t - 15. Let b(c) = a(c) + 18*k(c). Let q(g) = -7*g**2 - g - 7. Let i(w) = 15*b(w) + 6*q(w). Factor i(x).
3*(x - 1)**2
Suppose 5*u = -15 - 0. Let y = u + 5. Let -3*z**2 - 2*z**y + 0*z**3 + 4*z**2 + 1 - z**3 + z = 0. What is z?
-1, 1
Let f(a) be the second derivative of 2/9*a**3 + 5*a + 0 + 1/18*a**4 + 1/9*a**6 + 0*a**2 - 4/15*a**5. Let f(b) = 0. Calculate b.
-2/5, 0, 1
Let i = 161/228 - 3/76. Let j = -65/3 - -22. Determine p so that j*p**2 + 1/3 - i*p = 0.
1
Let g(u) be the third derivative of -u**9/181440 + u**8/12096 - u**7/1890 + u**6/540 + u**5/20 + 2*u**2. Let h(k) be the third derivative of g(k). Factor h(z).
-(z - 2)**2*(z - 1)/3
Let c(p) = 18*p**4 - 18*p**3 - 9*p**2 + 3*p + 3. Let q(z) = -53*z**3 + 8*z + 55*z**4 + 0 - 26*z**2 + 5 + 3. Let s(y) = -8*c(y) + 3*q(y). Factor s(x).
3*x**2*(x - 1)*(7*x + 2)
Suppose 17 = 4*n - v, -n + 4 = -2*v - 2. Factor 3*j**4 + n*j**5 - 3*j**5 + 0*j**4 - 2*j**5 + j**2 - 3*j**3.
-j**2*(j - 1)**3
Let t = -96 - -98. Suppose -1/4*v**3 - 1/4*v + 0 - 1/2*v**t = 0. What is v?
-1, 0
Determine w so that 0 + 2/5*w**2 + 4/5*w = 0.
-2, 0
Let n(o) be the third derivative of 5*o**8/336 - 2*o**7/21 + o**6/4 - o**5/3 + 5*o**4/24 - 7*o**2. Determine d so that n(d) = 0.
0, 1
Let m(d) = -13*d - 6. Let h be m(-3). Factor 21*n**2 - 6 + 3*n**3 - h*n**2 + 19*n - 4*n.
3*(n - 2)*(n - 1)**2
Let n be 4/14 + 36/21. Factor 0 + 1/3*t + 1/3*t**n.
t*(t + 1)/3
Let j(w) be the second derivative of w**5/6 - 11*w**4/12 + 2*w**3/3 - 3*w**2/2 + 4*w. Let o(v) be the first derivative of j(v). Solve o(g) = 0 for g.
1/5, 2
Let c(n) be the second derivative of n**5/120 - 5*n**4/72 + 2*n**3/9 - n**2/3 + 24*n. Factor c(p).
(p - 2)**2*(p - 1)/6
Let y(m) be the first derivative of -2*m**3/15 + 2*m**2/5 - 2*m/5 + 17. Factor y(d).
-2*(d - 1)**2/5
Let s(h) be the first derivative of -h**6/2 - 9*h**5/5 - 9*h**4/4 - h**3 + 8. Suppose s(r) = 0. Calculate r.
-1, 0
Let q = 9 + -7. Suppose -q*r + 0*r + 4 = 0. Determine m, given that m**4 + m**3 + 0*m + 1/3*m**r + 0 + 1/3*m**5 = 0.
-1, 0
Suppose 4 = 4*q - s - 12, 4*s + 4 = -4*q. Let w = 14 - 12. What is u in 2*u + u**q + u**w + u**2 - u = 0?
-1, 0
Find b, given that 3/5*b**3 - 3/5*b + 0*b**2 + 0 = 0.
-1, 0, 1
Let s(q) be the third derivative of -3*q**5/25 + q**4/120 + q**3/15 + 5*q**2. Determine g, given that s(g) = 0.
-2/9, 1/4
Let x(c) be the second derivative of -c**5/110 + c**4/66 + c**3/33 - c**2/11 - 4*c. Let x(a) = 0. What is a?
-1, 1
Let w = 2 + -2. Suppose -4*g + 3*g**2 + w*g + 3 - g - g = 0. What is g?
1
Let s(v) be the third derivative of v**5/60 - v**4/4 + 3*v**3/2 - 2*v**2. Factor s(q).
(q - 3)**2
Let p(g) be the third derivative of -g**8/420 - 2*g**7/525 + g**6/75 - 19*g**2. Factor p(s).
-4*s**3*(s - 1)*(s + 2)/5
Let l(o) be the third derivative of -o**5/420 - o**4/28 - 4*o**3/21 - 15*o**2. Solve l(m) = 0 for m.
