e the second derivative of 0*s**3 + 0 + 1/90*s**6 - s + y*s**5 + 0*s**2 - 1/36*s**4. Factor q(k).
k**2*(k - 1)*(k + 1)/3
Let a be (-28)/(-6) + ((-84)/(-3))/(-7). Suppose -1/3*k + 0 - 1/6*k**4 - 5/6*k**2 - a*k**3 = 0. What is k?
-2, -1, 0
Let x(r) be the third derivative of -r**8/2240 + r**6/80 + r**5/20 + r**4/4 + 8*r**2. Let w(z) be the second derivative of x(z). Factor w(s).
-3*(s - 2)*(s + 1)**2
Find h such that 2 + 12*h**2 + h + 0*h - 5*h - 18*h**2 = 0.
-1, 1/3
Let b(x) be the second derivative of x**6/45 - x**4/9 + x**2/3 + 7*x. Factor b(v).
2*(v - 1)**2*(v + 1)**2/3
Let p(t) be the second derivative of t**8/504 + t**7/315 + 3*t**2/2 + 8*t. Let g(x) be the first derivative of p(x). Determine z so that g(z) = 0.
-1, 0
Let j be (0 - (3 - 2))*-3. Let r(g) be the third derivative of -g**2 + 0 + 0*g - 1/6*g**4 - 1/30*g**5 - 1/3*g**j. Factor r(n).
-2*(n + 1)**2
Let x(t) be the second derivative of 25*t**4/4 - 10*t**3 + 6*t**2 - t. Factor x(m).
3*(5*m - 2)**2
Let s(x) be the third derivative of -x**8/20160 - x**5/20 + x**2. Let v(a) be the third derivative of s(a). Solve v(w) = 0 for w.
0
Let b be (-3 + 3)/((-3)/3). Factor 12*l**3 - l**5 + 3*l**4 + l**2 + b*l**4 - 15*l**3.
-l**2*(l - 1)**3
Let o(z) be the first derivative of 1/3*z**3 + 0*z + 4 - 1/2*z**2. What is y in o(y) = 0?
0, 1
Let q(x) be the first derivative of -x**4/8 + 2*x**3/3 - x**2 + 32. Solve q(t) = 0.
0, 2
Let u be (-4 - (-8)/2)/(-1). Let s(i) be the third derivative of u*i - 3*i**2 + 0 + 0*i**4 + 1/480*i**6 - 1/6*i**3 + 1/80*i**5. Factor s(m).
(m - 1)*(m + 2)**2/4
Let j be 1/2*40/60. Factor 1/3*u**3 - 2/3*u**2 + j*u + 0.
u*(u - 1)**2/3
Let m(d) = -3*d + 3 + 9*d**2 - 6 + d - 4*d**2. Let v(r) = r**2 - 1. Let p(i) = m(i) - 4*v(i). Find c, given that p(c) = 0.
1
Let d(u) = 2*u**4 + 3*u**3 - 2*u**2 - 3*u. Let l(j) = -j**4 - j**3 + j**2 + j. Let n(x) = 5*d(x) + 15*l(x). Factor n(i).
-5*i**2*(i - 1)*(i + 1)
Let x(f) be the second derivative of -2*f**6/15 + 3*f**5/5 - f**4/3 - 2*f**3 + 4*f**2 - 8*f. Find o such that x(o) = 0.
-1, 1, 2
Let t(v) be the first derivative of -4*v**3/3 - 8*v**2 - 16*v - 19. Factor t(a).
-4*(a + 2)**2
Let c(t) = 2*t**2 - 30*t. Let p be c(15). Factor 0 + 2/7*u**4 - 2/7*u**2 + 0*u**3 + p*u.
2*u**2*(u - 1)*(u + 1)/7
Let g be 12/30 - (-136)/10. Suppose -4*z + 17 = -3*x, -7*z + x + g = -4*z. Factor 0*t**4 + 2/11*t**z + 0*t + 0*t**2 + 0 + 0*t**3.
2*t**5/11
Suppose -3*f - 9 + 39 = 5*a, -3*f + 3 = -4*a. Suppose -a*g + 28 = 5*b + 7, 2*g - 7 = -b. Solve -1/3 - 1/3*r**3 + 1/3*r**g + 1/3*r = 0 for r.
-1, 1
Let l = -349/2 - -175. Factor -h**2 + 0 - l*h - 1/2*h**3.
-h*(h + 1)**2/2
Let z(y) be the third derivative of -3*y**6/160 - y**5/40 + 5*y**4/24 - y**3/3 + 5*y**2. Factor z(l).
-(l + 2)*(3*l - 2)**2/4
Let s(t) = 4*t**4 + 16*t**3 - 3*t**2 + 3*t - 3. Let y(g) = -3*g**4 - 15*g**3 + 2*g**2 - 2*g + 2. Let n(w) = 4*s(w) + 6*y(w). What is b in n(b) = 0?
