*5 + 8/9*t**3 + 0*t + 0 = 0.
-2, 0, 1
Let w(y) = -2*y**2 + 25*y - 76. Let b be w(6). Factor 0 + 2/3*k**4 + 2/9*k**3 + 0*k - 4/9*k**b.
2*k**2*(k + 1)*(3*k - 2)/9
Let w = 62 + -60. Factor -6/5*z + 0 - 3*z**3 + 21/5*z**w.
-3*z*(z - 1)*(5*z - 2)/5
Let z(o) = -2*o**2 + 12*o - 7. Let w be -3*(-14)/6 - 2. Let q be z(w). Suppose -q*j + 3/4*j**4 - 9/4*j**2 + 3 + 3/2*j**3 = 0. Calculate j.
-2, 1
Let z(d) be the second derivative of -3*d**7/28 - 7*d**6/20 - 3*d**5/20 - 4*d. Factor z(b).
-3*b**3*(b + 2)*(3*b + 1)/2
Let o = -151/28 + 65/12. Let v(d) be the second derivative of 0*d**3 - 4*d - o*d**7 - 1/30*d**6 + 0 + 1/20*d**5 + 1/12*d**4 + 0*d**2. Factor v(f).
-f**2*(f - 1)*(f + 1)**2
Let l(z) = -9*z**2 + 7*z. Let v(s) = -18*s + 8*s + 5*s**2 + 6*s. Let h(f) = -4*l(f) - 7*v(f). Factor h(o).
o**2
Let d(f) = 5*f - 10. Let v be d(7). Factor 2*n + 26*n**3 + 4*n**2 - v*n**3 - n**2.
n*(n + 1)*(n + 2)
Factor -3/7*v**3 + 3/7*v**2 + 6/7*v + 0.
-3*v*(v - 2)*(v + 1)/7
Let z(g) be the third derivative of -6*g**2 + 0*g**3 + 0*g**5 - 1/60*g**4 + 1/300*g**6 + 0 + 0*g. Factor z(v).
2*v*(v - 1)*(v + 1)/5
Let k be (-1)/1*(5 + -5). Determine h, given that -4*h**3 + 0*h**3 + k*h**3 + 4*h**2 = 0.
0, 1
Let n(b) be the first derivative of 0*b + 2 + 1/30*b**5 + 0*b**3 - 3/2*b**2 - 1/6*b**4. Let f(o) be the second derivative of n(o). Factor f(y).
2*y*(y - 2)
Suppose d**2 + 4*d**2 - 3*d**2 - 6*d + 4 + 0*d**2 = 0. Calculate d.
1, 2
Let t(b) be the second derivative of -b**8/6720 + b**7/840 - b**5/30 + b**4/6 + 4*b. Let s(f) be the third derivative of t(f). Solve s(z) = 0 for z.
-1, 2
Let c(v) = v + 12. Let z be c(-4). Solve 5*t**5 - z*t**3 - 4*t**2 + 2*t**3 - 3*t**5 = 0.
-1, 0, 2
Let v(o) = -25*o**2 + 31*o - 6. Let z(g) = 12*g**2 - 15*g + 3. Suppose 3*i - 30 = -2*i. Let y be (-39)/i + 1/2. Let b(n) = y*v(n) - 13*z(n). Factor b(k).
-3*(k - 1)*(2*k - 1)
Let z = 67/258 - 4/43. Factor 0*j - 1/6*j**3 - z*j**4 + 0*j**2 + 0.
-j**3*(j + 1)/6
Let p be (-7)/(-3) + (-14)/(-21). Factor -15*t**4 + p*t**3 - 6*t - 43*t**3 + 4*t**3 - 27*t**2.
-3*t*(t + 1)**2*(5*t + 2)
Let y be ((-54)/90)/((-1)/5). Let k(h) be the second derivative of y*h + 0*h**2 + 1/30*h**6 + 0 - 1/3*h**3 - 1/12*h**4 + 1/10*h**5. Factor k(r).
r*(r - 1)*(r + 1)*(r + 2)
Let o = 3 + -1. Suppose 3*h + h = 8. Solve 0*y**3 - 2*y**3 + 0 + h*y + 2*y**o + 3 - 5 = 0 for y.
-1, 1
Let s be (-4)/(-2)*(-2)/(-8). Factor -s*p + 0 + 1/2*p**3 + 0*p**2.
p*(p - 1)*(p + 1)/2
Let o(f) be the first derivative of -2*f**6 - 9*f**5/5 + 27*f**4/4 - 2*f**3 - 7. Find r such that o(r) = 0.
-2, 0, 1/4, 1
Let c(j) be the third derivative of -j**5/750 + 3*j**4/100 - 8*j**3/75 - 15*j**2. Factor c(l).
