, -1, 1
Factor 3*q + 0 - 8/3*q**2 - 1/3*q**3.
-q*(q - 1)*(q + 9)/3
Let -7/3*y**3 - 1/3*y**4 + 1/3*y**2 + 2*y + 1/3*y**5 + 0 = 0. What is y?
-2, -1, 0, 1, 3
Let l = 31 + -26. Let t(p) = 8*p**3 - 6*p**2 - 8*p + 11. Let i(c) = 15*c**3 - 12*c**2 - 15*c + 21. Let m(j) = l*i(j) - 9*t(j). Factor m(b).
3*(b - 2)*(b - 1)*(b + 1)
Suppose 18 = 5*m + 2*p, -5*p + 10 = -m - 4*m. Suppose g**2 + 3*g**2 + 4*g**m - 4*g + 7*g**3 - 11*g**3 = 0. What is g?
0, 1
Let t(n) be the third derivative of n**8/84 - 8*n**7/105 + 14*n**5/15 - 17*n**4/6 + 4*n**3 - 188*n**2. Factor t(f).
4*(f - 3)*(f - 1)**3*(f + 2)
Let s(n) = 2*n + 42. Let q be s(-20). Find w, given that -13*w**2 + 5*w**q + 16*w + 19*w + 30 - 7*w**2 = 0.
-2/3, 3
Let o(v) be the first derivative of v**3/7 - 3*v**2/2 - 180*v/7 - 834. Factor o(y).
3*(y - 12)*(y + 5)/7
Factor 66/7*j**2 + 2/7*j**4 - 22/7*j**3 - 100/7 - 10/7*j.
2*(j - 5)**2*(j - 2)*(j + 1)/7
Factor 8/3 - 2*w**2 + 0*w**3 - 8/9*w + 2/9*w**4.
2*(w - 3)*(w - 1)*(w + 2)**2/9
Determine i so that 4*i + 36/5 + 1/5*i**2 = 0.
-18, -2
Let t(f) be the third derivative of -1/840*f**8 + 0*f**4 - 1/525*f**7 + 1/150*f**5 + 0 + 0*f + 3*f**2 + 1/300*f**6 + 0*f**3. Factor t(m).
-2*m**2*(m - 1)*(m + 1)**2/5
Let h(s) be the first derivative of -1/4*s**4 + 19 + 0*s**2 + s**3 + 0*s. Let h(r) = 0. Calculate r.
0, 3
What is a in -80/7*a + 12/7 + 160/7*a**3 + 68/7*a**2 = 0?
-1, 1/5, 3/8
Let l(t) = -t**4 - t**3 + 1. Let k(p) = 16*p**4 + 24*p**3 + 8*p**2 - 12. Let q be 0*(1 + -2) - -1. Let m(u) = q*k(u) + 12*l(u). Suppose m(i) = 0. What is i?
-2, -1, 0
Let k = -209 + 209. Determine y so that k + 1/3*y**2 - 1/3*y**5 + 1/3*y**3 + 0*y - 1/3*y**4 = 0.
-1, 0, 1
Let i(z) be the second derivative of 17*z + 3/4*z**2 + 0 + 1/2*z**3 + 1/8*z**4. Factor i(x).
3*(x + 1)**2/2
Let g(o) = 5*o**4 - 158*o**3 + 6721*o**2 - 12964*o + 6420. Let z(m) = -4*m**4 + 159*m**3 - 6721*m**2 + 12963*m - 6415. Let j(x) = -3*g(x) - 4*z(x). Factor j(t).
(t - 80)**2*(t - 1)**2
Factor 20*s + 159*s**2 + 6*s - 6*s**3 + 15*s**3 + 52*s - 3*s**3.
3*s*(s + 26)*(2*s + 1)
Let v(z) be the second derivative of -z**4/138 - 20*z**3/69 - 90*z. Suppose v(k) = 0. What is k?
-20, 0
Let s(i) be the second derivative of -i**4/12 - i**3 - 9*i**2/2 - 89*i + 2. Find h such that s(h) = 0.
-3
Let r(z) be the third derivative of -1/12*z**5 + 0*z - 5/24*z**6 + 0*z**3 - 1/21*z**7 - 15*z**2 + 5/12*z**4 + 0. Factor r(x).
-5*x*(x + 1)*(x + 2)*(2*x - 1)
Suppose w + 81 = 4*w. Let -w*x**2 + x**4 + x**3 + 0*x**4 + 25*x**2 = 0. What is x?
-2, 0, 1
Determine w, given that -1/3*w**4 + 10*w - 10*w**3 + 75 - 224/3*w**2 = 0.
-15, -1, 1
Let g = 31 + -15. Factor -8*m**3 + 18*m**2 - 38*m**2 - 32*m + 4*m**3 - g.
