e y, given that n(y) = 0.
2
Let y(s) be the third derivative of s**6/90 + s**5/45 - s**4/18 - 2*s**3/9 - 4*s**2. Factor y(r).
4*(r - 1)*(r + 1)**2/3
Suppose -5*m - 5 + 15 = 0. Let q be ((-2)/6)/((-4)/6). Solve -1/2 - t - q*t**m = 0.
-1
Let b = -367/3 - -125. Let r(o) be the first derivative of 2 + 4*o - 3/2*o**4 - b*o**3 + o**2. Factor r(t).
-2*(t + 1)**2*(3*t - 2)
Suppose -5*o = -m + 25, 4*o + 0*o + 20 = m. Let k(a) be the second derivative of -a + 1/3*a**3 + m + 0*a**2 + 1/12*a**4. Determine l, given that k(l) = 0.
-2, 0
Let z = 13/12 - 3/4. Suppose 7/6*l**3 - z*l**2 + 0 + 0*l = 0. What is l?
0, 2/7
Let b(v) be the second derivative of -v**4/6 + 4*v**3/3 - 4*v**2 - 2*v. Find y, given that b(y) = 0.
2
Let p(h) = 10*h**5 + 10*h**4 - 10*h**3 - 15*h**2. Let f(y) = -15*y**5 - 15*y**4 + 15*y**3 + 23*y**2. Let s(g) = -5*f(g) - 8*p(g). Factor s(j).
-5*j**2*(j - 1)*(j + 1)**2
Suppose 0*d = d. Suppose d*p = p - 3. Factor 2*c**p + 16/3*c**2 + 14/3*c + 4/3.
2*(c + 1)**2*(3*c + 2)/3
Suppose 6*w + 2*w = w. Let v(n) be the second derivative of w*n**4 - 3*n - 1/10*n**5 + 0*n**3 + 0 + 0*n**2. Factor v(m).
-2*m**3
Let n be -5 + 2 - 265/(-75). Let d(b) be the second derivative of 0*b**2 - 3/5*b**5 - 1/7*b**7 + b + 0 + 1/3*b**3 + n*b**6 + 0*b**4. Factor d(a).
-2*a*(a - 1)**3*(3*a + 1)
Find h, given that -2/3*h**2 + 0*h + 2/3 = 0.
-1, 1
Let c(j) be the first derivative of 5*j**6/6 - 4*j**5 + 5*j**4 + 10*j**3/3 - 25*j**2/2 + 10*j - 32. Factor c(f).
5*(f - 2)*(f - 1)**3*(f + 1)
Suppose -2*p = -3*t - 4, -2*t = -p + t + 2. Let n(i) be the first derivative of -4 - 1/12*i**3 + 1/16*i**4 + 1/20*i**5 + 0*i**p + 0*i - 1/24*i**6. Factor n(x).
-x**2*(x - 1)**2*(x + 1)/4
Factor 6*j**2 + 2*j**5 + j**5 + 0*j**5 - 3*j - 6*j**4.
3*j*(j - 1)**3*(j + 1)
Let l(t) be the third derivative of t**7/1470 + 5*t**2. Factor l(o).
o**4/7
Let b = -51 - -51. What is c in 0*c - 4/11*c**2 + b + 10/11*c**3 = 0?
0, 2/5
Let l = -137/55 + 34/11. Factor -l*q**2 - 1/5*q + 0 - 1/5*q**4 - 3/5*q**3.
-q*(q + 1)**3/5
Let -4*w**4 - 4 + 1 + 7 - 3*w**2 + 16*w - 13*w**3 = 0. Calculate w.
-2, -1/4, 1
Let d(g) = -3*g**3 + 54*g**2 - 319*g + 643. Let p(v) = 3*v**3 - 54*v**2 + 318*v - 642. Let q(a) = 6*d(a) + 5*p(a). Factor q(z).
-3*(z - 6)**3
Suppose -t = -2*u + 6, t - 5*t = -2*u + 6. Let d(a) be the first derivative of 2 + 10/7*a**u + 2/7*a - 8/7*a**2 - 32/35*a**5 + 4/7*a**4. What is k in d(k) = 0?
-1, 1/4, 1
Let t be 306/(-85)*5/(-4). Solve 1/2*y**2 + t + 3*y = 0.
-3
Let h(b) = -b**5 + b**4 - b**3 - b**2 - 1. Let z(k) = -7*k**5 - 2*k**4 - 7*k**3 - 4*k**2 - 4. Let v(c) = -4*h(c) + z(c). Factor v(o).
-3*o**3*(o + 1)**2
Let l(g) = -8*g**4 - 12*g**3 + 9*g**2 + 7*g + 9. Let r(d) = 20*d**4 + 30*d**3 - 22*d**2 - 18*d - 22. Let i(u) = 12*l(u) + 5*r(u). Factor i(o).
