 j(k) be the first derivative of -k**6/180 + k**5/20 - k**4/6 - k**3/3 + 3. Let h(z) be the third derivative of j(z). Factor h(p).
-2*(p - 2)*(p - 1)
Let m(w) = -w**2 - w + 1. Let r(g) = -6*g**2 + 3*g + 8. Let h(y) = 5*m(y) - r(y). Let f be h(9). Let 3*u - u + 3*u**2 - f - 5*u + 0*u = 0. What is u?
-1, 2
Let g(w) be the first derivative of w**6/3 - 2*w**5/5 - w**4/2 + 2*w**3/3 + 3. Determine n, given that g(n) = 0.
-1, 0, 1
Let y(x) be the first derivative of -2/3*x + 5 - x**2 + 1/2*x**4 + 10/9*x**3 - 8/15*x**5. What is b in y(b) = 0?
-1, -1/4, 1
Let z = 19 - 19. Let f(m) be the second derivative of z - m + 0*m**2 + 1/9*m**3 - 1/36*m**4. Suppose f(a) = 0. What is a?
0, 2
Let a = -20/37 - -117/148. Factor 0 + a*c**3 - 1/2*c - 1/4*c**2.
c*(c - 2)*(c + 1)/4
Let u(l) be the second derivative of l**5/90 + l**4/27 - 5*l. Solve u(b) = 0 for b.
-2, 0
Suppose -t + 5 = 5*g, -4*g - 5*t - 5 = -30. Suppose 2/5*p**4 + 2/5*p**2 + 0 + 4/5*p**3 + g*p = 0. What is p?
-1, 0
Let f(r) = -r**2 - 9*r - 2. Let y be f(-7). Suppose 2*a + y = 3*n, -2*a + 15 = -7*a. Factor 2/3*i**3 + 0*i**n + 0*i + 0 + 2/3*i**4.
2*i**3*(i + 1)/3
Let k(s) be the second derivative of -3*s**5/20 - 3*s**4/4 - 3*s**3/2 - 3*s**2/2 + 2*s. Factor k(o).
-3*(o + 1)**3
Let x(f) be the first derivative of 16*f**5/45 - f**4 + 2*f**3/9 + 2*f**2/9 + 6. Suppose x(v) = 0. What is v?
-1/4, 0, 1/2, 2
Let q(g) = -4*g**4 + 4*g**3 + 8*g**2 + 3*g - 6. Let d = -9 + 8. Let b(i) = -i**2 - i + 1. Let m(f) = d*q(f) - 5*b(f). Factor m(t).
(t - 1)**2*(2*t + 1)**2
Let x(k) be the first derivative of -3 + 0*k + 1/12*k**6 + 1/3*k**4 - k**2 - 4/3*k**3 + 13/30*k**5. Let a(d) be the second derivative of x(d). Factor a(y).
2*(y + 1)*(y + 2)*(5*y - 2)
Let b = 1/135 + 59/135. Let b - 2/9*j**2 + 2/9*j = 0. Calculate j.
-1, 2
Let y(w) be the second derivative of w**4/54 - w**3/9 - 2*w. Factor y(v).
2*v*(v - 3)/9
Factor 0 - 3*t**4 - 9/5*t**2 + 3/5*t**5 + 21/5*t**3 + 0*t.
3*t**2*(t - 3)*(t - 1)**2/5
Let y be 11/44 + (-38)/(-8). Let p(d) = -d**3 + 3*d**2 + 5*d - 2. Let c be p(4). Find j, given that -2*j**y - 19*j + 17*j + 2*j**3 + c*j**3 = 0.
-1, 0, 1
Suppose 1 - 7 = 2*s. Let m be 2/(-3)*s/7. Factor -m*n + 0 + 2/7*n**2.
2*n*(n - 1)/7
Let v(l) be the third derivative of l**8/504 - 4*l**7/315 + l**6/45 + l**5/45 - 5*l**4/36 + 2*l**3/9 + 2*l**2 - 47. Factor v(s).
2*(s - 2)*(s - 1)**3*(s + 1)/3
Suppose -3*q + 4 - 13 = -3*t, 5*t + 5*q - 25 = 0. Let 3*x**4 - 3*x**t + x**4 - x**2 = 0. What is x?
-1, 0, 1
Let s = 4 - 0. Factor 0*c**4 + 3 - 2*c**2 - 4*c**3 - 2*c**s - 3.
-2*c**2*(c + 1)**2
Let x be (-21)/(-98) - 2/(-7). Let v(n) be the first derivative of 3/8*n**2 - x*n - 1 - 1/12*n**3. Let v(r) = 0. What is r?
1, 2
Let k(j) be the second derivative of 1/3*j**3 + 1/10*j**5 + 0 - 5*j - 1/3*j**4 + 0*j**2. Suppose k(d) = 0. What is d?
