. Suppose g(y) = 0. What is y?
-2, -1
Let t = 262/3 + -87. Let i(b) be the second derivative of t*b**3 + 1/21*b**7 + 0*b**4 - 1/5*b**5 + 2*b + 0*b**2 + 0*b**6 + 0. Factor i(k).
2*k*(k - 1)**2*(k + 1)**2
Let y(s) be the second derivative of -s**5/10 + 5*s**4/6 - 4*s**3/3 - s. Factor y(m).
-2*m*(m - 4)*(m - 1)
Determine b, given that 1476*b - 2*b**2 - 1472*b + 0*b**2 + 6 = 0.
-1, 3
Suppose 7 = 7*v - 2*v + d, 4*d + 10 = -v. Factor -15*m - 3 - 30*m**v - 8*m**3 - 7*m**4 - 22*m**3 - 8*m**4 - 3*m**5.
-3*(m + 1)**5
Let q(z) be the second derivative of -8*z - 32/5*z**2 + 1/100*z**5 + 0 + 8/5*z**3 - 1/5*z**4. What is d in q(d) = 0?
4
Let c(l) = -l + 8. Let o be c(4). Let j be (-4)/8 - 15/(-6). Factor -z**2 - o*z**2 + 3*z**j + 4*z.
-2*z*(z - 2)
Let -7/2*g**5 - 53/2*g**3 - 33/2*g**4 + 0*g + 2 - 31/2*g**2 = 0. What is g?
-2, -1, 2/7
Let n = 1153/21 - 163/3. Solve -2/7*r + n - 2/7*r**2 = 0.
-2, 1
Let q be ((-4)/(-5))/(12/180). Suppose 3*b + h - 7 = 0, 5*b + 2*h - q = -0*h. Factor 2 - 7/2*s**b + 6*s.
-(s - 2)*(7*s + 2)/2
Suppose 0 = 3*z + 3*c + 9, -7*z + c = -3*z - 3. Factor z + 3*m - 6*m**3 - 21/2*m**2.
-3*m*(m + 2)*(4*m - 1)/2
Let a = 144 + -1006/7. Factor a*u**2 + 6/7*u + 4/7.
2*(u + 1)*(u + 2)/7
Determine a, given that -2/15*a**2 + 2/15*a + 0 = 0.
0, 1
Let b be (-22)/4 - (-30)/20. Let x(r) = -1. Let g(z) = -z**3 + 4*z**2 - 5*z + 5. Let d(m) = b*g(m) - 12*x(m). Factor d(n).
4*(n - 2)*(n - 1)**2
Let -14*j**4 - 120*j**3 - 96*j - 21 - 280*j**2 - 14*j**4 + 108*j**2 + 5 = 0. Calculate j.
-2, -1, -2/7
Let h(l) be the second derivative of l**7/315 - l**5/90 - 5*l**2/2 - 4*l. Let k(d) be the first derivative of h(d). Determine c so that k(c) = 0.
-1, 0, 1
Let q(x) be the first derivative of 0*x**3 + 0*x**2 + 1/12*x**4 + 2 - 3*x. Let l(n) be the first derivative of q(n). Suppose l(w) = 0. Calculate w.
0
Let r(c) be the first derivative of c**6/1800 - c**5/100 + 3*c**4/40 - c**3 - 3. Let z(f) be the third derivative of r(f). Factor z(q).
(q - 3)**2/5
Let a(x) be the first derivative of 3/4*x**4 + 3*x**3 - 2 + 3*x**2 + 0*x. Determine c so that a(c) = 0.
-2, -1, 0
Let n(f) be the first derivative of -f**2 - 1/3*f**3 - 10 + 0*f. Let n(d) = 0. Calculate d.
-2, 0
Let f = 444 - 441. Let -2/9*c**f + 0*c**2 + 0 + 0*c = 0. Calculate c.
0
Let q(u) be the second derivative of 0 + 0*u**5 + 0*u**3 + 1/5*u**2 - 1/15*u**4 + 1/75*u**6 - 4*u. Factor q(d).
2*(d - 1)**2*(d + 1)**2/5
Factor -1/5*i**4 + 0*i + 0 + 2/5*i**3 - 1/5*i**2.
-i**2*(i - 1)**2/5
Let f(n) be the third derivative of -n**8/336 + n**7/210 + n**6/120 - n**5/60 + 14*n**2. Determine o, given that f(o) = 0.
-1, 0, 1
Let l(v) be the first derivative of -v**5/45 + v**4/72 + 3*v**2/2 - 2. Let s(r) be the second derivative of l(r). Determine o, given that s(o) = 0.
0, 1/4
Let w = -62 + 188/3. Let c(m) be the third derivative of m**2 + 2/15*m**5 - w*m**4 - 3/7*m**7 + 0*m + 7/10*m**6 + 0*m**3 + 0. Find p such that c(p) = 0.
