. Let h(t) = 4*t**3 + 4*t**2 - 4*t - 1. Let v(w) = x*h(w) - 3*o(w). Factor v(b).
-(b - 1)*(b + 1)**2
Suppose 0 = 2*m - 2*h + 10, 3*h = -2*h + 25. Let l(x) be the second derivative of -3*x + 0*x**3 + 1/36*x**4 + m - 1/6*x**2. Factor l(k).
(k - 1)*(k + 1)/3
Let f(q) = -2*q - 3*q**2 - 1 + 4*q**2 + q. Let z(v) = 7*v**2 - 6*v - 4. Let n(l) = 4*f(l) - z(l). Find r such that n(r) = 0.
0, 2/3
Let o(f) be the first derivative of f**7/210 + f**6/30 + f**5/15 + 2*f**3 + 5. Let i(z) be the third derivative of o(z). Factor i(q).
4*q*(q + 1)*(q + 2)
Let d(k) = 3*k**2 - 14*k - 5. Let v be d(5). Suppose v + 0*i - 1/4*i**2 = 0. What is i?
0
Let -3*k**2 + 1961 + 2*k - 1961 + k**3 = 0. Calculate k.
0, 1, 2
Factor -10/13*s**2 - 2/13*s**3 + 10/13 + 2/13*s.
-2*(s - 1)*(s + 1)*(s + 5)/13
Let z be 2/(-16)*(-6)/30. Let l(r) be the second derivative of -1/24*r**4 + 1/4*r**2 - 4*r - 1/12*r**3 + 0 + z*r**5. Factor l(g).
(g - 1)**2*(g + 1)/2
Let w(k) be the second derivative of 2*k**7/21 + 2*k**6/5 + 3*k**5/5 + k**4/3 - 5*k. Determine p, given that w(p) = 0.
-1, 0
Let o(i) be the second derivative of i**6/10 - 3*i**5/10 - 2*i. What is z in o(z) = 0?
0, 2
Let z(d) be the second derivative of -d**7/42 + d**6/5 - 3*d**5/5 + 5*d**4/6 - d**3/2 + 2*d. Let z(t) = 0. What is t?
0, 1, 3
Let x(p) be the third derivative of -p**5/300 - p**4/40 - p**3/15 + 2*p**2. Find y, given that x(y) = 0.
-2, -1
Let y = 266 - 264. Factor 4/7 + 2/7*q**y + 6/7*q.
2*(q + 1)*(q + 2)/7
Let r = 141 + -138. Factor 1/3*n**2 - 1/3*n**r - 1/3*n**4 + 0 + 1/3*n.
-n*(n - 1)*(n + 1)**2/3
Factor 4/7*y**2 + 8/7*y + 0.
4*y*(y + 2)/7
Let f = 10 + -6. Factor 1/5*r**f + 1/5*r**3 - 1/5*r**2 - 1/5*r + 0.
r*(r - 1)*(r + 1)**2/5
Let o = -79 - -127. Suppose y + 4*r + 56 = 5*y, -3*y = 4*r - 42. Factor -8*s - 6 - 25*s + y*s**3 - o*s**2 - 16*s**3 - 19*s**3.
-3*(s + 1)**2*(7*s + 2)
Factor 2*z**4 - 2*z**4 + 0*z - 3*z + 3*z**4 - 3*z**2 + 3*z**3.
3*z*(z - 1)*(z + 1)**2
Let q(i) = -3*i**3 - 6*i**2 - 3*i - 2. Let t(c) = -c**4 - c**3 - c + 1. Let h be (1 + 0)*2/(-2). Let r(s) = h*t(s) - q(s). What is b in r(b) = 0?
-1
Let w(j) be the first derivative of j**6/1260 - j**3/3 - 3. Let n(r) be the third derivative of w(r). Factor n(z).
2*z**2/7
Factor -o**3 + 10*o**2 - 6*o**3 - o**3 + 8 - 16*o + 6*o**3.
-2*(o - 2)**2*(o - 1)
Let u(b) = b**2 - 5*b - 4. Let h be u(6). Let s(l) be the third derivative of 1/30*l**5 + 1/12*l**4 + l**h + 0*l**3 + 0*l + 0. Factor s(k).
2*k*(k + 1)
Let h(l) be the second derivative of -l**9/37800 + l**7/3150 - l**5/300 - l**4/6 - 2*l. Let b(s) be the third derivative of h(s). What is w in b(w) = 0?
-1, 1
Let d = 958/553 - 24/79. Determine s, given that d*s**3 - 10/7*s - 4/7 - 2/7*s**2 + 6/7*s**4 = 0.
-1, -2/3, 1
Let n(g) = g**2 - g + 1. Let y be n(1). Let r be -3*((-2)/3)/y. What is l in 3*l**2 - 2 + 2*l - 2*l**2 + l**r - 2*l**3 = 0?
