
Let z(x) = -16*x**3 + 20*x**2. Let y(r) be the second derivative of -r**5/20 + r**4/12 - r**3/6 - 14*r. Let u(v) = -12*y(v) + z(v). Factor u(w).
-4*w*(w - 3)*(w + 1)
Factor -o**3 - 4/3*o + 1/3*o**5 + 8/3*o**2 + 0 - 2/3*o**4.
o*(o - 2)*(o - 1)**2*(o + 2)/3
Let v(z) = -40*z**3 + 328*z**2 - 90*z + 16. Let r(y) = -4*y**3 - 2*y**2 - y - 1. Let f(x) = -8*r(x) - v(x). Let f(i) = 0. Calculate i.
1/6, 4
Suppose -4*u - 11 = 5, 2*u = 4*x. Let t(m) = -26*m**2 - 41*m + 45. Let s(n) = -5*n**2 - 8*n + 9. Let p(r) = x*t(r) + 11*s(r). Let p(d) = 0. What is d?
-3, 1
Let a(p) = -13*p - 31. Let o be a(8). Let q be (o/(-10))/(-3) - -4 - -3. Factor 0 + 5/2*n - 25/2*n**3 - q*n**2 - 15/2*n**4.
-5*n*(n + 1)**2*(3*n - 1)/2
Let n(f) be the third derivative of f**5/360 - f**4/18 + 7*f**3/36 + 36*f**2 - 3*f. Factor n(v).
(v - 7)*(v - 1)/6
Let s(k) = k**2 - 3*k - 3. Let i(c) = 12*c**2 + 94*c - 141. Let v(y) = i(y) - 7*s(y). Suppose v(d) = 0. What is d?
-24, 1
Determine l, given that 273 - 278 - l + 0*l + l**2 - 3*l = 0.
-1, 5
Let g(r) be the first derivative of -r**5/20 - r**4/4 - r**3/2 + 19*r**2/2 - 14. Let j(i) be the second derivative of g(i). Factor j(q).
-3*(q + 1)**2
Let b(q) = q**3 - q**2 + 33*q + 454. Let l be b(-6). Find i, given that 3/5*i**l - 9/5 + 24/5*i + 0*i**3 - 18/5*i**2 = 0.
-3, 1
Let x(b) be the second derivative of -b**8/1680 + 2*b**7/315 - b**6/36 + b**5/15 + 3*b**4/4 + 38*b. Let o(m) be the third derivative of x(m). Factor o(p).
-4*(p - 2)*(p - 1)**2
Let u = -3 + 5. Suppose 3 = -3*y, -4 = -4*r - u*y + 6. Factor -11*k - k**2 + r*k + 9*k.
-k*(k - 1)
Let b = -877/4 - -2633/12. Let m be (-2)/4*4/(-6). Factor b + m*g + 1/6*g**2.
(g + 1)**2/6
Suppose 4*p = 7*p - 75. Let b = -49/2 + p. Factor x**3 - 1/2*x**5 + x**2 - 1/2*x - 1/2 - b*x**4.
-(x - 1)**2*(x + 1)**3/2
Solve -g**2 + 4/3*g**3 + 1/3 + 4/3*g**4 - 2/3*g = 0.
-1, 1/2
Let j(q) be the second derivative of -q**7/28 - 3*q**6/20 - 9*q**5/40 - q**4/8 - 2*q - 6. Factor j(b).
-3*b**2*(b + 1)**3/2
Let j(n) = 21*n**4 - 36*n**3 - 48*n**2 + 63*n. Let y(r) = 3*r**4 - 5*r**3 - 7*r**2 + 9*r. Let b(g) = -4*j(g) + 27*y(g). Factor b(c).
-3*c*(c - 3)*(c - 1)*(c + 1)
Solve -11/5*l**3 - 17/5*l - 43/5*l**2 + 6/5 + 9/5*l**4 = 0 for l.
-1, 2/9, 3
Let l = -1887/2 + 944. Factor 0 - 1/4*x**2 - l*x.