-2/5, 0, 2/3
Let y = -471/2 - -236. Factor 0 - j - y*j**2.
-j*(j + 2)/2
Let g(m) be the third derivative of m**8/8400 + 5*m**3/6 - 6*m**2. Let s(l) be the first derivative of g(l). Solve s(k) = 0.
0
Let t(x) be the third derivative of -x**7/210 + x**5/20 + x**4/12 + 8*x**2. Factor t(v).
-v*(v - 2)*(v + 1)**2
Let h(i) = -3*i**2 - 8*i - 2. Let n(a) = -10*a**2 - 25*a - 6. Let u(p) = -7*h(p) + 2*n(p). Let z be u(-6). Factor -m**4 - 2 + m**2 + z.
-m**2*(m - 1)*(m + 1)
Let q(a) be the first derivative of -14*a**3/3 + 5*a**2 + 4*a + 11. What is j in q(j) = 0?
-2/7, 1
Let b(l) be the first derivative of 5*l**4/4 + 5*l**3 + 15*l**2/2 + 5*l - 12. Determine n so that b(n) = 0.
-1
Factor -2*v**4 - 25*v**2 - 8*v**3 + 13*v**2 + 0 - 8*v - 2.
-2*(v + 1)**4
Let p(j) be the third derivative of j**6/30 - 4*j**2. Solve p(s) = 0.
0
Let o = 15 + -12. Let l(i) be the third derivative of 1/48*i**4 + 0 + 0*i - i**2 + 0*i**5 - 1/240*i**6 + 0*i**o. Determine d, given that l(d) = 0.
-1, 0, 1
Let r(o) be the second derivative of -1/30*o**3 - 1/100*o**5 + 0 + 5*o + 0*o**2 + 1/30*o**4. Solve r(q) = 0 for q.
0, 1
Suppose -4*i - 2 = u, -2*i - i = 2*u - 1. Let o be (-4)/(u/(-4) - 0). Find c such that o*c**2 - 5*c + c**3 - 6*c**3 + 1 + c**3 = 0.
1/2, 1
Let d(h) = 2*h**4 + 2*h**2 - 3*h + 2. Let z be 6 + -3 + -2 + 2. Let s(i) = 3*i**3 - 2*i**2 - i**4 - 1 - 3*i**3 + 2*i. Let f(u) = z*s(u) + 2*d(u). Factor f(x).
(x - 1)**2*(x + 1)**2
Let -824*o - 5*o**4 - 7*o**3 + 25*o**2 + 809*o + 2*o**3 = 0. Calculate o.
-3, 0, 1
Let j(y) be the first derivative of 23*y**3/9 + 25*y**2/6 + 2*y/3 + 56. What is f in j(f) = 0?
-1, -2/23
Let i be (2 + -3)*2/(-6). Let d(q) be the first derivative of 1/3*q**3 + 2 + i*q - 1/2*q**2 - 1/12*q**4. Factor d(l).
-(l - 1)**3/3
Let s(n) be the first derivative of n**5/20 - 5*n**4/12 + 4*n**3/3 - 2*n**2 + 3*n + 2. Let a(w) be the first derivative of s(w). Determine g so that a(g) = 0.
1, 2
Let z = 13/25 - -311/75. Solve 0 + 4/3*a + 10/3*a**3 - z*a**5 - 6*a**4 + 6*a**2 = 0 for a.
-1, -2/7, 0, 1
Factor 6/13*q**3 + 4/13 + 20/13*q**2 + 18/13*q.
2*(q + 1)*(q + 2)*(3*q + 1)/13
Let b(f) be the third derivative of f**6/240 + 11*f**5/240 + 13*f**4/96 + f**3/6 + 9*f**2. Factor b(l).
(l + 1)*(l + 4)*(2*l + 1)/4
Let i = -7 - -7. Let b(w) be the third derivative of 1/160*w**6 - 2*w**2 - 1/840*w**7 + 1/96*w**4 + i*w**3 - 1/80*w**5 + 0*w + 0. Factor b(g).
-g*(g - 1)**3/4
Let j be 21/5*55/198. Determine d so that j*d**5 + 0*d**2 + 0 + 5/6*d**4 - 1/3*d**3 + 0*d = 0.
-1, 0, 2/7
Let g(s) = 8*s**2 - 6*s - 2. Let w(f) = 7*f**2 - 6*f - 1. Let a(m) = -4*g(m) + 5*w(m). Find z, given that a(z) = 0.
1
Let m = 3/7 + -5/28. Factor 0*w**3 + m + 1/4*w**4 - 1/2*w**2 + 0*w.
