6*l**3. Solve n(q) = 0.
-2, -1
Suppose -m + 8 = 1