
3*d**3*(d - 1)
Let q(d) = -14*d**4 - 20*d**3 + 11*d**2 - 11*d - 11. Let r(u) = 5*u**4 + 7*u**3 - 4*u**2 + 4*u + 4. Let c(p) = 4*q(p) + 11*r(p). Factor c(x).
-x**3*(x + 3)
Determine z so that 2/11*z**2 + 8/11 + 8/11*z = 0.
-2
Let d(u) be the first derivative of u**3/18 - u**2/6 - u/2 - 1. Find t such that d(t) = 0.
-1, 3
Let a(s) be the second derivative of -3*s**6/55 - 5*s**5/22 - 7*s**4/22 - s**3/11 + 2*s**2/11 - 31*s. Solve a(y) = 0 for y.
-1, 2/9
Let x(b) be the first derivative of -b + b**2 - 7/4*b**4 - 1/6*b**3 + 2. Let w(d) be the first derivative of x(d). Determine r so that w(r) = 0.
-1/3, 2/7
Let h(a) be the first derivative of -2*a**3/27 - 4*a**2/9 - 2*a/3 + 61. Determine m so that h(m) = 0.
-3, -1
Let n(y) = y**2 + 7*y + 9. Let x be n(-7). Factor -6*w - 4*w**5 - 27*w**3 - 15*w**4 + x*w**2 - w**5 + 2*w**5 - 30*w**2.
-3*w*(w + 1)**3*(w + 2)
Let j(x) be the third derivative of -x**2 + 0*x + 0*x**3 + 0 + 1/6*x**5 - 1/6*x**4. Factor j(a).
2*a*(5*a - 2)
Suppose 0 = -5*r + 4*l + 6, 0 = 2*r - 6*r + 5*l + 3. Let t = 0 + 5. Determine m so that -2/3*m**4 + 1/3*m + 0*m**3 - 1/3*m**t + 2/3*m**r + 0 = 0.
-1, 0, 1
Let 14/9*c**2 + 32/9*c + 2/9*c**3 + 8/3 = 0. What is c?
-3, -2
Suppose -12 = 2*v - 4*v. Determine o, given that -2*o - 5*o**3 + v*o**2 + 24*o**3 + o**3 = 0.
-1/2, 0, 1/5
Let f = -16 - -16. Let p(b) be the second derivative of f*b**2 - 1/30*b**4 + 0*b**3 + 0 + 1/50*b**5 - b + 1/75*b**6 - 1/105*b**7. Let p(m) = 0. What is m?
-1, 0, 1
Let d(t) be the first derivative of t**5/25 - 7*t**4/20 + 13*t**3/15 + 3*t**2/10 - 18*t/5 + 5. Factor d(o).
(o - 3)**2*(o - 2)*(o + 1)/5
Find m, given that -293*m**4 + 13*m**2 - 11*m**3 + 0*m**3 + 2 + 278*m**4 + 11*m = 0.
-1, -2/5, -1/3, 1
Let s(k) be the third derivative of -7*k**2 - 1/20*k**4 - 2/15*k**3 + 0 + 0*k - 1/150*k**5. Suppose s(j) = 0. Calculate j.
-2, -1
Let h(q) be the second derivative of 5*q**4/102 + 2*q**3/51 - 3*q**2/17 - 3*q + 1. Factor h(o).
2*(o + 1)*(5*o - 3)/17
Find a, given that -23/2*a**3 + 7/2*a**2 + 1/2 + 7/2*a + 8*a**5 - 4*a**4 = 0.
-1, -1/4, 1
Let p(o) = -2*o - 5. Suppose 3*z - 16 = 2*z - 5*x, -z - 12 = -2*x. Let s be p(z). Suppose -40/7*i + 24/7*i**s - 26/7*i**2 - 8/7 = 0. What is i?
-2/3, -1/4, 2
Factor 5/2*s + 1/2*s**2 + 3.
(s + 2)*(s + 3)/2
Factor 0 - 3/5*h - 3*h**2 - 12/5*h**3.
-3*h*(h + 1)*(4*h + 1)/5
Let v = -4/7 + 6/7. Solve 0 - v*x - 2/7*x**2 = 0 for x.
-1, 0
What is l in -4/11*l**3 - 2/11*l**2 + 2/11*l**4 + 4/11*l + 0 = 0?
-1, 0, 1, 2
Factor v**4 - 8*v**3 - 2*v**4 - 2*v**2 + 5*v**3 + 6*v**2.
-v**2*(v - 1)*(v + 4)
Let n(x) = x**2 + 4*x + 5. Let s be n(-4). Let 52*m**2 + 4 - 4 - 3*m**3 - 55*m**2 + 3*m**4 + 3*m**s = 0. Calculate m.
