y**2 + 504*y**2 + 10*y**3 - 5*y.
-5*y*(y - 1)**2*(y + 1)**2
Let d be (78/(-156))/(30/(-80)). Let 0 - 8/3*x - d*x**2 = 0. What is x?
-2, 0
Let b(f) = 11*f**3 + 132*f**2 + 42*f. Let m(i) = 4*i**3 + 44*i**2 + 14*i. Suppose 3*p - 6 = -0. Let h(s) = p*b(s) - 7*m(s). Let h(w) = 0. Calculate w.
-7, -1/3, 0
Let k be (-8)/(-42)*825/550. Find m, given that 0 + k*m**2 - 2/7*m = 0.
0, 1
Let p(x) = -3*x**2 + 28*x - 7. Let k be p(9). What is i in 8 + 3*i**2 - i**k - 10*i + 2*i**2 + 2*i**3 - 4*i = 0?
-4, 1
Suppose -1175*p = -1179*p + 5*b - 23, -3*p = -2*b + 5. Let -2/3*o**p - 16*o + 32/3 + 6*o**2 = 0. What is o?
1, 4
Determine y so that -1/7*y**2 - 1/7*y**3 + 10/7*y - 8/7 = 0.
-4, 1, 2
Let x be ((-2)/(-3))/((-2)/6). Let t(d) = -d**2 - 1. Let p(v) = 69*v**2 - 59*v**2 + 6*v + 2941 - 2939. Let k(r) = x*p(r) - 22*t(r). Solve k(i) = 0 for i.
3
Suppose -3*z = t + 86, 3*t + 44 = -5*z - 106. Let u = z + 30. Factor -10/3*o**2 + 0 - 4/3*o + 2/3*o**4 + 2/3*o**5 - 2*o**u.
2*o*(o - 2)*(o + 1)**3/3
Let o(u) be the third derivative of -u**6/180 - u**5/9 + 11*u**4/36 + 2*u**2 - 113. Factor o(g).
-2*g*(g - 1)*(g + 11)/3
Let k = 5151/20 - 979/4. Determine u so that -64/5 - 64/5*u**4 - 34/5*u**3 + 236/5*u**2 - 2*u**5 - k*u = 0.
-4, -2/5, 1
Let x(q) be the third derivative of 0*q**3 + 0 + 1/840*q**8 + 3/100*q**6 + 0*q + 2/75*q**5 + 0*q**4 + 2/175*q**7 + 14*q**2. What is a in x(a) = 0?
-4, -1, 0
Let t(i) = i**2 - 3*i + 2. Let a(g) = -1 - g**2 + 2*g**2 - 42*g + 2 + 40*g. Let n(s) = 3*a(s) - 2*t(s). Factor n(y).
(y - 1)*(y + 1)
Let k(m) be the second derivative of 2*m**4/5 - 23*m**3/10 - 9*m**2/10 - m + 3. Solve k(a) = 0 for a.
-1/8, 3
Suppose -4*o + 16 = -4*s, 5*o + 2*s - 4*s = 14. Factor -4*d**o + 157 - 79 - 78 + 4*d**4 + 12*d - 12*d**3.
4*d*(d - 3)*(d - 1)*(d + 1)
Suppose -2*v = -2*m + 12, 3*m + 3*v = -13 - 5. Determine i, given that 0 + 6/7*i**2 + 6/7*i**3 + m*i = 0.
-1, 0
Determine m so that 6/7*m**3 - 2/7*m**5 - 4/7*m - 2/7*m**2 + 0 + 2/7*m**4 = 0.
-1, 0, 1, 2
Factor -13*i**3 + 4*i**3 - i**4 - 13*i**3 - 3*i**4 - 2*i**3.
-4*i**3*(i + 6)
Let b(p) = -12*p**3 - 405*p**2 - 19995*p. Let c(x) = 2*x**3 + x**2 - x. Let w(h) = b(h) + 5*c(h). Factor w(j).
-2*j*(j + 100)**2
Let -4/3*g**5 + 0*g**3 + 4/3*g**4 + 0*g + 0*g**2 + 0 = 0. What is g?
0, 1
Let v(r) be the second derivative of -17*r - 1/42*r**4 + 2/21*r**3 + 0 - 1/7*r**2. Suppose v(y) = 0. What is y?
1
Let i(y) = y**4 + y**2 - 1. Let d(m) = 5*m**3 - 15*m**2 + 1. Let n(v) = 5*d(v) + 5*i(v). What is s in n(s) = 0?
-7, 0, 2
Let z(m) be the third derivative of m**6/600 + m**5/25 + 2*m**4/5 + 5*m**3/3 + 4*m**2. Let w(u) be the first derivative of z(u). Find s such that w(s) = 0.