-x*(x + 2)/4
Let i be 51/9 + (-4)/(-3). Suppose -4*y + i*y + 2*w - 5 = 0, -2*y = 4*w + 2. Find u such that -1/5*u**y - 1/5*u**4 + u**2 + 0 - 3/5*u = 0.
-3, 0, 1
Let a be 6/(-2 + 4) + -1. Factor -12*v**3 + 3*v**4 + 0*v**4 + 123*v**a - 111*v**2 + 0*v**4.
3*v**2*(v - 2)**2
Let p(l) be the first derivative of -10*l**6 + 424*l**5/5 + 250*l**4 + 416*l**3/3 - 86*l**2 - 72*l + 141. Solve p(c) = 0.
-1, -1/3, 2/5, 9
Let s(i) be the third derivative of -i**5/10 - 17*i**4/45 - 4*i**3/9 + 2*i**2 - 5. Let s(p) = 0. What is p?
-10/9, -2/5
Suppose p + 5*u = -p + 138, -4*p + 3*u + 276 = 0. Let a = p + -67. Solve 1/4*w**4 + 0*w + 0 - 1/4*w**a + 0*w**3 = 0 for w.
-1, 0, 1
Find j, given that -15/4*j**2 - 12 - 12*j - 3/8*j**3 = 0.
-4, -2
Find d such that -4*d**5 - 9 + 12 - 3 + 20*d**4 - 45*d**2 - 3*d**2 + 32*d**3 = 0.
-2, 0, 1, 6
Let w be (-5 + 5)/(-3 + -2). Factor w*h + 0 + 2/19*h**3 - 2/19*h**2.
2*h**2*(h - 1)/19
Let x(k) be the first derivative of k**6/21 + 8*k**5/35 + k**4/7 - 8*k**3/21 - 3*k**2/7 + 116. Let x(c) = 0. Calculate c.
-3, -1, 0, 1
Let q(p) = -p**2 - 9*p + 27. Let w be q(-10). Suppose 5*u - u**2 + w - 4 - 13 = 0. Calculate u.
0, 5
Let f be 8*(0 + 1)*(-1)/(-2). Suppose -f*s + 82 + 4*s**2 - 82 = 0. Calculate s.
0, 1
Let i = 110 + -100. Factor 6*c**4 + 8*c**5 + c**3 - i*c**5 - 3*c**3 - 2*c**3.
-2*c**3*(c - 2)*(c - 1)
Let j(v) be the second derivative of -v**6/1140 + v**4/228 - 3*v**2/2 - 11*v. Let o(z) be the first derivative of j(z). Determine n, given that o(n) = 0.
-1, 0, 1
Let v be 91/(-26)*(-6)/28. Let x(p) = -p**3 + 11*p**2 + 2*p - 20. Let d be x(11). Factor 1/4*u + 0 + v*u**d.
u*(3*u + 1)/4
Let j(g) be the second derivative of g**6/120 + g**5/60 - 5*g**4/24 + g**3/2 + 19*g**2/2 + 39*g. Let b(i) be the first derivative of j(i). Factor b(k).
(k - 1)**2*(k + 3)
Factor u**3 + 5*u**2 - 4*u**2 - 7*u**2 - 8 + 12*u + 0*u**3.
(u - 2)**3
Suppose 5*n + 6 = 16. Let n*h**2 + 186 + 0*h**4 + 6*h - 6*h**3 + 2*h**4 - 190 = 0. Calculate h.
-1, 1, 2
Let g(r) be the third derivative of r**9/5040 + r**8/2240 - r**4/3 + r**2. Let m(d) be the second derivative of g(d). Factor m(b).
3*b**3*(b + 1)
Let m be (2/(-3))/((-4)/18). Determine w so that 3*w + w**4 + 26*w**2 - m*w + w**5 - 27*w**2 - w**3 = 0.