-4*(m + 1)*(m + 2)**2
Find u, given that u + 3*u**3 - 2*u**2 + u**3 - 7*u**5 + 1 - 6*u**3 + 8*u**5 + u**4 = 0.
-1, 1
Let h be -16 + -3 + 8 + -1. Let m be (h/8 - 0)/(6*-1). Factor 1/4*o**4 + 0 - 1/4*o**2 - 1/4*o + m*o**3.
o*(o - 1)*(o + 1)**2/4
Let w be (-26)/(-3) + 170/51. Suppose -8*z + 18/5*z**4 + 74/5*z**2 + 8/5 - w*z**3 = 0. What is z?
2/3, 1
Let g(s) = -14*s + 142. Let c be g(10). Let f(h) be the first derivative of 12/5*h**5 + 3/2*h**c - 3 - 4*h**3 - 3/4*h**4 + 0*h. Factor f(m).
3*m*(m - 1)*(m + 1)*(4*m - 1)
Let n(d) = -33*d**3 - 36*d**2 + 21*d - 13. Let i(q) = -8*q**3 - 9*q**2 + 5*q - 3. Let o(r) = 26*i(r) - 6*n(r). Determine v so that o(v) = 0.
-2, 0, 1/5
Let j(a) = 9*a**3 - 15*a**2 + 54*a. Let z(s) = -27*s - 3*s**2 + s**3 + 21*s + 17*s + s**3. Let n(p) = -5*j(p) + 24*z(p). Factor n(c).
3*c*(c - 1)*(c + 2)
Suppose -3*a - 12 = -0*a. Let b be 32/(-280)*10/a. Factor 0 + b*z**2 + 8/7*z.
2*z*(z + 4)/7
Let u(s) = s**2 - 49*s + 393. Let d be u(10). Factor 0 + 5/4*w**4 + 5/2*w**2 + 15/4*w**d + 0*w.
5*w**2*(w + 1)*(w + 2)/4
Let c(u) = -109*u + 2616. Let i be c(24). Factor 0 + i*l + 2/9*l**2.
2*l**2/9
Let a(o) be the third derivative of o**7/210 - 11*o**6/120 + 3*o**5/20 + 119*o**4/24 + 49*o**3/3 - 39*o**2. Solve a(r) = 0 for r.
-2, -1, 7
Let t(o) be the third derivative of o**5/270 - o**4/27 - 5*o**3/27 - 200*o**2 - 2*o. Factor t(l).
2*(l - 5)*(l + 1)/9
Let c(p) = -p - 4. Let i be c(0). Let f be ((-21)/(-14))/((-2)/i). Determine k, given that 3/5*k + 2/5 - 1/5*k**f + 0*k**2 = 0.
-1, 2
Let v(f) be the first derivative of -f**5/20 - 7*f**4/48 - f**3/12 + f**2/8 + 4*f - 4. Let y(n) be the first derivative of v(n). Suppose y(o) = 0. What is o?
-1, 1/4
Let i(a) = -2*a**3 - 74*a**2 - 9*a + 63. Let z(m) = m**3 + 25*m**2 + 3*m - 21. Let b(o) = -4*i(o) - 11*z(o). Factor b(q).
-3*(q - 7)*(q - 1)*(q + 1)
Let n(c) be the third derivative of -41*c**6/40 + 39*c**5/20 + 21*c**4/2 + 2*c**3 + 149*c**2. Suppose n(g) = 0. Calculate g.
-1, -2/41, 2
Suppose -c + 179 - 177 = 0. Let j be (6/(-15)*c)/(2/(-5)). Solve -j - 2/3*y**2 + 8/3*y = 0.
1, 3
Find k, given that -1/3*k + 1/3*k**4 + 4 - 13/3*k**2 + 1/3*k**3 = 0.
-4, -1, 1, 3
Let d = 10751/15 + -2149/3. Let d*c - 4/5*c**2 + 2/5 = 0. What is c?
-1/2, 1
Let c(g) be the second derivative of 27*g**5/20 + 113*g**4/4 - 232*g**3/9 + 26*g**2/3 + g + 105. Factor c(f).
(f + 13)*(9*f - 2)**2/3
Factor -1/4*f**4 - 225 - 181/4*f**2 - 11/2*f**3 - 165*f.
-(f + 5)**2*(f + 6)**2/4
Let b(r) be the first derivative of 12*r**5/25 - 32*r**4/5 + 356*r**3/15 - 176*r**2/5 + 112*r/5 - 702. Let b(i) = 0. What is i?
2/3, 1, 2, 7
Let w = 3541 - 3541. Factor 10/13*z**3 + 2/13*z**4 + 14/13*z**2 + w + 6/13*z.
2*z*(z + 1)**2*(z + 3)/13
Let n(r) = -40*r**2 - 25*r + 80. Let o(q) = -3*q**2 + q. Let k(m) = -n(m) + 15*o(m). Factor k(c).