0, 1
Let v(a) be the second derivative of -a**4/30 + a**2/5 + 4*a. What is u in v(u) = 0?
-1, 1
Let a(r) = -r - 4. Let s be a(-6). Find v, given that 3 + s - 5 - v**2 + v = 0.
0, 1
Let y(t) be the second derivative of -3/170*t**5 + 0 + 0*t**2 + 1/255*t**6 - 1/102*t**4 + 1/119*t**7 + 0*t**3 + 8*t. Solve y(u) = 0 for u.
-1, -1/3, 0, 1
Suppose 2 + 2 = 2*b. Let q(r) = 3*r**2 + 4*r - 9. Let l(h) = 9*h**2 + 11*h - 27. Let x(c) = b*l(c) - 7*q(c). Factor x(f).
-3*(f - 1)*(f + 3)
Solve 20/7*z**4 + 0 - 8/7*z**3 + 8/7*z - 20/7*z**2 = 0 for z.
-1, 0, 2/5, 1
Let s = -33 + 37. Let m(z) be the second derivative of 0*z**2 + 2*z + 0 + 1/24*z**3 + 1/48*z**s. Factor m(g).
g*(g + 1)/4
Find o, given that -10*o**2 - 9*o**2 + 20*o**3 - 10*o**2 + 24*o**2 = 0.
0, 1/4
Let y = -27 - -37. Let s be 100/15*2/y. Let s*h**2 - 2/3*h**4 - 4/3*h**3 + 2/3*h - 2/3 + 2/3*h**5 = 0. What is h?
-1, 1
Let f = 1 - 1. Let o = 8 + -5. Factor 0 + f*j**2 - j**3 - 1 - 3*j**2 - o*j.
-(j + 1)**3
Let p(g) be the third derivative of -g**6/30 + 23*g**5/105 - 10*g**4/21 + 8*g**3/21 - 7*g**2. Determine a so that p(a) = 0.
2/7, 1, 2
Let n(z) be the first derivative of -z**3/3 - 3*z**2/2 - 2*z + 20. Factor n(l).
-(l + 1)*(l + 2)
Let t(a) be the first derivative of a**4 + a**3/3 - 2*a**2 - 4*a - 5. Let g(z) = -z - 1. Let j(v) = -12*g(v) + 3*t(v). Find y such that j(y) = 0.
-1/4, 0
Factor 12/7 - 8/7*j**2 + 2/7*j + 2/7*j**3.
2*(j - 3)*(j - 2)*(j + 1)/7
Let f = -3 + 6. Factor 2*c**f + 3*c - 6*c + c**3.
3*c*(c - 1)*(c + 1)
Let r(y) be the first derivative of y**6/15 + 6*y**5/25 + 17. Factor r(j).
2*j**4*(j + 3)/5
Suppose 0 = 5*h - 5*h - 5*h. What is f in 3/2*f**3 + 0*f**2 + h + 0*f = 0?
0
Let h(g) be the second derivative of g**6/75 - g**5/50 - g**4/15 + 15*g. Solve h(k) = 0.
-1, 0, 2
Let h = 663 + -663. Factor h + 0*n**2 - 2/9*n**3 + 0*n.
-2*n**3/9
Let c(y) = -5*y**3 - 25*y**2 - 20*y. Let r(b) = 5*b**3 + 24*b**2 + 20*b. Let q(s) = 4*c(s) + 5*r(s). Factor q(h).
5*h*(h + 2)**2
Let i(l) be the first derivative of -l**3/3 + 3*l**2/2 - 2*l + 4. Determine c, given that i(c) = 0.
1, 2
Solve -o**2 + 53*o + 2*o**2 - 54*o = 0.
0, 1
Find c, given that 21*c**2 - 28*c**4 - 56*c + 17*c**3 - 13*c**2 - 12*c**2 + 35*c**3 + 4*c**5 + 32 = 0.
-1, 1, 2, 4
Let b(j) be the second derivative of 3*j + 0 + 0*j**3 + 0*j**2 + 1/30*j**5 + 0*j**4. Factor b(y).
2*y**3/3
Let m = 25 + -25. Let u(p) be the second derivative of 2/21*p**3 - p - 1/42*p**4 - 1/7*p**2 + m. Factor u(b).
-2*(b - 1)**2/7
Let u(c) be the second derivative of -c**6/30 + c**5/5 - c**4/4 - 2*c**3/3 + 2*c**2 - 2*c. Suppose u(h) = 0. What is h?
-1, 1, 2
Suppose -10 = -2*r - 3*r. Let p(b) be the first derivative of r + b - 3/4*b**2 + 3/8*b**4 - 1/6*b**3 - 1/10*b**5. What is i in p(i) = 0?