-13, 0
Factor -4*p**2 + 16*p - 18*p + 6*p**2.
2*p*(p - 1)
Let z(v) = v - 1. Let t(f) = 5*f**2 + f - 4*f**2 - 1 - 1. Let x(r) = -2*t(r) + 6*z(r). Suppose x(h) = 0. What is h?
1
Let n = 612 - 611. Factor -k + n + 1/4*k**4 + 1/2*k**3 - 3/4*k**2.
(k - 1)**2*(k + 2)**2/4
Let a(f) = 4*f**2 + 5*f - 5. Suppose -3*i - 20 = i + p, -3*i + 5*p = -8. Let x(u) = 3*u**2 + 4*u - 4. Let r(k) = i*a(k) + 5*x(k). Solve r(b) = 0 for b.
0
Let r = 23 + -10. Let b = r - 13. Determine t so that b*t**3 - 2/3 + 0*t - 2/3*t**4 + 4/3*t**2 = 0.
-1, 1
Let s(f) be the third derivative of -f**7/1575 + f**6/450 + f**5/150 - f**4/45 - 4*f**3/45 + 4*f**2. What is o in s(o) = 0?
-1, 2
Let w = 43/196 + 26/49. Factor w*o + 0 - 3/4*o**2.
-3*o*(o - 1)/4
Let f = 138 - 412/3. Let n be ((-2)/6)/((-1)/10). Suppose 16/3*u - 8/3 + f*u**3 - n*u**2 = 0. Calculate u.
1, 2
Suppose -4*f + 28 = -2*v + 6, 0 = -4*f - 5*v - 13. Let a(b) be the second derivative of -1/8*b**4 - 2*b + 0 - 3*b**2 - b**f. Factor a(c).
-3*(c + 2)**2/2
Let w = 24 - 13. Let r = w - 7. Factor -1/3*c + 0 + 1/3*c**3 - c**r + c**2.
-c*(c - 1)*(c + 1)*(3*c - 1)/3
Let c be 8/14 + (-82984)/280. Let a = c + 299. Let -376/5*j**2 - a - 96*j**3 - 45*j**4 - 128/5*j = 0. What is j?
-2/3, -2/5
Let t(v) be the third derivative of v**9/37800 + v**8/8400 - v**6/900 - v**5/300 - v**4/6 - 4*v**2. Let u(k) be the second derivative of t(k). Factor u(p).
2*(p - 1)*(p + 1)**3/5
Suppose 5*z - z + 17 = -5*x, 2*z + 21 = -5*x. Suppose -b - z*b = -3. Factor -b - 1/2*c + 1/2*c**2.
(c - 2)*(c + 1)/2
Factor -3/7*d**4 + 15/7*d**2 - 3/7*d**3 - 9/7*d + 0.
-3*d*(d - 1)**2*(d + 3)/7
Let q be (-4)/(-10) - 4/10. Let x(r) = -r**2 - 8*r + 9. Let o be x(-9). Solve -b**3 + q + 2/3*b**2 - 2/3*b**4 + b**5 + o*b = 0.
-1, 0, 2/3, 1
Suppose -2*g = 5*o - 24, -16*g + 12 = -12*g + o. Solve 2/13*n**3 - 4/13*n**g + 0 + 0*n = 0.
0, 2
Let n(y) be the third derivative of -y**8/2016 + y**6/240 - y**5/180 + 2*y**2 - 3. Factor n(s).
-s**2*(s - 1)**2*(s + 2)/6
Let d(z) be the first derivative of -3/2*z**2 + 1/4*z**4 - 6 + 0*z**3 + 2*z. Determine f, given that d(f) = 0.
-2, 1
Let r = -4 - 0. Let v(g) = -2 + 3*g**3 + 3*g + 0 - 4 + 4*g**2. Let c(x) = -x**3 - x**2 + 1. Let z(b) = r*c(b) - v(b). Let z(i) = 0. Calculate i.
-2, 1
Suppose -2*o = 3*s + s - 6, 0 = -4*s - 3*o + 3. Determine c so that 2*c**2 - 30*c**s + 33*c**3 + c**2 = 0.
-1, 0
Let b(o) be the second derivative of o**6/30 + o**5/20 - o**4/4 - 5*o**3/6 - o**2 - 9*o. Factor b(g).
(g - 2)*(g + 1)**3
Let q(x) be the third derivative of -x**8/50400 - x**5/12 + x**2. Let y(t) be the third derivative of q(t). Factor y(b).
-2*b**2/5
Let x(l) be the first derivative of -2 + 1/15*l**3 + 1/20*l**4 - 1/5*l**2 + 0*l. What is j in x(j) = 0?