-1, 0, 1
Factor -20*q**2 - 36*q - q**3 + 41*q + 16*q**3.
5*q*(q - 1)*(3*q - 1)
Let i(n) = -30*n**2 + 21*n + 120. Let w(y) = -3*y**2 + 2*y + 12. Let d(j) = -2*i(j) + 21*w(j). Solve d(p) = 0.
-2, 2
Let o(z) = 29 - 8*z + 3*z**2 + z - 5*z - z**2. Let m(r) = -r**2 + 6*r - 15. Let g(k) = 11*m(k) + 6*o(k). Factor g(h).
(h - 3)**2
Factor 1/2*p**2 + 3*p**4 + 0*p + 0 + 5/4*p**5 + 9/4*p**3.
p**2*(p + 1)**2*(5*p + 2)/4
Factor -1/3*g**3 + 4/3*g - g**2 + 0.
-g*(g - 1)*(g + 4)/3
Factor -2/5*g**3 + 8/5*g**2 - 6/5*g + 0.
-2*g*(g - 3)*(g - 1)/5
Let z(r) = 2*r + 30. Let w be z(-14). Factor 2/11*v**w - 4/11 - 2/11*v.
2*(v - 2)*(v + 1)/11
Solve 14*c - 6*c**3 + 24*c - 34*c + 8*c**3 - 1 - 5*c**2 = 0 for c.
1/2, 1
Let d(f) be the first derivative of -f**3/3 - 3*f**2 + 9*f - 3. Let v be d(-7). Find g such that g**5 + g**3 - g**2 + 0*g**2 + g**v - 2*g**4 = 0.
0, 1
Let f(g) be the third derivative of 11*g**7/1260 + g**6/30 + g**5/24 + g**4/72 + 10*g**2 - 3. Factor f(o).
o*(o + 1)**2*(11*o + 2)/6
Let j(y) be the second derivative of 0 - 1/42*y**4 + y - 2/21*y**3 - 1/7*y**2. Suppose j(i) = 0. What is i?
-1
Let q(j) be the first derivative of 0*j + 0*j**3 - 1/120*j**6 + 1 + 1/60*j**5 + 1/2*j**2 + 0*j**4. Let y(m) be the second derivative of q(m). Factor y(s).
-s**2*(s - 1)
Let j(v) be the second derivative of -v**4/36 - v**3/6 - v**2/3 - 2*v. Factor j(f).
-(f + 1)*(f + 2)/3
Let t(a) be the second derivative of -3*a - 1/480*a**6 + 0*a**4 - 1/120*a**5 + 0*a**3 - 3/2*a**2 + 0. Let o(v) be the first derivative of t(v). Factor o(y).
-y**2*(y + 2)/4
Let u(m) be the second derivative of m**7/210 - m**5/60 + 7*m**2/2 - 5*m. Let q(o) be the first derivative of u(o). Determine w so that q(w) = 0.
-1, 0, 1
Let o = -299/3 - -101. Let b(t) be the first derivative of -2/3*t**3 - 1/3*t**2 - 2 + o*t. Find a, given that b(a) = 0.
-1, 2/3
Let q(i) be the first derivative of i**8/1120 + i**7/840 - i**6/720 - 5*i**3/3 - 4. Let a(o) be the third derivative of q(o). Factor a(j).
j**2*(j + 1)*(3*j - 1)/2
Let g(b) be the third derivative of b**7/1050 + b**6/150 + b**5/60 + b**4/60 + 2*b**2. Suppose g(k) = 0. Calculate k.
-2, -1, 0
Let y = 32 + -29. Let g(k) be the third derivative of 0*k**y + k**2 - 1/132*k**4 + 1/330*k**5 + 0 + 0*k. Factor g(b).
2*b*(b - 1)/11
Find b such that -2*b**3 + 4*b**5 + 4*b - 6*b**2 + 30*b**2 - 12*b**4 - 3*b**3 - 12 - 3*b**3 = 0.
-1, 1, 3
Suppose 0 = 3*y - 0*y - 24. Let f(o) = 4*o**2 - 8*o + 12. Let z(d) = -d. Let g(s) = y*z(s) + f(s). Solve g(a) = 0 for a.
1, 3
Factor 16/17 - 184/17*f - 1274/17*f**3 + 686/17*f**4 + 756/17*f**2.
2*(f - 1)*(7*f - 2)**3/17
Find m, given that -3*m**2 + 3 + 30*m - 3*m**3 + 0 - 27*m = 0.
-1, 1
Let n(v) = v**3 - 7*v**2 + 5*v + 7. Let i(o) = o**3 - 13*o**2 + 9*o + 13. Let l(t) = -3*i(t) + 5*n(t). What is j in l(j) = 0?