-4, -2
Let d(u) be the third derivative of u**6/1800 - u**5/600 + u**3/2 - u**2. Let x(w) be the first derivative of d(w). Factor x(y).
y*(y - 1)/5
Suppose 220 = 2*r - 7*r. Let y = 46 + r. Determine m so that -m**4 + 1/3 + 2/3*m**y - m + 2/3*m**3 + 1/3*m**5 = 0.
-1, 1
Let f(t) be the first derivative of -t**3/5 + 27*t/5 + 12. Suppose f(z) = 0. Calculate z.
-3, 3
Factor -g**2 - 2*g**4 - g**3 + g**3 + 2*g**3 + g**4.
-g**2*(g - 1)**2
Suppose 0 = 34*i - 29*i - 5. Let a(q) be the first derivative of 1/2*q**2 + 0*q**3 - 2/3*q - i - 1/12*q**4. Factor a(x).
-(x - 1)**2*(x + 2)/3
Suppose -2*o + 16 = 3*b + 3, 0 = -2*o - 8. Let r = 9 - b. Solve -1/4*u**4 + 1/4*u + 0 - 1/4*u**3 + 1/4*u**r = 0 for u.
-1, 0, 1
Let o(s) be the third derivative of s**8/1344 - s**7/420 + s**5/120 - s**4/96 + 6*s**2. Find z, given that o(z) = 0.
-1, 0, 1
Let y be (-438)/130 + 5 + -2. Let g = 2/65 - y. Factor -g*k**5 - 2/5*k**2 - 6/5*k**4 + 0 + 0*k - 6/5*k**3.
-2*k**2*(k + 1)**3/5
Let y(n) = -8*n**2 - 2*n - 2. Let j(u) = -24*u**2 - 7*u - 6. Let k be 15/(-6)*(-34)/5. Let a(l) = k*y(l) - 6*j(l). Find g such that a(g) = 0.
-1/2
Let u be (1 + -1)/(-6 + 0 + 5). What is m in 3/5*m**3 + u + 0*m + 6/5*m**2 = 0?
-2, 0
Factor -3*a - 1/4*a**4 + 2 + 1/2*a**2 + 3/4*a**3.
-(a - 2)**2*(a - 1)*(a + 2)/4
Suppose 12*m = 11*m. Suppose 2/3*y + m + 1/3*y**2 = 0. Calculate y.
-2, 0
Suppose -2*a = -3*s - 0*s - 162, 4*s = 2*a - 160. Let o be -2 - (-7)/(a/32). Factor 0*t**4 + 0*t**2 - 2/3*t + 0 + 4/3*t**3 - o*t**5.
-2*t*(t - 1)**2*(t + 1)**2/3
Let u(w) be the second derivative of w**7/378 - w**5/90 + w**3/54 - 22*w. Factor u(d).
d*(d - 1)**2*(d + 1)**2/9
Let n be (-4)/1*(-28)/(-8). Let c(v) = 6*v**3 + 5*v**2 + 6*v - 7. Let z(h) = h**3 + h**2 + h - 1. Let t(p) = n*z(p) + 2*c(p). Factor t(f).
-2*f*(f + 1)**2
Let r be (-5)/(20/168)*4. Let z be (3 - 6)/(r/16). Factor 0 + 2/7*h + z*h**2.
2*h*(h + 1)/7
Let c be (12/(-2))/(2 + -1). Let b(h) be the second derivative of -h**4/6 + h**3/3 - 2*h. Let z(g) = -g**2 + g. Let u(k) = c*b(k) + 14*z(k). Factor u(p).
-2*p*(p - 1)
Let n(v) = v**2 + 7*v + 8. Suppose -3*w - w = 24. Let c be n(w). Determine i, given that 1/2*i + 0 + 1/4*i**c = 0.
-2, 0
Determine r so that -2/21*r + 2/21*r**2 - 4/21 = 0.
-1, 2
Let h(z) be the third derivative of -z**8/4480 - z**7/3360 - 2*z**5/15 + 10*z**2. Let u(b) be the third derivative of h(b). What is y in u(y) = 0?
-1/3, 0
Suppose -5*a - 6 = 2*r, r - 4*a = -a + 8. Factor -1 - 4*y + 6*y + r*y**2 + 1.
2*y*(y + 1)
Suppose 3 = 3*n - 12. Suppose 9*v - 4*v + n*i = 5, -v - 4 = -4*i. Suppose 0 + 1/6*u**4 + v*u - 1/6*u**3 + 0*u**2 = 0. What is u?
0, 1
Factor 4*v**5 + 55 + 8*v**2 - 12*v - 12*v**4 + 8*v**3 - 100 + 49.
