- t, 0 = 2*v + 2*a - 16. Factor 6*f**4 - 5*f**4 + v*f**4 + 4*f**2 + 8*f**3 - f**4 + f**5.
f**2*(f + 1)*(f + 2)**2
Let h(o) be the first derivative of o**5/300 - o**4/30 + 2*o**3/15 + o**2 - 4. Let m(x) be the second derivative of h(x). What is v in m(v) = 0?
2
Let r be 1/(-4) - (-725)/20. Let t be r/(-33) - (-5 + 3). Factor 0 - 4/11*m + 16/11*m**3 - 2/11*m**2 - t*m**4.
-2*m*(m - 1)**2*(5*m + 2)/11
Let q(b) be the second derivative of -b**5/240 + b**4/24 - b**3/8 + b**2/2 + 7*b. Let o(i) be the first derivative of q(i). Factor o(y).
-(y - 3)*(y - 1)/4
Let h(w) be the third derivative of -w**8/168 - w**7/35 + 2*w**5/15 + 9*w**2. What is m in h(m) = 0?
-2, 0, 1
Factor -a**2 - 2/3 + 5/3*a.
-(a - 1)*(3*a - 2)/3
Let m be (75/(-9))/((-1)/3). Let p = m - 74/3. Determine i so that -1/3*i**3 + 2/3*i**4 + 0*i**2 + 0 - p*i**5 + 0*i = 0.
0, 1
Factor 0*v + 0 - 1/4*v**4 + 0*v**3 + 0*v**2.
-v**4/4
Let g(i) = -2*i**5 + 7*i**4 + 2*i**3 - i**2 + 3*i - 3. Let x(d) = 3*d**5 - 13*d**4 - 5*d**3 + d**2 - 5*d + 5. Let o(s) = -5*g(s) - 3*x(s). Factor o(t).
t**2*(t + 1)**2*(t + 2)
Let v = -44 - -12. Let i = v + 37. Factor 0*d + 0 - 4/5*d**3 - 7/5*d**i + 0*d**2 - 16/5*d**4.
-d**3*(d + 2)*(7*d + 2)/5
Factor 3*w**3 + 3*w - 3*w**3 - 8 - 15*w + 4*w**3.
4*(w - 2)*(w + 1)**2
Suppose 0 = 4*a - 31 + 3. Factor j**2 - a*j**2 + 0*j - 3*j**3 - 3*j**3 - 2*j**4 - 2*j.
-2*j*(j + 1)**3
Let b be 8/(-36) + (-20)/(-9). Solve x**4 + 7*x - x**5 + 2*x**3 - 9*x + b*x = 0.
-1, 0, 2
Let l(u) = 20*u**2 - 125*u + 120. Let t(j) = -5*j**2 + 31*j - 30. Let w(q) = 4*l(q) + 15*t(q). Factor w(z).
5*(z - 6)*(z - 1)
Let w = 279/2 - 1669/12. Let d(t) be the third derivative of -w*t**4 + 0*t - 1/60*t**6 + 2/15*t**5 - 2*t**2 + 0 + 2/3*t**3. Factor d(u).
-2*(u - 2)*(u - 1)**2
What is w in 2*w**4 + 5*w**5 - 2*w**2 - 10*w**5 + 0*w**2 - 2*w**3 + 7*w**5 = 0?
-1, 0, 1
Let q = -2/7 - -4/7. Let u = 65 - 63. What is v in q*v**u + 0*v + 0 = 0?
0
Let b be (-1 + 2)/((-46)/(-138)). Factor -2*l**b + 0 - 4/3*l + 10/3*l**2.
-2*l*(l - 1)*(3*l - 2)/3
Factor -3*m**3 + 0*m + 4*m**2 - 6 + 3*m - 3*m**2 + 5*m**2.
-3*(m - 2)*(m - 1)*(m + 1)
Find w such that 9*w**2 + 16*w - 6*w**3 + 7*w**2 + 6*w**3 + 4*w**3 = 0.
-2, 0
Let a(b) be the first derivative of -2/35*b**5 - 20/7*b**2 - 16/7*b - 1/2*b**4 - 12/7*b**3 - 3. What is x in a(x) = 0?
-2, -1
Let g(k) = -k**3 + k + 1. Let v(z) = 5*z**2 - 8*z + 2. Let i(b) = -g(b) - v(b). Factor i(w).
(w - 3)*(w - 1)**2
Let n(o) be the second derivative of -o**5/50 - o**4/5 - 3*o**3/5 + 8*o. Find y such that n(y) = 0.
-3, 0
Let j = 251 - 1753/7. Factor -2/7*l**5 + 2/7*l**4 - 2/7*l - j*l**2 + 2/7 + 4/7*l**3.
-2*(l - 1)**3*(l + 1)**2/7
Suppose -88*t = -79*t. Let q(c) be the second derivative of -1/4*c**4 - c**3 + 3/20*c**5 + 0*c**2 + t + 3*c. Factor q(a).