2*(o - 1)*(o + 1)**2*(2*o + 1)
Let n(q) = -6*q**3 - 11*q**2 - 23*q - 5. Let g(w) = -5*w**3 - 12*w**2 - 22*w - 6. Let a = -13 + 9. Let z(k) = a*n(k) + 6*g(k). Factor z(x).
-2*(x + 2)**2*(3*x + 2)
Suppose -5*s - g + 19 = 0, s + 0*s + 17 = 5*g. Factor 6*z - s*z - 7*z + 3 + 2*z**2 - 1.
2*(z - 1)**2
Factor -2/9*s**2 + 0 + 0*s - 2/9*s**3.
-2*s**2*(s + 1)/9
Let i(y) be the second derivative of -y**8/3360 - y**7/840 + y**6/240 - y**3/3 - 7*y. Let z(a) be the second derivative of i(a). Factor z(g).
-g**2*(g - 1)*(g + 3)/2
Let y(u) = u**2 - 4*u + 3. Let a be y(4). Suppose -i + 5 = t, -3*i = 2*i + a*t - 15. Find n such that 1/3*n**3 + 0 + 1/3*n**4 + i*n + 0*n**2 = 0.
-1, 0
Factor 4*s**3 - 32*s - 8*s**2 + 32*s.
4*s**2*(s - 2)
Let y = 1 + 1. Let s = 6 - y. Factor s*j**2 + j + j - 2*j**2.
2*j*(j + 1)
Suppose -4*r = -3*h - 0*h + 26, -2*h - 1 = r. Suppose -3*p + 5 = 2*k + 1, h*k + 6 = 2*p. Factor q**5 - 2*q - 5*q**5 + p*q**5 + 4*q**3.
-2*q*(q - 1)**2*(q + 1)**2
Let r(j) be the third derivative of j**7/315 - j**6/60 + j**5/90 + j**4/12 - 2*j**3/9 - 38*j**2. Factor r(p).
2*(p - 2)*(p - 1)**2*(p + 1)/3
Let a = 49 - 145/3. Factor 0*m + 0 + 0*m**2 + 2/3*m**4 + a*m**3.
2*m**3*(m + 1)/3
Let r(b) = -b**2 - 4*b - 1. Let z be r(-3). Let q be (-6)/4*32/(-6). Determine l so that -3*l + q*l**2 + z*l + 2*l + l = 0.
-1/4, 0
Let x(j) be the third derivative of 0 + 9/70*j**5 + 1/21*j**3 + 0*j - 6*j**2 + 9/140*j**6 + 3/28*j**4. Factor x(t).
2*(3*t + 1)**3/7
Let w(z) be the third derivative of z**8/20160 - z**7/3780 + z**6/2160 - z**4/24 + z**2. Let f(i) be the second derivative of w(i). Factor f(x).
x*(x - 1)**2/3
Factor 3*u**5 - 7*u + 6*u**3 + 4*u**4 + u - 9*u**2 + 5*u**4 - 3*u**3.
3*u*(u - 1)*(u + 1)**2*(u + 2)
Suppose -2*n + 10 = -0*n, 3*n = 3*g - 3. Let k(z) = -z**4 - z**3. Let m(f) = 104*f**4 + 146*f**3 - 6*f**2 - 40*f + 8. Let w(a) = g*k(a) + m(a). Factor w(l).
2*(l + 1)**2*(7*l - 2)**2
Let s(o) be the first derivative of -6*o**5/25 + o**4/10 + 7. Find v such that s(v) = 0.
0, 1/3
Let n(h) = h**3 + 5*h**2 - 4*h + 3. Let f be n(-6). Let o = 11 + f. Suppose 0*u**o + 2/3*u**4 + 2/3*u**3 + 0 + 0*u = 0. Calculate u.
-1, 0
Let i(p) be the third derivative of p**9/45360 + p**8/1680 + p**7/140 + p**6/20 + p**5/15 - 4*p**2. Let j(w) be the third derivative of i(w). Factor j(l).
4*(l + 3)**3/3
Let f be ((-8)/(-10))/(10/100). Let f*c**4 + 6*c**2 - 3*c + 5*c**3 - 2*c**3 - 14*c**4 = 0. What is c?
-1, 0, 1/2, 1
Factor 0*q**2 + 1/2*q**4 - 1/2*q**5 + 0 + 0*q + 0*q**3.
-q**4*(q - 1)/2
Solve 2*n + 13/6*n**2 + 2/3 + 1/6*n**4 + n**3 = 0.
-2, -1
Let v(k) = -5*k**2 + 40*k - 91. Let x(o) = o**2 - 8*o + 18. Let q(l) = -2*v(l) - 11*x(l). Find r such that q(r) = 0.
4
What is p in p - 1/3 - p**2 + 1/3*p**3 = 0?