-1, 1
Factor -2/7 + 8/7*d**2 + 6/7*d.
2*(d + 1)*(4*d - 1)/7
Let h(k) be the third derivative of -k**8/2520 - 2*k**7/1575 + k**6/75 - 7*k**5/225 + k**4/36 + 6*k**2. Solve h(f) = 0 for f.
-5, 0, 1
Let p be (-1)/(-2) - 15/(-10). Find x, given that 6*x + 4*x**2 + 2 - 2*x**p - 4*x + 2*x = 0.
-1
Let w(k) be the third derivative of 0 - 5/9*k**4 + 0*k + 8/9*k**3 + 1/5*k**5 + 3*k**2 + 1/315*k**7 - 7/180*k**6. Factor w(l).
2*(l - 2)**3*(l - 1)/3
Suppose 5 = -4*a + 17. Factor -6*z**2 - 2*z**4 - z**3 + 2*z + 0*z**4 - 5*z**a - 4*z.
-2*z*(z + 1)**3
Let m(n) be the second derivative of -n**6/180 - n**5/30 - n**4/18 + 3*n**2/2 - 2*n. Let c(w) be the first derivative of m(w). Factor c(u).
-2*u*(u + 1)*(u + 2)/3
Let 15/7*f**3 - 6/7*f - 6/7*f**4 + 0 - 3/7*f**2 = 0. What is f?
-1/2, 0, 1, 2
Let h = 1/36 + 13/18. Let n(p) be the first derivative of 3 + 0*p - 12/35*p**5 - h*p**4 + 3/14*p**2 - 2/7*p**3. Factor n(a).
-3*a*(a + 1)**2*(4*a - 1)/7
Suppose 0 = -2*t + 20 - 30. Let z be t/(-9) + 6/(-27). Factor -1/3 + 0*q + z*q**2.
(q - 1)*(q + 1)/3
Let j(t) = -3*t**2 + 24*t - 21. Let p(x) = -3*x**2 + 25*x - 22. Let g(i) = -4*j(i) + 3*p(i). Factor g(z).
3*(z - 6)*(z - 1)
Let c(m) = 34*m + 10. Let t be c(-5). Let i be (-5)/(-2)*(-16)/t. What is k in 0*k + 1/4*k**2 + 1/4*k**3 + 0 - 1/4*k**5 - i*k**4 = 0?
-1, 0, 1
Factor 3 + 953*z - 967*z - 2*z**3 + 10*z**2 + 3.
-2*(z - 3)*(z - 1)**2
Suppose -2*k = -c + 5*c - 46, -c = 3*k - 79. Factor -3*r**4 - k*r**2 - 4 + 1 - 12*r**3 - 12*r + 9*r**2.
-3*(r + 1)**4
Let r be 2/(-1) + -9 + 8. Let u be -3 + (1 - r) - -1. Determine g so that 4/5 - 2/5*g**u - 2/5*g = 0.
-2, 1
Let k(n) = -2*n**2 + 5*n - 3. Let z(t) be the second derivative of 1/6*t**4 + 0 - t - t**3 + 2*t**2. Let d(f) = 6*k(f) + 4*z(f). Factor d(i).
-2*(i - 1)*(2*i - 1)
Let a(m) be the second derivative of m**5/30 - m**4/6 - m**3/9 + m**2 - 3*m. Factor a(i).
2*(i - 3)*(i - 1)*(i + 1)/3
Let w = -39 + 41. Let a(u) be the first derivative of 1/20*u**4 - 3 + 1/2*u**w - 4/15*u**3 - 2/5*u. Factor a(r).
(r - 2)*(r - 1)**2/5
Let g(k) be the third derivative of k**5/20 + k**4/8 - k**3 - 29*k**2. Suppose g(i) = 0. Calculate i.
-2, 1
Let z(n) be the first derivative of n**6/9 - 4*n**5/15 - n**4/2 + 8*n**3/9 + 4*n**2/3 - 73. Factor z(j).
2*j*(j - 2)**2*(j + 1)**2/3
Let x be (0 + 3/(-15))*(-3)/6. Let n(s) be the second derivative of 1/15*s**6 + 1/3*s**3 - 1/6*s**4 - 2*s + 0*s**2 + 0 - x*s**5. Factor n(u).
2*u*(u - 1)**2*(u + 1)
Let c(h) = 24*h - 20. Let u(o) = o**2 - o + 1. Let l(d) = c(d) - 4*u(d). Determine x so that l(x) = 0.
1, 6
Let u(n) be the third derivative of -n**5/90 + 2*n**4/9 - 7*n**3/9 + 11*n**2. Determine r, given that u(r) = 0.
