**3/3 - 5. Let a(y) be the third derivative of m(y). Find i such that a(i) = 0.
-1, 1
Let r be 2/(-42)*(17 + -23). Factor r*h - 4/7 + 2/7*h**2.
2*(h - 1)*(h + 2)/7
Let r(a) = a**3 + 4*a**2 + 5. Let c be r(-4). Let l = 7 - c. Factor -3*h**2 + 8*h**4 + h**3 - 7*h**3 + h**l.
2*h**2*(h - 1)*(4*h + 1)
Suppose 2/9*i**2 - 8/9*i**3 + 0*i + 0 = 0. Calculate i.
0, 1/4
Let r(o) be the second derivative of 2*o**7/105 - o**6/15 - o**5/15 + o**4/3 - 5*o**2/2 - 6*o. Let m(a) be the first derivative of r(a). Factor m(k).
4*k*(k - 2)*(k - 1)*(k + 1)
Factor 9/2*v + 4 + 1/2*v**2.
(v + 1)*(v + 8)/2
Let c be (-2)/(-5) + (-48)/(-30). Let a be c/(-8)*32/(-24). Suppose 0*q**3 - a*q + 0 + 2/3*q**4 + 1/3*q**5 - 2/3*q**2 = 0. What is q?
-1, 0, 1
Let y(r) be the second derivative of r**8/3360 - r**7/1260 - 5*r**4/12 - 4*r. Let d(a) be the third derivative of y(a). Determine q, given that d(q) = 0.
0, 1
Let j(a) be the third derivative of a**9/151200 + a**8/10080 + a**7/1575 + a**6/450 - a**5/60 + a**2. Let l(c) be the third derivative of j(c). Factor l(z).
2*(z + 1)*(z + 2)**2/5
Let m(b) be the third derivative of b**8/504 - b**6/180 - 3*b**2 - 13. Factor m(k).
2*k**3*(k - 1)*(k + 1)/3
Let w(o) be the first derivative of -1/4*o**6 + 9/10*o**5 + 9/4*o**2 - 3/2*o + 5 - 3/4*o**4 - o**3. Factor w(q).
-3*(q - 1)**4*(q + 1)/2
Let g be (0 + 2 + -24)/((-30)/6). Let p(h) be the first derivative of -1 + h**6 - 2*h + g*h**5 + 7*h**4 - h**2 + 4*h**3. Factor p(o).
2*(o + 1)**4*(3*o - 1)
Let v(o) = -o**3 + o**2 + o. Let k be v(2). Let x be 4/8*-1*k. Factor -x - 3/2*f - 1/2*f**2.
-(f + 1)*(f + 2)/2
Suppose -3*z + 1 = -11. Suppose 0 = -w - z*o - 8, -w + 3 - 8 = 3*o. Let -2*j**w - 2*j**3 + 1 - 1 = 0. What is j?
-1, 0
Let d(a) = -10*a**2 + 15*a + 15. Let s(r) = -r**2 + r + 1. Let b(p) = 2*d(p) - 22*s(p). Factor b(z).
2*(z + 2)**2
What is b in 5*b - 10*b - 4*b + 12*b**4 - 2 + 19*b**3 = 0?
-1, -1/4, 2/3
Let q(n) = -n**3 + 2*n**2 + 15*n. Let t be q(5). Solve t*d**3 - 3/4*d - 3/2*d**2 + 3/4*d**5 + 0 + 3/2*d**4 = 0.
-1, 0, 1
Let -1/5*b**5 - 2/5*b**4 + 1/5*b + 0*b**3 + 2/5*b**2 + 0 = 0. What is b?
-1, 0, 1
Let h(n) = -n + 11. Let l(q) = -q**3 + 8*q**2 + q + 1. Let v be l(8). Let b be h(v). Solve -1 + 2 + w**b - 2 = 0.
-1, 1
Let d(x) be the first derivative of x**8/112 + x**7/70 - x**6/40 - x**5/20 - x**2 - 2. Let r(q) be the second derivative of d(q). Find z such that r(z) = 0.
-1, 0, 1
Let p be (-6)/2 - (-4 + 1)*1. Factor 0*u**2 + p - 2/3*u**3 + 0*u**4 + 1/3*u + 1/3*u**5.
u*(u - 1)**2*(u + 1)**2/3
Suppose -4 = y - 6. Let 1/2*s**3 - s**y - 1/2*s + 1 = 0. What is s?
-1, 1, 2
Let q(p) = 8*p**3 + 12 - 7*p - 10*p**2 + 0*p**4 - 2*p**4 - 5*p. Let k(n) = 5*n**4 - 17*n**3 + 21*n**2 + 25*n - 25. Let d(a) = -4*k(a) - 9*q(a). Factor d(h).