-4
Let y be (-27)/18*(0 + -2). Determine n, given that -5/6*n - 1/6*n**y - 1/3 - 2/3*n**2 = 0.
-2, -1
Let b(n) be the first derivative of -3/2*n**2 - 9*n + 22 - 1/12*n**3. Factor b(a).
-(a + 6)**2/4
Let j(k) be the third derivative of -k**5/15 - 3*k**4/8 + k**3/2 - 4*k**2. Let g(v) = 20*v**2 + 44*v - 16. Let d(s) = 3*g(s) + 16*j(s). Factor d(m).
-4*m*(m + 3)
Let n(y) = -y**2 - y. Let m(s) = 6*s**2 + 6*s - 4. Suppose -5*l + 14 = -3*l - 3*w, 4*w + 24 = 4*l. Let t(b) = l*n(b) + m(b). Find g, given that t(g) = 0.
-2, 1
Factor 135*a**2 + 48*a**3 + 132*a + 3/2*a**4 + 87/2.
3*(a + 1)**3*(a + 29)/2
Suppose 11734*p + 64 = 11766*p. Let 14/25*n**4 + 42/25*n**3 - 62/25*n**p - 8/25*n - 2/5*n**5 + 24/25 = 0. Calculate n.
-2, -3/5, 1, 2
Let g be 2/(-8)*((-17)/(-3) + -7). What is m in -1/3 + 2/3*m - g*m**2 = 0?
1
Let y(k) = 188*k + 2823. Let u be y(-15). Factor -21*i**u + 96 + 99/2*i**2 + 168*i + 3/2*i**4.
3*(i - 8)**2*(i + 1)**2/2
Let f(w) be the third derivative of -w**5/90 - w**4/2 - 17*w**3/9 + 173*w**2. Determine x so that f(x) = 0.
-17, -1
Let p(k) be the second derivative of k**6/60 + k**5/20 - 5*k**4/24 - k**3/2 - 202*k. Solve p(t) = 0.
-3, -1, 0, 2
Let b(k) be the third derivative of -k**8/420 - 2*k**7/105 + 9*k**3/2 + 8*k**2. Let m(j) be the first derivative of b(j). Factor m(x).
-4*x**3*(x + 4)
Let x(a) be the second derivative of -49*a**4/4 + 105*a**3 - 675*a**2/2 - 18*a + 1. Factor x(z).
-3*(7*z - 15)**2
Let i(r) = -4*r**3 - 28*r**2 - 71*r - 48. Let j(b) = -4*b**3 - 28*b**2 - 70*b - 48. Let a(k) = 6*i(k) - 7*j(k). Factor a(l).
4*(l + 2)**2*(l + 3)
Let t = 2711 - -745. Factor -864*c**2 + 2*c**3 - 4*c**4 + 80*c**3 - 5184 + t*c + 14*c**3.
-4*(c - 6)**4
Let p(g) be the third derivative of g**7/2100 - g**6/450 + g**5/300 - g**3/3 + 2*g**2. Let a(w) be the first derivative of p(w). Factor a(c).
2*c*(c - 1)**2/5
Let 3*z**3 + 76/5 + 301/5*z**2 + 308/5*z = 0. Calculate z.
-19, -2/3, -2/5
Factor 67*m + 1260*m**2 + 1252*m**2 - 2511*m**2.
m*(m + 67)
Suppose 0 = -d + 5*k - 9 - 2, 3*d - 4*k = 0. Let h(g) be the third derivative of 1/150*g**5 - 1/20*g**d + 2*g**2 + 2/15*g**3 + 0*g + 0. Factor h(q).
2*(q - 2)*(q - 1)/5
Let t(n) = -n**3 - 5*n**2 - 5*n + 6. Let f be t(-3). Factor 12*w**2 - 11*w**4 + 6*w**4 - 9 - 6*w**f + 6*w + 2*w**4.
-3*(w - 1)**2*(w + 1)*(w + 3)
Let j = 6 + -6. Suppose -3*n + j = 4*q - 2, -q = 1. Let 3*s**3 + 1 + 9*s**n - 6 - 3*s**4 - 1 - 3*s = 0. Calculate s.
-1, 1, 2
Let l(j) be the first derivative of j**4/22 - 8*j**3/33 + 3*j**2/11 + 178. Factor l(u).
2*u*(u - 3)*(u - 1)/11
Let v(n) = 10*n**3 + 14*n**2 - 24*n + 18. Let y(r) = 8*r**3 + 14*r**2 - 25*r + 18. Let d(l) = -5*v(l) + 6*y(l). Solve d(w) = 0 for w.
1, 3
Let p(u) = -20*u**2 + 110*u - 205. Let g(f) = -3*f**2 - f + 1. Let x(y) = 5*g(y) - p(y). Find k, given that x(k) = 0.
2, 21
Let f(v) be the first derivative of -3*v**4 - 25*v**3 - 57*v**2 - 24*v + 528. Factor f(z).