1
Let c(k) be the second derivative of -2/9*k**4 + 1/9*k**3 + 0*k**2 - 1/30*k**5 + 0 + 4/45*k**6 + k. Solve c(f) = 0 for f.
-1, 0, 1/4, 1
Let t(r) be the first derivative of -r**5/10 + r**4/8 + r**3/3 + 28. Determine f so that t(f) = 0.
-1, 0, 2
Let d(q) be the first derivative of -q**4/4 - 2*q**3/9 + q**2/6 + 11. Factor d(a).
-a*(a + 1)*(3*a - 1)/3
Let x be -11 + 12 - 2*-2. Let t(p) be the third derivative of 0*p - 1/120*p**6 + 0*p**3 + 1/120*p**x + 0*p**4 + 0 - p**2. Let t(i) = 0. Calculate i.
0, 1/2
Find i, given that 8/7 - 16/7*i - 2/7*i**3 + 10/7*i**2 = 0.
1, 2
Suppose 8*x = 13*x - 10. Suppose x*o = 4*r - 10, 3 = o + 8. Find b, given that 0*b**3 + 4/9*b**5 + r + 0*b + 2/9*b**2 - 2/3*b**4 = 0.
-1/2, 0, 1
Let s(h) = -h**5 + h**4. Let j(p) = p**5 + p**4. Let z(c) = -j(c) - 3*s(c). Factor z(y).
2*y**4*(y - 2)
Factor -9*m**3 + 2*m + 11*m**3 + 2 - 4*m + 0*m**3 - 2*m**2.
2*(m - 1)**2*(m + 1)
Let f(j) = 5*j**4 - 140*j**3 + 1100*j**2 - 4340*j + 6480. Let m(k) = -k**3 + k**2 - k. Let s(r) = -f(r) + 20*m(r). Factor s(w).
-5*(w - 6)**4
Let y = 3 + -1. Factor -3*z**2 - 3*z**4 + z**2 - y*z**3 + 2*z**4 + 2*z + 3*z**4.
2*z*(z - 1)**2*(z + 1)
Let r(d) be the second derivative of 3*d**5/20 + d**4/2 - 14*d. Factor r(m).
3*m**2*(m + 2)
Let t be 32/(-80) + 108/70. Factor -10/7*q - 2/7*q**3 - 4/7 - t*q**2.
-2*(q + 1)**2*(q + 2)/7
Let d(x) be the second derivative of -x**7/315 - x**6/90 - x**2/2 + 3*x. Let r(z) be the first derivative of d(z). Factor r(b).
-2*b**3*(b + 2)/3
Factor 3/4*k - k**2 + 1/4.
-(k - 1)*(4*k + 1)/4
Factor 2*x**4 + 15*x**3 + 3*x**4 + 0*x**4 + 10*x**2.
5*x**2*(x + 1)*(x + 2)
Let r(z) be the second derivative of -z**4/72 + z**3/3 - 3*z**2 - 12*z. Factor r(y).
-(y - 6)**2/6
Suppose -6*h + h = -20. Suppose z = -5*j + 3*z - 4, h*j + 2 = z. Factor -1/5*c**2 + 1/5*c**5 + 0 + j*c - 3/5*c**4 + 3/5*c**3.
c**2*(c - 1)**3/5
Let w(c) be the first derivative of -c**4/6 - 8*c**3/9 + c**2 + 12*c + 23. What is j in w(j) = 0?
-3, 2
Suppose 8*a - 8 = 6*a. Let y(x) be the second derivative of -1/14*x**a + 3*x - 1/7*x**2 - 1/7*x**3 - 1/70*x**5 + 0. Suppose y(u) = 0. What is u?
-1
Solve 28 + 414*h**2 - 8 - 15*h**5 + 15*h**3 - 469*h**2 + 35*h**4 = 0 for h.
-1, -2/3, 1, 2
Factor -2/9*s**2 + 2/3 + 4/9*s.
-2*(s - 3)*(s + 1)/9
Let p(l) be the second derivative of 1/20*l**5 + 1/12*l**4 + 0 + 0*l**2 + 0*l**3 + 2*l. Solve p(o) = 0.
-1, 0
Let g(f) = -f**3 - 23*f**2 - 7*f + 5. Let m(i) be the second derivative of -i**4 - i**3/2 + 3*i**2/2 - 4*i. Let y(t) = 3*g(t) - 5*m(t). Factor y(x).
-3*x*(x + 1)*(x + 2)
Suppose 5*y = 2*y + 9. Let z(g) be the second derivative of 0 - 1/7*g**2 + 2*g - 1/70*g**5 - 1/14*g**4 - 1/7*g**y. Factor z(s).
-2*(s + 1)**3/7
Find o such that -o**2 - 137*o**4 + o**2 - 2*o**2 - 48*o**3 + 12*o - 2 + 105*o**