-2*(h - 1)**2*(h + 2)**2
Let o(r) be the third derivative of -r**5/360 - 5*r**4/144 - r**3/9 - 2*r**2. Suppose o(d) = 0. What is d?
-4, -1
Let v(g) = 0*g - 8*g - 3 - g**2 - 1 - g. Let w(k) = -8*k - 4. Let z(u) = -2*v(u) + 3*w(u). Let n(y) = y**2. Let j(x) = 4*n(x) - z(x). Factor j(r).
2*(r + 1)*(r + 2)
Let f(r) = -r + 3. Let w be f(3). Suppose -2*n - 3*n + 15 = w. Factor -2 - g**n + 2 - g**4.
-g**3*(g + 1)
Let h(l) be the third derivative of 0*l - 1/84*l**4 - 1/420*l**6 + 0*l**3 + 0 + 1/105*l**5 - l**2. Find g such that h(g) = 0.
0, 1
Let d = 1 - -3. Suppose 3*o + 5*r - 9 = 0, 2*o - 2*r = 4 + 2. Factor 2*w**o - d*w**3 + 2*w**5 + 0*w**3.
2*w**3*(w - 1)*(w + 1)
Let r(y) = -y**2 + y - 1. Let a(n) = -11*n**2 + 20*n + 7. Let w(t) = -a(t) - r(t). Determine d, given that w(d) = 0.
-1/4, 2
Let o = 124/483 + 2/69. Solve o*h**2 + 0 + 0*h = 0.
0
Let o = 55/18 - 26/9. Let t(x) be the second derivative of 1/42*x**7 + 0*x**4 + o*x**3 + 0*x**6 + 0*x**2 - 1/10*x**5 - x + 0. Determine h so that t(h) = 0.
-1, 0, 1
Let i(p) be the first derivative of -p**4/7 + 2*p**2/7 + 9. Factor i(l).
-4*l*(l - 1)*(l + 1)/7
Let u(c) = 9*c + 3. Let i be u(-4). Let g be i/(-18) - (-1)/6. Determine s so that -s**2 - s**4 + 2*s**3 + 0*s**2 + 5*s**g - 5*s**2 = 0.
0, 1
Let a(s) = -5*s + s**3 + 6*s + 6 + 0*s - 2*s**3 - 6*s**2. Let o be a(-6). Factor o - 2/7*y**2 - 2/7*y**4 + 0*y - 4/7*y**3.
-2*y**2*(y + 1)**2/7
Let h(w) = 2*w - 5. Suppose 5*n - 5*o - 10 = 0, 2*o - 24 = -4*n - 2*o. Let i be h(n). Factor 0*s**3 + 2*s**2 + s**i + s**3.
2*s**2*(s + 1)
Suppose -3*x = -12, -2*o - x - 9 - 3 = 0. Let r = -5 - o. Let 1/5*f**5 - 2/5*f**r + 1/5*f - 2/5*f**2 + 1/5*f**4 + 1/5 = 0. Calculate f.
-1, 1
Let n = 263/360 + 5/72. Let l(i) be the second derivative of 0 - i + n*i**2 + 4/15*i**3 + 1/30*i**4. Let l(g) = 0. What is g?
-2
Let f(h) be the first derivative of 9*h**6/2 + 54*h**5/5 - 99*h**4/4 - 26*h**3/3 + 38*h**2 - 24*h - 4. Factor f(o).
(o + 1)*(o + 3)*(3*o - 2)**3
Let a(f) be the third derivative of f**8/84 - 2*f**7/105 - f**6/10 + f**5/15 + f**4/3 - 21*f**2. Suppose a(o) = 0. What is o?
-1, 0, 1, 2
Let h(y) be the third derivative of 0 + 1/42*y**4 - 1/21*y**3 - 3*y**2 + 0*y - 1/210*y**5. Factor h(x).
-2*(x - 1)**2/7
Let j(b) be the first derivative of b**6/360 - b**5/60 + 4*b**3/3 + 2. Let v(n) be the third derivative of j(n). Solve v(c) = 0 for c.
0, 2
Let q(v) be the first derivative of v**8/5040 - v**7/2520 - v**6/1080 + v**5/360 - 2*v**3/3 - 2. Let g(n) be the third derivative of q(n). Factor g(f).
f*(f - 1)**2*(f + 1)/3
Let b(k) be the first derivative of -2*k**3/15 - 8. Find p such that b(p) = 0.
0
Let l = 27 + -19. Factor 1 + q**4 - l*q**3 - q**5 - q - 3*q**2 + 10*q**3 + q**2.
-(q - 1)**3*(q + 1)**2
Factor -4 - 2*g**3 + 11*g - 7*g + 3*g - g.