-2*(l - 8)*(l - 1)/25
Let x(j) = 42*j**4 - 64*j**3 + 26*j**2 + 8*j + 6. Let o(s) = 83*s**4 - 128*s**3 + 51*s**2 + 16*s + 11. Let c(w) = -6*o(w) + 11*x(w). Factor c(h).
-4*h*(h - 1)**2*(9*h + 2)
Let v = -55/2 + 28. Let r be (-2 + (1 - -1))/1. Factor r*k - v*k**2 + 1/2.
-(k - 1)*(k + 1)/2
Let b be (-2 - (-4 + 0))/(19 - 13). Factor s + 2/3*s**2 - s**4 - 1/3*s**5 + b - 2/3*s**3.
-(s - 1)*(s + 1)**4/3
Suppose -8/5*h - 1/5*h**2 + 0 = 0. Calculate h.
-8, 0
Let d(x) = -3*x + 17. Let k be d(5). Let y(t) be the third derivative of 0 + 0*t**6 + 1/105*t**7 + 1/3*t**3 + 0*t + 2*t**k - 1/15*t**5 + 0*t**4. Factor y(b).
2*(b - 1)**2*(b + 1)**2
Let n = 57 - 55. Let z(h) be the third derivative of 0*h + 0*h**4 - n*h**2 - 1/60*h**5 + 0 + 1/6*h**3. What is k in z(k) = 0?
-1, 1
Factor -4/7 + 2/7*u**2 + 2/7*u.
2*(u - 1)*(u + 2)/7
Let x(l) be the first derivative of -5*l**3/6 + 2*l**2 - 3*l/2 + 2. Solve x(m) = 0 for m.
3/5, 1
Let l(u) be the first derivative of -u**7/840 + u**6/180 - u**5/120 + u**3/3 + 4. Let p(i) be the third derivative of l(i). Factor p(s).
-s*(s - 1)**2
Factor 0 + 6/5*x**2 + 0*x + 3/5*x**3.
3*x**2*(x + 2)/5
Let g(i) = 3*i + 3. Let d be g(-1). Solve d*m + 0 - 2/3*m**3 + 2/3*m**2 = 0.
0, 1
Let p = 10/3 + -13/4. Let w(o) be the second derivative of -p*o**4 - o + 0*o**2 + 1/6*o**3 + 0. Factor w(s).
-s*(s - 1)
Suppose o - 2 = p + 2*o, -2*o - 10 = 0. Factor -11/4*u**4 + 15/4*u**p + 3/4*u**5 + 1/2*u - 9/4*u**2 + 0.
u*(u - 1)**3*(3*u - 2)/4
Let u(c) = -3*c**5 + 15*c**4 - 4*c**3 + 2. Let v(s) = 23*s**5 - 119*s**4 + 31*s**3 - 17. Let h(n) = -51*u(n) - 6*v(n). Solve h(a) = 0 for a.
0, 2/5, 3
Suppose -12 = -d - 3*d. Factor p**4 + 2*p**2 - 2*p**3 + p**2 - p**d - p**2.
p**2*(p - 2)*(p - 1)
Let f(w) = w + 3. Let x be f(-6). Let g be (-4)/2*x/2. Suppose 18*m**g - 14*m**4 - 3*m**2 + 3*m**2 - 4*m**2 = 0. Calculate m.
0, 2/7, 1
Let u(f) be the first derivative of -f**3/9 - 2*f**2/3 - f - 8. Determine h so that u(h) = 0.
-3, -1
Factor 1/2*l**2 - 1/2*l**3 + 0*l + 0.
-l**2*(l - 1)/2
Suppose 2*k + t = -4882, -4*k + 3*k = 4*t + 2434. Let o = k - -7396/3. Factor -8/3 + 44/3*v + 25/3*v**3 - o*v**2.
(v - 2)*(5*v - 2)**2/3
Let u(f) be the first derivative of f**6/90 + f**5/15 + 4*f**3/3 - 1. Let c(o) be the third derivative of u(o). Factor c(z).
4*z*(z + 2)
Let s(d) be the first derivative of -6/5*d**3 - 2/5*d**5 - 1 - 2/5*d**2 + 0*d - 6/5*d**4. Determine u so that s(u) = 0.
-1, -2/5, 0
Let h(t) be the third derivative of 0*t - 1/1200*t**6 - 1/150*t**5 + 0 - 1/30*t**3 - 1/48*t**4 - 9*t**2. Suppose h(n) = 0. Calculate n.
-2, -1
Let n(y) = 5*y**3 + 35*y**2 + 79*y + 45. Let j(h) = -15*h**3 - 105*h**2 - 236*h - 135. Let f(q) = 4*j(q) + 11*n(q). Factor f(u).
-5*(u + 1)*(u + 3)**2
Let p = 27 - 22. Let a be -3 + (200/12)/p. Find c, given that 1/3*c - 1/3*c**3 - 1/3*c**2 + a = 0.
-1, 1
Suppose -15*w + 15 = -10*w. Factor -3*r + r**3 + 12*r**4 - 16*r**2 + 4*r**2 + 0*r**3 + 2*r**w.