3*a*(a - 2)*(a + 1)
Let m(i) be the second derivative of i**5/50 + i**4/30 - i**3/15 - i**2/5 + 5*i. Factor m(y).
2*(y - 1)*(y + 1)**2/5
Let x(h) = h**3 - 6*h**2 - 7*h + 3. Let i be x(7). Let p = i - 17/6. Suppose 1/6*a**3 + 1/6*a**4 - 1/6*a**2 + 0*a + 0 - p*a**5 = 0. What is a?
-1, 0, 1
Let h(a) be the first derivative of -7*a**6/24 + 13*a**5/10 - 27*a**4/16 + a**3/3 + a**2/2 + 1. Solve h(k) = 0.
-2/7, 0, 1, 2
Let x(w) be the second derivative of -10*w**7/21 - 5*w**6/6 - w**5/4 - 16*w. Let x(s) = 0. What is s?
-1, -1/4, 0
Suppose -6*j + j - 1 = 2*k, 2*k = 4*j + 8. Let 2/3*u**3 + k*u**2 - 2/3*u**4 - 4/3 - 2/3*u = 0. What is u?
-1, 1, 2
Determine n, given that 36/5*n + 3/5*n**2 + 108/5 = 0.
-6
Let t(v) = -4*v**3 + 9*v**2 - 12*v. Let r(k) = 7*k**3 - 17*k**2 + 23*k. Let m(u) = 3*r(u) + 5*t(u). Let m(a) = 0. Calculate a.
0, 3
Let i = 8/17 - 15/68. Determine d, given that 0 + 1/4*d**3 + i*d + 1/2*d**2 = 0.
-1, 0
Suppose 0 = -g - 3, 0 = -2*d - 2*d - 4*g + 48. Solve -15*a**2 + d*a**2 + 3*a**5 = 0 for a.
0
Let j(f) be the third derivative of -f**5/15 - f**4/3 - 2*f**2 + 7*f. Suppose j(c) = 0. What is c?
-2, 0
Let o(n) = -n**4 + n**3 + n**2 - n - 1. Let z(b) = 8*b**4 - 32*b + 36. Let d(i) = -12*o(i) - z(i). Factor d(r).
4*(r - 3)*(r - 1)**2*(r + 2)
Find b, given that -2/7*b - 4/7*b**2 + 8/7*b**3 - 6/7*b**5 + 0 + 4/7*b**4 = 0.
-1, -1/3, 0, 1
Suppose -36 = -7*g + g. Suppose 0 = g*b + b. Factor 2*f + 18*f**2 + 49/2*f**5 + 63*f**4 + b + 109/2*f**3.
f*(f + 1)**2*(7*f + 2)**2/2
Let l(w) be the second derivative of -w**7/24 + 23*w**6/120 + w**5/80 - 23*w**4/48 + w**3/4 + 47*w. Determine f, given that l(f) = 0.
-1, 0, 2/7, 1, 3
Suppose 0 = -2*x + 5*y + 30, 4*x = -3*y + 92 + 20. Let g = -21 + x. Solve -8/9*n**3 + 2/9 - 8/9*n + 4/3*n**2 + 2/9*n**g = 0.
1
Find t, given that -52/7*t**3 - 16/7*t + 0 - 4/7*t**5 + 48/7*t**2 + 24/7*t**4 = 0.
0, 1, 2
Let b(q) be the second derivative of q**7/11340 - q**6/1080 - q**4/6 - q. Let m(o) be the third derivative of b(o). Determine n, given that m(n) = 0.
0, 3
Solve 2*s**2 - 7*s**3 + 3*s**2 - 2*s + 7*s**3 - 2*s**3 = 0.
0, 1/2, 2
Let x be 50/225*(-1 + (-6)/(-4)). Let g(p) be the second derivative of 0 + x*p**3 + 0*p**2 + 1/30*p**5 - p - 1/9*p**4. Let g(w) = 0. What is w?
0, 1
Let 2*a**4 + 2*a**3 + 0*a**3 - 4*a**3 - 2*a**2 + 2*a**5 = 0. What is a?
-1, 0, 1
Let x(u) be the third derivative of 0*u + 7*u**2 - 2/75*u**5 - 1/60*u**4 - 4/525*u**7 + 0 - 1/840*u**8 - 1/50*u**6 + 0*u**3. Solve x(k) = 0.
-1, 0
Let n(b) = 6*b + 164. Let q be n(-27). Let -1/4 - 4*g**2 - q*g = 0. What is g?
-1/4
Let h = -20 - -20. Let z(a) be the third derivative of h*a - 1/168*a**8 + 0*a**6 - 1/105*a**7 + 0*a**4 + 2*a**2 + 0*a**3 + 0*a**5 + 0. Factor z(m).