-2*(g - 1)**2*(g + 2)
Let v(t) be the first derivative of t**7/42 - t**5/20 - 6*t + 7. Let s(q) be the first derivative of v(q). Suppose s(w) = 0. Calculate w.
-1, 0, 1
Factor -16/7*q**3 + 4/7*q**4 + 0*q**2 - 64/7 + 64/7*q.
4*(q - 2)**3*(q + 2)/7
Suppose 0 = 4*s - s - 9. Solve -2*l - 15*l**s - 4*l + 22*l**2 - 7*l**2 + 3*l**3 + 3*l**4 = 0 for l.
0, 1, 2
Let v be 4/6*9/2. Let x be (-1)/v + 26/6. Suppose -d + x*d**2 - 2*d**2 - 2*d**4 + 2*d**3 - d = 0. Calculate d.
-1, 0, 1
Let w(s) = -s**5 + s**4 - s**3 - s**2 + s. Let m(b) = 5*b**5 - 5*b**4 + 2*b**3 + 2*b**2 - 2*b. Let i(o) = m(o) + 2*w(o). Find r, given that i(r) = 0.
0, 1
Let b(i) be the third derivative of 0*i - i**2 + 0*i**4 + 0*i**3 - 1/20*i**5 + 0. Suppose b(w) = 0. Calculate w.
0
Suppose 2 = -3*g + 11. Determine y, given that 2*y + 4 - g*y**2 + y**2 - 4*y = 0.
-2, 1
Let p be 6/((-108)/(-42)) + 2/(-6). Suppose 4/11*v + 0 - 2/11*v**p = 0. What is v?
0, 2
Let t be (-18)/(-12) - 4/(10 - 6). What is j in -j**4 + 0 + t*j**5 + j**2 + 0*j - 1/2*j**3 = 0?
-1, 0, 1, 2
Factor -z**3 + 1/3*z**4 + z**2 + 0 - 1/3*z.
z*(z - 1)**3/3
Let o(h) be the third derivative of -h**6/480 - h**5/120 - h**4/96 - 7*h**2. Factor o(t).
-t*(t + 1)**2/4
Let v be (38/(-14) - -3) + 0. Factor -2/7 - v*w**2 + 4/7*w.
-2*(w - 1)**2/7
Let l be (-2)/(-11) - (-70)/825. Let r(j) be the first derivative of 2 - 8/9*j**3 + l*j**5 - 1/3*j**4 + 1/9*j**6 + 4/3*j + 1/3*j**2. Let r(z) = 0. Calculate z.
-2, -1, 1
Factor -10/3*f - 4/3 - 8/3*f**2 - 2/3*f**3.
-2*(f + 1)**2*(f + 2)/3
Let d(v) = 2*v**4 + v**3 - v**2 - v - 1. Let u(l) = 10*l**4 + 7*l**3 - 7*l**2 - 7*l - 3. Let g(h) = -3*d(h) + u(h). Suppose g(o) = 0. Calculate o.
-1, 0, 1
Let t(l) be the first derivative of 0*l**2 + 1/60*l**5 + 0*l + 1/6*l**4 + 3 - 1/180*l**6 - 1/3*l**3. Let o(f) be the third derivative of t(f). Factor o(w).
-2*(w - 2)*(w + 1)
Factor -312 - 15*s**3 + 3*s**4 + 9*s**2 + 300 + 2*s + 13*s.
3*(s - 4)*(s - 1)**2*(s + 1)
Let p = -1067 - -1069. Suppose 1/2*k**p + 1 - 3/2*k = 0. What is k?
1, 2
Let u(q) = q**2 - 5*q + 7. Let i(m) = -2*m**2 + 16*m - 22. Let k(c) = -3*i(c) - 8*u(c). Factor k(t).
-2*(t - 1)*(t + 5)
Let r(t) = -64*t + t**3 - 19 - 5*t**2 - 44*t**2 - 2 - 11. Let y(p) = -12*p**2 - 16*p - 8. Let f(h) = -2*r(h) + 9*y(h). Let f(d) = 0. What is d?
-2, -1
Factor -2/5*f**3 + 2/5*f + 2/5*f**2 + 0 - 2/5*f**4.
-2*f*(f - 1)*(f + 1)**2/5
Factor 0 + 20/3*u**2 - 8/3*u + 4/3*u**5 - 4/3*u**4 - 4*u**3.
4*u*(u - 1)**3*(u + 2)/3
Let p(y) = y + 1. Let s(k) be the second derivative of -k**5/20 + k**4/4 - k**3/3 + k**2 + 3*k. Let h(a) = -p(a) + s(a). Find o such that h(o) = 0.
1
Let f(l) be the third derivative of -l**5/70 + l**4/21 + 4*l**3/21 - 20*l**2. Factor f(p).
-2*(p - 2)*(3*p + 2)/7
Suppose -1/3*v**2 