-2, 0, 1
Let l be ((-176)/(3 + -5))/1. Let q = 266/3 - l. Factor q*g**2 + 4/3 + 2*g.
2*(g + 1)*(g + 2)/3
Let t(a) be the second derivative of -1/10*a**4 - 3/10*a**2 + 1/70*a**7 + 3/50*a**6 - 3/10*a**3 - 5*a + 0 + 3/50*a**5. Determine i, given that t(i) = 0.
-1, 1
Let h = -25 + 19. Let q be (-8)/15*h/4. Factor -4/5*x**2 + 2/5*x + 2/5*x**5 - q*x**3 + 2/5*x**4 + 2/5.
2*(x - 1)**2*(x + 1)**3/5
Solve -8*k - k**2 + 5*k**2 + 6*k**3 + 29*k**4 - 33*k**4 + 2*k**3 = 0.
-1, 0, 1, 2
Let k(t) be the first derivative of 4*t**3/3 + 60*t**2 + 900*t - 70. Determine d, given that k(d) = 0.
-15
Let m be (42/12 - 8)*(-2)/6. Let 0 + m*g + 3/2*g**2 = 0. Calculate g.
-1, 0
Let l(a) be the first derivative of 1/24*a**6 - 3/8*a**2 - 3/20*a**5 + 1/8*a**4 - 3 + 1/6*a**3 + 1/4*a. Solve l(r) = 0.
-1, 1
What is y in -18 + 0*y**3 - 17*y**2 - 3*y**3 + 5*y**3 + 3*y**2 + 30*y = 0?
1, 3
Let u = 244/3 + -81. Factor -o**4 - 1/3*o**5 + 0*o + 0 - o**3 - u*o**2.
-o**2*(o + 1)**3/3
Determine g so that 2/3*g**3 + 2*g + 0 + 8/3*g**2 = 0.
-3, -1, 0
Let g(u) be the second derivative of -u**7/14 - u**6/2 - 3*u**5/2 - 5*u**4/2 - 5*u**3/2 - 3*u**2/2 + 2*u. Factor g(k).
-3*(k + 1)**5
Let m = 212/3 + -70. Find d, given that m + 2/3*d**2 + 4/3*d = 0.
-1
Let v be 122/8 + 13/(-52). Factor -13*p**3 + 9*p**4 - 21*p - 29 + 114*p**2 + 2 - v*p - 47*p**3.
3*(p - 3)**2*(p - 1)*(3*p + 1)
Let t be 2/4 - 3/(-2). Determine s so that -2*s**t + 3*s + 4 + 2*s - 3*s = 0.
-1, 2
Factor 3*y**2 - y**2 + y**2 + 3*y**3.
3*y**2*(y + 1)
Find y, given that -21 - 18*y**2 + 9*y**3 + 3*y**4 - 53 + 2 - 84*y = 0.
-2, 3
Let b(w) = 5*w**2 + 2*w**2 - w + w**3 - 2 - 3. Let u be b(-7). Determine p, given that 2/3*p**4 + 0*p**3 + 0 + 0*p**u + 0*p = 0.
0
Let -8*u**2 - 62*u**2 + 72*u + u**4 - 27 - 4*u**4 + 4*u**2 + 24*u**3 = 0. Calculate u.
1, 3
Factor -x**2 + 1/2*x**5 + 1/2*x - x**3 + 1/2*x**4 + 1/2.
(x - 1)**2*(x + 1)**3/2
Let d(x) be the third derivative of x**5/210 + x**4/42 + 7*x**2. Let d(w) = 0. Calculate w.
-2, 0
Let g(a) be the third derivative of -3*a**7/280 + a**6/16 - 3*a**5/20 + 3*a**4/16 - a**3/8 + 2*a**2. Factor g(s).
-3*(s - 1)**3*(3*s - 1)/4
Suppose u - 3*y + 10 = 0, -5*y + 2*y = -15. Suppose 4*m - o + 5 = 14, u*m + 3*o = 7. Factor 3*j**2 - 1 + 3 + 8*j**3 + 8*j + m*j**4 + 9*j**2.
2*(j + 1)**4
Solve 0*j + 2/3*j**4 - 2/3*j**2 + j**3 + 0 - j**5 = 0.
-1, 0, 2/3, 1
Let -1/2*o**3 - 5*o**2 - 6 + 23/2*o = 0. What is o?
-12, 1
Let m(v) be the first derivative of -v**5/10 + v**4/2 - v**3/6 - 3*v**2/2 + 23. Suppose m(c) = 0. What is c?
-1, 0, 2, 3
Factor 3/5*y + 0 - 3/5*y**2.
-3*y*(y - 1)/5
Let z(d) be the first derivative of 2/9*d**3 + 1/3*d**2 - 1/6*d**4 - 7 - 2/3*d