3*r*(r - 1)*(r + 1)*(4*r + 1)
Solve -5/3*l**5 - 15*l**3 + 9*l**4 + 0 + 29/3*l**2 - 2*l = 0.
0, 2/5, 1, 3
Let r = -7 - -7. Let t(v) = -v**2 - v + 2. Let u be t(0). Factor -n**u + 3*n**2 + r*n - 2*n.
2*n*(n - 1)
Let c(g) = -6*g**3 - 42*g**2 + 92*g - 46. Let s(w) = 7*w**3 + 43*w**2 - 92*w + 45. Let l(t) = 3*c(t) + 2*s(t). Solve l(r) = 0 for r.
-12, 1
Let h(f) be the third derivative of -f**8/96 + f**7/35 - f**6/80 - f**5/60 + f**2. Factor h(y).
-y**2*(y - 1)**2*(7*y + 2)/2
Factor 3*w**5 + 3*w**2 - 6*w**3 - w**4 - 2*w**4 + 3*w**3.
3*w**2*(w - 1)**2*(w + 1)
Let r(d) be the second derivative of d**7/168 - 7*d**6/360 + d**5/60 - d**3/3 + 3*d. Let i(o) be the second derivative of r(o). Factor i(j).
j*(j - 1)*(5*j - 2)
Suppose -r = 6*r. Factor 0 + r*o**2 + 2/9*o - 2/9*o**3.
-2*o*(o - 1)*(o + 1)/9
Suppose 0 = -6*r + 3*r + 6. Solve -2/9*y + 2/9*y**4 + 0 + 2/3*y**r - 2/3*y**3 = 0.
0, 1
Suppose 4*f - 3 - 5 = 0. Find h such that 5*h**3 - f*h**3 - 4*h**3 = 0.
0
Let n(t) = 8*t**4 - 6*t**3 + 7*t**2 + 7. Let z(w) = -w**4 + w**3 - w**2 - 1. Let m(i) = -5*n(i) - 35*z(i). Find u such that m(u) = 0.
-1, 0
Let m(i) be the first derivative of -i**6/900 + i**4/60 - i**3/3 - 1. Let s(j) be the third derivative of m(j). Let s(o) = 0. What is o?
-1, 1
Let b(p) be the second derivative of 3*p**5/20 - p**4/4 - 26*p. Solve b(a) = 0.
0, 1
Let b(t) be the second derivative of 3*t**5/110 + 2*t**4/33 - 13*t**3/33 + 6*t**2/11 + 2*t. Solve b(p) = 0 for p.
-3, 2/3, 1
Let r(b) = 2*b**3 - 4*b**2 + 2*b. Let w be r(2). Let c(f) be the first derivative of 0*f**3 - 1/4*f**w + 1/2*f**2 - 2 + 0*f. Factor c(u).
-u*(u - 1)*(u + 1)
Let a = -39 + 36. Let t be 6 + a + -3 + 3. Factor -2/3*d**t - 4/9*d + 0 - 10/9*d**2.
-2*d*(d + 1)*(3*d + 2)/9
Find z, given that 1/3*z**3 + 0*z**2 + 0*z + 0 - 1/6*z**4 = 0.
0, 2
Factor 11*z**2 + 7*z**4 - 4*z**4 - 11*z**2 + 3*z**5.
3*z**4*(z + 1)
Let i(l) = 2 - 8*l + 1 + 5*l**2 - 4*l**2. Let h be i(8). Let x**2 + x**3 + h - 1 - 2 = 0. What is x?
-1, 0
Let s = 1/50 + 97/150. Suppose -4*l + 19 - 7 = 0. Factor 0*c**2 + 0*c + 0 + 2/9*c**l + 4/9*c**4 - s*c**5.
-2*c**3*(c - 1)*(3*c + 1)/9
Suppose -y = -2*y + 3. Let z = 6 - y. Factor 0*a + a**4 - a**2 - a**z + a + 0*a.
a*(a - 1)**2*(a + 1)
Let s(b) = -b**4 + b**3 + b. Let h(i) = -3*i**4 + 13*i**3 - 15*i**2 + 3*i. Let l(k) = h(k) + 2*s(k). Factor l(v).
-5*v*(v - 1)**3
Let r(m) be the third derivative of -m**5/50 - m**4/2 - 5*m**3 + 4*m**2. Factor r(i).
-6*(i + 5)**2/5
Let s(x) be the first derivative of x**6/14 - 6*x**5/35 + 3*x**4/28 + 6. Factor s(w).
3*w**3*(w - 1)**2/7
Factor -12/7*t**3 + 0 - 16/7*t**2 + 8/7*t**4 + 16/7*t + 4/7*t**5.
4*t*(t - 1)**2*(t + 2)**2/7
Suppose 0 = -5*h + 2*b + 6, 8*h - 5*b - 15