-5*(c - 4)**2
Let l(n) be the second derivative of -n**4/90 - 64*n**3/45 - 21*n**2/5 - 285*n. Factor l(c).
-2*(c + 1)*(c + 63)/15
Factor -10*m - 368*m**2 + 48*m + 371*m**2 + 29*m + 29*m.
3*m*(m + 32)
Let v(p) be the third derivative of 3*p**2 - 5/3*p**4 + 0 + 0*p + 1/12*p**5 + 40/3*p**3. Suppose v(n) = 0. What is n?
4
Suppose 2*n = 8*n - 54. Let i be (n/(-6))/(3/(-6)). Factor 0*u**2 + 26 - 17 - 6*u - i*u**2.
-3*(u - 1)*(u + 3)
Let t(f) = 2*f**3 + 3*f**2 - 20*f. Let u(x) = 5*x**3 + 10*x**2 - 60*x. Let a(d) = -10*t(d) + 3*u(d). What is o in a(o) = 0?
-2, 0, 2
Let s = -61 + 64. Factor -35 + 102*x + 23*x**3 + 8*x - 120*x**2 - 5*x**4 + 27*x**s.
-5*(x - 7)*(x - 1)**3
Let o(z) be the third derivative of z**8/252 + 4*z**7/21 + 157*z**6/45 + 132*z**5/5 - 27*z**4/2 - 1620*z**3 - 644*z**2. Solve o(m) = 0.
-9, -5, 2
Let w(c) = -221*c**3 + c**2 - 2*c - 1. Let n be w(-1). Determine p, given that -68*p**3 - 26*p**3 + 48*p**4 + 68*p**2 - 122*p**3 + n*p**2 - 108*p + 12 = 0.
1/4, 2
Let x(g) be the second derivative of -g**7/168 + 3*g**6/40 - 13*g**5/40 + 3*g**4/8 + 9*g**3/8 - 27*g**2/8 + 8*g + 2. Factor x(m).
-(m - 3)**3*(m - 1)*(m + 1)/4
Let f(v) be the third derivative of 1/3*v**3 - 1/60*v**5 - 1/24*v**4 + 0 + 0*v + v**2. Suppose f(j) = 0. Calculate j.
-2, 1
Let v(p) be the third derivative of p**5/24 - 85*p**4/36 - 115*p**3/36 - 194*p**2 - 2. Factor v(i).
5*(i - 23)*(3*i + 1)/6
Let n = 23 - 20. Suppose 4*b = 6*v - n*v + 14, 14 = 2*b - 5*v. Factor 0 - b*g**2 + 4 + 2 + 4*g.
-2*(g - 3)*(g + 1)
Suppose -2*r - 4*c + 9 = -5*c, c = -1. What is g in g**r - 2 + 5*g**2 + 2 - 6*g**4 = 0?
-1, 0, 1
Let x = 0 - -4. Factor -s**2 - 4*s**4 - 8*s**2 + 5*s**x + 2*s**4 + 6*s**3.
3*s**2*(s - 1)*(s + 3)
Let z = 1/274 - -119/4932. Let r(q) be the third derivative of 1/180*q**6 + 0 - z*q**4 + 0*q + 1/315*q**7 - 1/30*q**5 + 2/9*q**3 + 4*q**2. Factor r(s).
2*(s - 1)**2*(s + 1)*(s + 2)/3
Let s be 2 + 1 - (3 - 3). Suppose s*m + d - 11 = 0, m - d - 1 = -0*d. Factor 2*b**m + 1/2*b + 0 - 5/2*b**2.
b*(b - 1)*(4*b - 1)/2
Let a(l) = -44*l**3 - l**2 - l. Let y be a(-1). Suppose -3*c + 7*c = d + 179, 0 = -5*c + d + 223. Determine b so that 5*b**2 - 4*b**2 - y + c - 2*b**3 + b = 0.
-1/2, 0, 1
Let x(v) = -v**5 + v**4 + v**2 - v. Let w(j) = 4*j**5 + 2*j**4 - 8*j**3 - 6*j**2 + 6*j. Let g(q) = -w(q) - 6*x(q). Let g(n) = 0. Calculate n.
0, 2
Let o(v) = 148*v**2. Let t be o(-1). Let f = 1038/7 - t. Factor -4/7*s**2 + 0 + 0*s - f*s**3.
-2*s**2*(s + 2)/7
Let c = 8 - 6. Suppose -12 = -4*w + 4. Solve x - 5*x**3 - c*x**2 + 4*x**3 + x**w + x**2 = 0.
-1, 0, 1
Let b(o) be the third derivative of -o**10/37800 + o**9/7560 - o**8/5040 + 14*o**5/15 - 27*o**2. Let n(r) be the third derivative of b(r). Solve n(s) = 0 for s.
0, 1
Let o be -1 + 2 + 0 - (-6834)/12366. Let f = o + 2/687. Find