1, 7
Let z(i) = i**3 + 3*i**2 - 5*i - 2. Let b be z(-4). Suppose 3*x = -q - b + 3, 3*q - 16 = 4*x. Factor -q*r**2 + 8/3*r - 2/3 - 2/3*r**4 + 8/3*r**3.
-2*(r - 1)**4/3
Suppose -5 = 2*j + 5*x, 3*x + 1 = 5*j - 2. Suppose 5*p + 6*o = 4*o + 15, j = -2*o. Find n, given that 0*n**2 - 1/2*n + 1/2*n**p + 0 = 0.
-1, 0, 1
Solve -4*b**2 + 4/5*b**3 - 16/5 + 32/5*b = 0.
1, 2
Suppose -p - 100 = -3*p. Let a be 2/10*p/15. Suppose 1/3*o**2 + o + a = 0. Calculate o.
-2, -1
Factor -9/7 + 5/7*f**2 + 3/7*f + 1/7*f**3.
(f - 1)*(f + 3)**2/7
Let k(h) be the third derivative of 0*h**4 - 1/224*h**8 + 1/140*h**7 + 0 + 0*h - 1/40*h**5 - 4*h**2 + 1/80*h**6 + 0*h**3. Solve k(c) = 0 for c.
-1, 0, 1
Suppose 2*o - o + 12 = 0. Let z be 95/60 - o/16. Determine q so that -z*q**2 - 5/3*q**3 + 0 - 2/3*q = 0.
-1, -2/5, 0
Let t(j) be the first derivative of -4/3*j**3 + 3/2*j**2 + 4*j + 2. Let y(r) = 5*r**2 - 4*r - 5. Let v(b) = -4*t(b) - 3*y(b). Factor v(o).
(o - 1)*(o + 1)
Let u(k) be the second derivative of k**6/60 - 17*k**4/24 - 3*k**3 - 5*k**2 - k + 16. Solve u(m) = 0 for m.
-2, -1, 5
Let k(c) = c**2 + 9*c + 8. Let z be k(-9). Let -3 + 6*b + z*b**3 + 2*b - 12*b**2 + 1 - 2*b**4 = 0. Calculate b.
1
Let y(w) = -w**3 + 2*w**2 + 4*w - 2. Let i(t) = 6*t**3 - 11*t**2 - 23*t + 11. Let h(c) = -6*i(c) - 34*y(c). Factor h(v).
-2*(v - 1)*(v + 1)**2
Let q = -19 - -29. Suppose -2*x - q = -7*x. Suppose -x*i**3 - i + 4*i**3 + 2*i**5 - 3*i**5 = 0. What is i?
-1, 0, 1
Suppose -2*b + 2*n = -16, b + 4*n = 2 - 19. Factor 25 - 25 - h**2 + h**b.
h**2*(h - 1)
Let q = 35 + -17. Determine t so that -q*t**5 - 16/3*t**2 - 36*t**4 + 0*t + 0 - 24*t**3 = 0.
-2/3, 0
Let n be 4 + (0/1)/2. Find c such that 0 - 2*c**3 + 0*c - 8/3*c**n + 2/3*c**2 = 0.
-1, 0, 1/4
Suppose 0 = -5*c + c. Factor w**5 - 3*w**3 + c*w**3 + w + w**3.
w*(w - 1)**2*(w + 1)**2
Factor 0 + 6/7*x**4 - 13/7*x**3 + 12/7*x**2 - 1/7*x**5 - 4/7*x.
-x*(x - 2)**2*(x - 1)**2/7
Let u(h) be the first derivative of h**3/4 - 3*h + 11. Factor u(s).
3*(s - 2)*(s + 2)/4
Let v(s) be the third derivative of -1/540*s**6 - 1/135*s**5 + 0 + 0*s - 1/108*s**4 + 0*s**3 - 3*s**2. Factor v(d).
-2*d*(d + 1)**2/9
Let n(p) = -p + 3. Let l be n(7). Let g = -2 - l. Factor 0 - 2*h - 6*h**g + 0*h + 5*h**2 - 1.
-(h + 1)**2
Suppose 0 = -k - 3 + 5. Factor 0*g - 2*g**k - 2*g + 3*g**2 + g**2.
2*g*(g - 1)
Let a = 62 + -184/3. Determine n, given that a + 1/3*n**2 - n = 0.
1, 2
Let d(t) be the third derivative of -t**6/220 + t**5/165 + t**4/11 - 8*t**3/33 - t**2. Solve d(n) = 0.
-2, 2/3, 2
Let j be 3 + 2 - (6 + -3). Let w(l) be the third derivative of -1/12*l**4 + 0*l - 2/3*l**3 - l**j + 1/10*l**5 + 0 - 1/105*l**7 + 1/60*l**6. Factor w(p).
-2*(p - 2)*(p - 1)*(p + 1)**2
Let u = -203 + 1829/9. Let c(h) be the first derivative of 