-1, 1, 2
Solve -30*q - 5*q**2 + 9*q**4 + 6*q**4 - 10*q**4 + 30*q**3 = 0.
-6, -1, 0, 1
Let g be (-80)/64*(-4)/10. Factor -1/4*f**4 + 1/2*f**2 + 1/4*f**5 - 1/4 + 1/4*f - g*f**3.
(f - 1)**3*(f + 1)**2/4
Let h(a) be the second derivative of -7*a**8/120 + a**7/6 + a**6/60 - a**5/3 - a**4/3 - a**3/3 + 3*a. Let l(n) be the second derivative of h(n). Factor l(w).
-2*(w - 1)**2*(7*w + 2)**2
Let t be (-28)/6 - (-3)/(-9). Let y be 3/(-15) + (-1)/t. Find p such that -4/3*p**2 + 2/3*p**4 + 0*p**3 + 2/3 + y*p = 0.
-1, 1
Suppose 3*k + 4*d + 6 = d, k + 4*d = -14. Solve -1/4 + 3/4*c**k + 1/2*c = 0 for c.
-1, 1/3
Let y(g) be the third derivative of g**6/180 + g**5/15 - 29*g**2. Solve y(q) = 0.
-6, 0
Let b(g) be the second derivative of g**6/105 - g**4/42 - 8*g. Find h such that b(h) = 0.
-1, 0, 1
Let x(a) = -a**2 + 7*a - 10. Let u be x(3). Let d(h) be the first derivative of -h**3 - 2 - 3/2*h**u + 0*h. Factor d(c).
-3*c*(c + 1)
Let z = -201 + 108. Let l be z/(-84) + 1/(-4). Solve -l*b + 2/7 + 6/7*b**2 - 2/7*b**3 = 0.
1
Factor 1/2*w**2 + 2*w + 2.
(w + 2)**2/2
Suppose -3*n + 2*n + 2 = -2*k, 2*k + 2 = 2*n. Factor n + 2/3*d + 2/3*d**2.
2*d*(d + 1)/3
Let d(s) be the first derivative of 0*s - 1 + 1/6*s**3 - 1/10*s**5 + 1/8*s**4 - 1/4*s**2. Factor d(m).
-m*(m - 1)**2*(m + 1)/2
Let o(y) be the first derivative of -6 - 2/3*y**3 - y**2 + 0*y. Find a such that o(a) = 0.
-1, 0
Let t(o) be the third derivative of 0*o**3 + 0*o + 0 + 0*o**4 - 1/315*o**7 - 1/90*o**5 + 2*o**2 + 1/90*o**6. Factor t(s).
-2*s**2*(s - 1)**2/3
Factor -6*q**2 + 3*q**2 - q**2 + 8*q**2.
4*q**2
Let g = -9 - -14. Suppose g*p - 14 = -3*v, 0*v + 2*v + 4*p = 10. Factor 0*m**5 + m**5 - 4*m**4 + 0*m**5 - v*m**5 - 2*m**3.
-2*m**3*(m + 1)**2
Let g(j) = 2*j**2 + 2 - 3*j**2 + 6*j + 0 - 4. Let d be g(5). Factor 4/3*k**2 + 2/3*k**5 - 4/3*k**4 + 0*k**d - 2/3*k + 0.
2*k*(k - 1)**3*(k + 1)/3
Let p(b) be the first derivative of b**3/12 - b**2/4 - 3*b/4 + 1. Factor p(v).
(v - 3)*(v + 1)/4
Suppose -3*t + 6 + 4 = -2*r, 0 = -4*r - 2*t - 4. Let w(y) = -2*y**2 + 2*y. Let c(i) = -i**2 + i. Let j(l) = r*w(l) + 2*c(l). Factor j(u).
2*u*(u - 1)
Let t(f) be the third derivative of -f**7/1260 + f**6/360 - 7*f**2. Factor t(j).
-j**3*(j - 2)/6
Suppose -22/7*t + 10/7*t**2 + 6/7*t**3 + 6/7 = 0. What is t?
-3, 1/3, 1
Let g(l) = 4*l**4 + l**3 - 2*l + 5. Let c(k) = 3*k - 11*k**3 - k**2 - 5*k**4 - k - 6 + 9*k**3. Let q(o) = -5*c(o) - 6*g(o). Suppose q(f) = 0. Calculate f.
-2, -1, 0
Let g(p) = 7*p**3 + 3*p**2 - 13*p + 13. Let d(k) = -4*k**3 - 2*k**2 + 7*k - 7. Let r(l) = -5*d(l) - 3*g(l). Factor r(n).
-(n - 2)*(n - 1)*(n + 2)
Let o(a) be the third derivative of a**7/420 + a**6/480 - 9*a**2. Find d such that o(d) = 0.
-1/2, 0
Suppose 4*j + 4*k -