(w - 1)**2*(w + 1)**2/4
Factor -16*a + 26*a**3 + 16 - 12*a**3 - 10*a**3 - 4*a**2.
4*(a - 2)*(a - 1)*(a + 2)
Let p be (-27)/(-54)*(-2 + 14/4). Factor z - 1/4*z**2 - p.
-(z - 3)*(z - 1)/4
Let y(f) = -10*f**3 - 26*f**2 + 52*f - 13. Let p(q) = 10*q**3 + 26*q**2 - 52*q + 14. Let h(k) = -3*p(k) - 2*y(k). Factor h(c).
-2*(c - 1)*(c + 4)*(5*c - 2)
Let m(f) = -f**3 - 8*f**2 + 10*f + 12. Let s be m(-9). Suppose -s*d = -1 - 11. Factor -4*y**2 + 18*y**3 - 18*y - 4*y**2 - 2*y**2 + 7*y**4 - d + 7*y**4.
2*(y - 1)*(y + 1)**2*(7*y + 2)
Let r(w) = w**2 - 8*w + 5. Let i be r(8). Let z(s) be the second derivative of -s - 1/15*s**3 + 0*s**2 + 1/75*s**6 + 0 - 1/30*s**4 + 1/50*s**i. Factor z(a).
2*a*(a - 1)*(a + 1)**2/5
Let c(s) = 6*s**2 + 12*s + 3. Let d(q) = -8*q**2 - 9 + 2 - 23*q - 3*q**2. Let i(z) = 5*c(z) + 3*d(z). Factor i(o).
-3*(o + 1)*(o + 2)
Let y = 127/35 + -24/7. Factor 4/5 + y*x**2 - 4/5*x.
(x - 2)**2/5
Suppose -h - 9 = -2*h. Suppose -3*d = -3*j - h, 3 = -4*j + 3*d - 4. Factor a**j + 2*a - 19*a**2 - 24*a**3 - 10*a**4 - 6*a.
-2*a*(a + 1)**2*(5*a + 2)
Let y(n) = 4*n**2 - 5*n - 19. Suppose 1 + 5 = 3*a. Let d(r) = r**2 - 2*r - 6. Let g(f) = a*y(f) - 7*d(f). What is u in g(u) = 0?
-2
Let a(y) be the second derivative of -8*y + 0*y**2 + 0 - 1/8*y**4 + 1/2*y**3. Factor a(z).
-3*z*(z - 2)/2
Factor 8*w + w**2 + 4 - 4*w**2 + 7*w**2.
4*(w + 1)**2
Let v = 64/7 + -136/21. What is l in 1/3*l**2 - v*l + 4/3 + l**3 = 0?
-2, 2/3, 1
Let z(o) = o**2 - 4*o - 2. Let p be z(5). Let v(g) be the first derivative of 0*g + 1/20*g**5 + 0*g**2 + 0*g**p + 3 - 1/8*g**4. Factor v(b).
b**3*(b - 2)/4
Let c(g) = 2*g**2 - 3*g + 2. Let s be c(2). Find h, given that -7*h**5 + s*h**2 + 2 - 2*h**4 - 2 - 7*h - 2 + 14*h**3 = 0.
-1, -2/7, 1
Let m(t) be the third derivative of -t**9/68040 + t**8/15120 - t**7/11340 + t**4/8 - t**2. Let h(b) be the second derivative of m(b). Factor h(v).
-2*v**2*(v - 1)**2/9
Let y(p) = -4*p**3 - 7*p**2 - 3*p + 5. Let v(l) = -2*l**3 - 3*l**2 - l + 3. Let k(g) = -5*v(g) + 3*y(g). Factor k(m).
-2*m*(m + 1)*(m + 2)
Let k(v) be the third derivative of 3*v**2 - 2/3*v**3 + 1/6*v**5 + 0*v + 1/4*v**4 + 0. Factor k(a).
2*(a + 1)*(5*a - 2)
Solve -32*p**2 - 184/3*p**3 - 25/3*p**5 - 16/3*p - 40*p**4 + 0 = 0 for p.
-2, -2/5, 0
Let w(c) = c**3 - 8*c**2 - c + 8. Let d be w(8). Factor 0*t**3 + 0 + 2/7*t**2 + d*t - 2/7*t**4.
-2*t**2*(t - 1)*(t + 1)/7
Let a(s) = -4*s**3 + 4*s - 8. Let j(d) = d**3 - d + 3. Let t(c) = -3*a(c) - 8*j(c). Factor t(w).
4*w*(w - 1)*(w + 1)
Let q(g) be the third derivative of -g**7/60 + 3*g**6/80 - g**5/60 - 8*g**2. Factor q(n).
-n**2*(n - 1)*(7*n - 2)/2
Suppose 3*y + 5*d + 4 = 0, 3*y - 3*d - 6 =