-2*m**4*(m + 1)
Let y(m) be the second derivative of -4*m**7/45 - 23*m**6/75 - 13*m**5/150 + 4*m**4/15 - 4*m**3/45 + 5*m. Determine b so that y(b) = 0.
-2, -1, 0, 1/4, 2/7
What is v in 0*v**3 + 0*v**2 + 0 + 0*v**4 - 3/2*v**5 + 0*v = 0?
0
Suppose -2*u + 5*x + 14 = -u, -2*u + x = -10. Suppose 4*l**4 + 4*l**2 - 2*l - 8*l**u - 2*l + 4*l**3 = 0. Calculate l.
-1, 0, 1
Suppose 0 + 35/3*d**4 + 10/3*d**3 - 5/3*d**2 + 0*d + 20/3*d**5 = 0. What is d?
-1, 0, 1/4
Let f = 43/3 + -14. Factor 4/3 - 4/3*x + f*x**2.
(x - 2)**2/3
Let f(g) be the third derivative of -g**6/660 + g**5/330 - 6*g**2. Determine x so that f(x) = 0.
0, 1
Suppose -b - 1 = -3. Suppose b*h + h = 0. Let -1 - 3*n**2 + h*n + 4*n**3 - n**4 - 3*n**2 + 4*n = 0. What is n?
1
Let m(c) be the third derivative of -c**8/50400 - c**7/12600 - c**5/20 - 3*c**2. Let f(l) be the third derivative of m(l). Factor f(u).
-2*u*(u + 1)/5
Let l = -332 - -1662/5. What is a in l*a**2 + 0*a + 2/5*a**3 + 0 = 0?
-1, 0
Let -2/11*m**4 + 0*m**3 - 2/11 + 0*m + 4/11*m**2 = 0. Calculate m.
-1, 1
Let s = 62 + -56. Let p(n) be the second derivative of 1/60*n**s + 0 + 0*n**2 - 1/24*n**4 + 1/168*n**7 + 0*n**5 - 1/24*n**3 + 3*n. Factor p(t).
t*(t - 1)*(t + 1)**3/4
Let m(z) be the third derivative of -z**7/140 + z**5/20 - z**3/4 + 7*z**2. Factor m(t).
-3*(t - 1)**2*(t + 1)**2/2
Let v(n) = -5*n**3 - 3*n**2. Let d(c) = 19*c**3 + 11*c**2 + c. Let w(a) = 2*d(a) + 9*v(a). Factor w(i).
-i*(i + 1)*(7*i - 2)
Let r be 11/22 - 1/2. Solve 6*b - 2*b**3 + 1 - 3 + r - 2 = 0.
-2, 1
Let -12*c**3 + 31*c**3 - 22*c**3 = 0. Calculate c.
0
Suppose -a + 0*j - 5*j = 22, 0 = -3*a + 3*j + 24. Let n(c) be the first derivative of 1/2*c**a - 2 + 1/4*c**2 - c. Let n(m) = 0. What is m?
-1, 2/3
Let c(y) = y. Let u be c(3). Factor -8*x**3 - 4*x**2 + u*x**4 + 14*x**3 + 7*x**4.
2*x**2*(x + 1)*(5*x - 2)
Let u(q) be the first derivative of 0*q - 1/2*q**4 - 2/3*q**3 + 1 + 0*q**2. Factor u(t).
-2*t**2*(t + 1)
Let b = 360809/5369 - -64/767. Let k = b - 67. Find q such that -2/7*q - k*q**3 - 4/7*q**2 + 0 = 0.
-1, 0
Let t be 9/(7425/(-190))*1/(-2). Let n(i) be the second derivative of 1/33*i**7 + i - 1/66*i**4 + 0*i**2 - t*i**6 - 2/33*i**3 + 0 + 3/22*i**5. Factor n(l).
2*l*(l - 1)**3*(7*l + 2)/11
Factor -2*g**2 - 5/4*g**3 + 1/2 - 1/4*g.
-(g + 1)**2*(5*g - 2)/4
Let h be ((-2)/(-8))/(1/8). Let -2*i**2 + h*i**2 + 2*i**2 + 0*i**2 - 6*i = 0. What is i?
0, 3
Factor 3/4*x**3 + 21/2*x**2 - 45/4*x + 0.
3*x*(x - 1)*(x + 15)/4
Factor 0 - 2*s**4 + s**4 + 2 - 3*s**3 + 2*s + s - s**2.
-(s - 1)*(s + 1)**2*(s + 2)
Let q(d) be the third derivative of -5*d**2 + 0*d - 1/360*d**6 + 0*d**5 + 0*d**3 + 0 + 1/72*d**4. What is v in q(v) = 0?
-1, 0, 1
Suppose 0*c - 4*l = 5*c - 26, -3*c + 2 = -l. Suppose 2*k - 4*f - c = 10, f + 5 = k. Factor o**3 + 2*o + 5*o**3