-2, -1, 1
Let x = -423 - -1192/3. Let a = -23 - x. Suppose 2*f**3 + f**5 + 0 + 0*f**2 + a*f**4 - 1/3*f = 0. Calculate f.
-1, 0, 1/3
Let u be 27/(-3)*2/3. Let p(a) = 19*a**2 + 13*a + 7. Let x(t) = 3*t**2 + 2*t + 1. Let z(m) = u*p(m) + 39*x(m). Factor z(d).
3*(d - 1)*(d + 1)
Let h(d) be the first derivative of -d**7/42 + d**6/30 + d**5/10 + d - 3. Let v(z) be the first derivative of h(z). Let v(b) = 0. Calculate b.
-1, 0, 2
Let j(z) be the second derivative of 0*z**3 + 0*z**4 + 0*z**2 + 0 + 3*z + 1/28*z**7 + 0*z**5 - 1/20*z**6. Factor j(l).
3*l**4*(l - 1)/2
Let i(p) be the first derivative of p**4/24 - p**3/6 + p**2/6 + 15. Factor i(m).
m*(m - 2)*(m - 1)/6
Find o such that 11*o**2 + 13 - 67*o**2 + 6*o**5 + 23 - 37*o + 100*o**3 - 5*o - 44*o**4 = 0.
-2/3, 1, 3
Let v(f) be the second derivative of f**6/40 + f**5/30 - f**2/2 - f. Let b(l) be the first derivative of v(l). Factor b(r).
r**2*(3*r + 2)
Let s be -3*(0 + 1) - -9. Let y be s - 4/2*1. Factor -4/5*c**y + 0*c + 0*c**2 + 2/5*c**3 + 0 - 6/5*c**5.
-2*c**3*(c + 1)*(3*c - 1)/5
Let k = 28 + -20. What is h in 9*h + 6 - 9*h + k*h - 2*h**2 - 4*h**3 = 0?
-1, 3/2
Solve 0*d**2 + 0 - d + 1/4*d**3 = 0 for d.
-2, 0, 2
Let f be (-6)/5*(-40)/12. Suppose -4 = f*y - 6*y, -2*y = 3*a - 10. Factor 3*j + 4*j - 2*j**a - 8*j + 3*j**2.
j*(j - 1)
Let m(u) = 3*u**3 + 3*u**2 - 8*u - 8. Let c(g) = 3*g**3 + 3*g**2 - 9*g - 9. Let f(r) = -5*c(r) + 6*m(r). Factor f(q).
3*(q - 1)*(q + 1)**2
Suppose -y + 1 = 2*p - 0, -p - 5*y - 13 = 0. Let x(w) be the third derivative of -1/8*w**4 - p*w**2 + 0*w**3 + 0 + 1/20*w**5 + 0*w. Find o such that x(o) = 0.
0, 1
What is i in -5*i**2 - 2*i - 10*i + 7*i + 15 - 5*i = 0?
-3, 1
Let m(h) be the third derivative of -h**7/210 + h**6/10 - 7*h**5/12 - h**4/2 + 6*h**3 - 28*h**2. Factor m(a).
-(a - 6)**2*(a - 1)*(a + 1)
Let t(k) be the third derivative of -k**8/1120 - k**7/140 - k**6/48 - k**5/40 + k**3 + 5*k**2. Let j(v) be the first derivative of t(v). Factor j(u).
-3*u*(u + 1)**2*(u + 2)/2
Let d(x) be the second derivative of x**6/360 + x**3/6 - 3*x. Let i(f) be the second derivative of d(f). Suppose i(m) = 0. Calculate m.
0
Let u(w) be the third derivative of -w**6/300 + w**5/30 - 2*w**4/15 + 4*w**3/15 + 5*w**2. Let u(c) = 0. Calculate c.
1, 2
Let v(f) = 17*f**2 - 25*f - 12. Let t(x) = -35*x**2 + 50*x + 25. Let g(l) = 2*t(l) + 5*v(l). Factor g(y).
5*(y - 2)*(3*y + 1)
Factor 3/2*k**2 + 27/2 - 9*k.
3*(k - 3)**2/2
Let o be (0 - 1) + 4/1. Factor -3*j**3 + 3*j**3 + 0*j**3 + 2*j - 2*j**o - 3*j**2.
-j*(j + 2)*(2*j - 1)
Let g(m) be the first derivative of -20*m**4/3 - 280*m**3/9 - 125*m**2/6 - 5*m - 22. Factor g(c).
-5*(c + 3)*(4*c + 1)**2/3
Let m(b) be the second derivative of b**7/7 - 2*b**6/15 - b**5 + 2*b**4 - b**3/3 - 2*b**2 - 48*b. Factor m(g).
2*(g - 1)**3*(g + 2)*(3*g + 1)
Let v