4*(v - 1)**4*(v + 1)
Let a(l) = l**3 + 6*l**2 + 1. Let z be 1/3 + 14/(-6). Let h(x) = x**3 + 5*x**2 + x + 1. Let m(y) = z*a(y) + 3*h(y). Factor m(j).
(j + 1)**3
Let f = 769/240 + -1/240. Solve -8/5 - 6/5*l**2 + f*l = 0.
2/3, 2
Suppose -4*t + 14 = -2. Let p(g) be the second derivative of 1/20*g**5 - 1/4*g**2 - 1/6*g**3 + 0 - g + 1/60*g**6 + 0*g**t. Factor p(w).
(w - 1)*(w + 1)**3/2
Let t be -7 + -2*(0 - -1). Let w be t/(-1 - -4) - -8. Suppose 11/4*u**2 + 0 - 1/4*u - 9*u**3 + 4*u**4 + 16*u**w = 0. Calculate u.
-1, 0, 1/4
Let t(s) = -3*s**3 + 4*s**3 - 3*s**3. Let l(b) = -2*b**3 - b**2 + b + 1. Let a(g) = -2*l(g) + t(g). Factor a(n).
2*(n - 1)*(n + 1)**2
Let z(v) = -15*v**2 + 25*v - 5. Let o(r) = -7*r**2 + 12*r - 3. Let t(g) = 5*o(g) - 2*z(g). Determine m, given that t(m) = 0.
1
Suppose -20 = c + a - 6*a, c - 2*a = -8. Suppose c = 4*i - 0 - 8. Factor -1/2*w**i + 1/2*w + 0.
-w*(w - 1)/2
Suppose -5*m + 2*y = -13, -4*m + 11 = 3*y - 4*y. Factor -27/7*x + 6/7 + m*x**2.
3*(x - 1)*(7*x - 2)/7
Factor 3*i**3 + 3/2*i**4 - 3/2*i**2 - 3*i + 0.
3*i*(i - 1)*(i + 1)*(i + 2)/2
Let f = -9 - -13. Factor z**2 + 4 + 7*z**2 - 4 - 4*z - f*z**3.
-4*z*(z - 1)**2
Let f(y) be the first derivative of y**3/6 - y**2/4 + 8. Factor f(t).
t*(t - 1)/2
Let m(i) be the first derivative of i**3/3 + i**2/2 + 2*i - 3. Let y be m(0). What is n in 5/3*n**y - 7/3*n**3 + 0 + n**4 - 1/3*n = 0?
0, 1/3, 1
Let l(s) be the third derivative of s**7/840 + s**6/80 + 7*s**4/24 - 3*s**2. Let b(o) be the second derivative of l(o). Factor b(x).
3*x*(x + 3)
Let m(x) be the second derivative of x**5/35 - 2*x**3/21 - x. Suppose m(v) = 0. Calculate v.
-1, 0, 1
Factor -2/3*z**4 + 2/3*z**3 - 2/9*z**2 + 2/9*z**5 + 0 + 0*z.
2*z**2*(z - 1)**3/9
Let f = 24 - 22. Suppose 6*c**2 + c**2 - 3*c**f + 8*c = 0. Calculate c.
-2, 0
Let o = 9 + -4. Suppose 0*m - 25 = -5*m, 5 = o*d - 2*m. Find s, given that -10*s**4 - s**3 + 0*s**4 + 4*s**2 - 5*s**d = 0.
-1, 0, 2/5
Let y(r) be the third derivative of r**4/24 - r**3/3 - 4*r**2. Let z be y(4). Factor 1/4*v**z - 1/2 - 1/4*v.
(v - 2)*(v + 1)/4
Let g(u) be the third derivative of -u**6/24 + u**5/12 + 5*u**4/12 - u**2. Solve g(j) = 0 for j.
-1, 0, 2
Let x(g) be the third derivative of g**10/126000 - g**9/37800 - g**8/50400 + g**7/6300 - g**5/20 - g**2. Let j(s) be the third derivative of x(s). Factor j(m).
2*m*(m - 1)**2*(3*m + 2)/5
Let d = 9/11 + -25/44. Solve 1/4*z + d*z**2 + 0 = 0.
-1, 0
Let u be (-3 + 2 - (-1)/1)/1. Let c(l) be the second derivative of 0 - 1/6*l**4 + u*l**2 + l + 1/10*l**5 + 0*l**3. Factor c(o).
2*o**2*(o - 1)
Let k be (-430)/(-200) + (-2)/5 + -1. Find r such that k*r**3 + 1/2*r**2 + 0*r + 0 = 0.
-2/3, 0
Let a(g) = g - 3*g**2 + g**5 + 2*g**4 + g**2 + 2*g - 2 - g. Let l(n) = n**2 - n + 1. Let o