-3*(z + 2)*(z + 4)*(4*z + 1)
Let k(b) = b**2 + b - 7. Let m be k(-5). Let 11*n**2 - 5*n**2 + 9*n**2 + m*n**2 - 8*n = 0. Calculate n.
0, 2/7
Suppose -16 + 4 = -6*o. Factor 4*a**2 + o*a**2 - 8*a**2 - 2*a**3.
-2*a**2*(a + 1)
Let p be (0 - 5)/(-6 - (-21 + 16)). Factor 0*q - 1/3*q**2 + 0 + 1/3*q**3 + 1/3*q**4 - 1/3*q**p.
-q**2*(q - 1)**2*(q + 1)/3
Let w(r) = 26*r**3 + 113*r**2 + 63*r - 29. Let f(z) = -40*z**3 - 170*z**2 - 94*z + 44. Let x(b) = 5*f(b) + 8*w(b). Factor x(s).
2*(s + 1)*(s + 6)*(4*s - 1)
Let k(u) be the first derivative of 1/24*u**4 - 1/120*u**5 + 0*u**3 - 1/3*u**2 - 9 - 5*u. Let p(b) be the first derivative of k(b). Factor p(o).
-(o - 2)**2*(o + 1)/6
Let r(q) = q - 1. Let w(m) = -3*m**2 + 12*m - 9. Suppose 4*c = -0*s + 2*s + 38, 0 = -c + 4*s + 20. Suppose z = 7 + c. Let b(o) = z*r(o) - w(o). Solve b(i) = 0.
-2, 1
Let t be 1/(-2) + 35/(-30)*-3. Let i(o) be the first derivative of 0*o + 3*o**2 + 4/3*o**t + 4. Factor i(g).
2*g*(2*g + 3)
Let c be 1 - 4 - (45/18 + -7). Suppose f - 7 = -2*r, f + 7 = 4*r - 4*f. Factor 0*o**r - 3/4 + c*o**2 + 0*o - 3/4*o**4.
-3*(o - 1)**2*(o + 1)**2/4
Let f(v) be the first derivative of 5*v**4/4 - 20*v**3/3 - 30*v**2 - 267. Let f(g) = 0. Calculate g.
-2, 0, 6
Let r(h) be the third derivative of -h**7/70 - h**6/40 + h**5/20 + h**4/8 - 178*h**2. Factor r(a).
-3*a*(a - 1)*(a + 1)**2
Let u(l) be the first derivative of l**2/2 + 11*l + 7. Let z be u(17). Let -3*m**5 + 19*m**4 + 0*m**4 + m**4 - z*m**3 - m**5 + 12*m**2 = 0. What is m?
0, 1, 3
Let k(t) = -12*t**2 + 5*t + 25. Let x(c) = 3*c**2 - c - 6. Let m(w) = -2*k(w) - 9*x(w). Let o(s) = 10*s**2 + 4*s - 13. Let b(z) = 21*m(z) + 6*o(z). Factor b(l).
-3*(l - 2)*(l + 1)
Let h(l) be the third derivative of l**6/1380 - 2*l**5/345 + 5*l**4/276 - 2*l**3/69 - 514*l**2. Find t, given that h(t) = 0.
1, 2
Suppose -5*a = 9 - 19. Suppose 0 = -3*b - 2*x - x, -a*b - 3*x = 3. Find c such that -6*c**3 + 2*c**5 - 3 + 2*c**3 + 2*c + b = 0.
-1, 0, 1
Let l(a) be the third derivative of 0 - 1/2*a**4 + 0*a - 1/40*a**6 + 0*a**3 + 10*a**2 + 1/4*a**5. Find i, given that l(i) = 0.
0, 1, 4
Let p(x) = -12*x**3 - 20*x**2 - 56*x - 32. Let z(g) = 2*g**3 - 2*g**2 - g - 1. Let s(h) = -p(h) - 4*z(h). Factor s(u).
4*(u + 1)*(u + 3)**2
Let v = -13 - -17. Factor -29*h**4 + 4*h**5 - 3*h**3 + 29*h**v + 4*h - 5*h**3.
4*h*(h - 1)**2*(h + 1)**2
Let k(t) be the second derivative of t**10/181440 - t**9/90720 - 5*t**4/6 - 7*t. Let c(b) be the third derivative of k(b). Find w such that c(w) = 0.
0, 1
Suppose -29 = 3*i - 35. Suppose 13 = -0*g + 3*g - 4*k, -2*g - 2*k + 4 = 0. Let -i + 13*x - 10 + 35*x + 27*x**g - 63*x**2 = 0. Calculate x.
2/3, 1
Let o(n) = 29 - 61 + 33. Let d(c) = 5*c**2 + 35*c - 10. Let j