-1, 0, 1
Suppose -4*y - 4*g = -164, 27 = 2*y - 2*g - 47. Solve y*z - 22*z + 90*z**3 + 69*z**2 - 44*z - 6 = 0.
-1, -1/6, 2/5
Let u(j) be the third derivative of j**8/336 - j**7/30 + 19*j**6/120 - 5*j**5/12 + 2*j**4/3 - 2*j**3/3 + 2*j**2 - 233. What is a in u(a) = 0?
1, 2
Let s(l) be the first derivative of l**5 + 40*l**4 + 100*l**3 - 328. Let s(f) = 0. What is f?
-30, -2, 0
Let y(g) be the first derivative of g**4/4 + g**3/2 - 44*g + 13. Let s(b) be the first derivative of y(b). Factor s(c).
3*c*(c + 1)
Let k(w) be the third derivative of 0*w + 1/200*w**6 + 0*w**3 + 1/240*w**4 + 0 - 7*w**2 + 1/525*w**7 + 1/150*w**5 + 1/3360*w**8. Factor k(m).
m*(m + 1)**4/10
Let z(a) = a**2 + 12*a + 11. Let y(v) = v**2 + 22*v + 21. Let o(x) = 3*y(x) - 5*z(x). Factor o(g).
-2*(g - 4)*(g + 1)
Find i, given that -30 - 18 - 17 + 68*i + 1 - 4*i**2 = 0.
1, 16
Suppose -6*d + 900 = 4*d. Let i = 272/3 - d. Suppose i*b**4 - 16*b + 44/3*b**2 + 6 - 16/3*b**3 = 0. Calculate b.
1, 3
Let h(a) be the first derivative of -a**6/18 - 4*a**5/5 - a**4/3 + 64*a**3/3 - 128*a**2/3 + 88. Solve h(c) = 0 for c.
-8, 0, 2
Let s(o) be the third derivative of -1/120*o**5 + 1/24*o**4 - 1/12*o**3 + 0 + 0*o + 14*o**2. Suppose s(a) = 0. What is a?
1
Let c(h) be the third derivative of -h**8/4480 - h**7/2520 + h**6/480 + h**5/120 + h**4/8 + 15*h**2. Let x(z) be the second derivative of c(z). Factor x(s).
-(s - 1)*(s + 1)*(3*s + 2)/2
Let z(u) be the third derivative of u**7/350 - 2*u**6/25 + 21*u**5/50 - u**4 + 13*u**3/10 + 2*u**2 + 8*u. Determine t so that z(t) = 0.
1, 13
Determine x, given that -62 + x + 29 + 33 - 2*x**5 + 6*x**3 + 27*x + 14*x**4 - 46*x**2 = 0.
-2, 0, 1, 7
Let d(h) = 60*h**3 - 25*h**2 - 75*h - 35. Let m(y) = -y**3 - 2*y**2 - y - 1. Let f(p) = -d(p) + 15*m(p). Factor f(r).
-5*(r - 1)*(3*r + 2)*(5*r + 2)
Let a = -24736 + 49475/2. Factor -1/2*o**4 + 2*o**3 + 2 - 2*o - a*o**2.
-(o - 2)**2*(o - 1)*(o + 1)/2
Suppose 130/9*d + 2*d**2 + 28/9 = 0. Calculate d.
-7, -2/9
Let f(v) be the second derivative of -v**7/6 + 71*v**6/90 + v**5/60 - 83*v**4/36 + 10*v**3/9 + 2*v**2 + 16*v - 3. Solve f(i) = 0.
-1, -2/7, 2/3, 1, 3
Let f(c) = c**2 - 2*c - 1. Let b be f(4). Suppose 5*l - 5 = 0, b*t - 2*t - 17 = 3*l. Suppose 2*o**3 - 8*o**4 + 5*o**2 - t*o**3 + 3*o**2 + 2*o = 0. Calculate o.
-1, -1/4, 0, 1
Let c be 0 + (2 - 1) + 13. Let h = 17 - c. Solve -2/9*a**h - 2/3*a + 2/3*a**2 + 2/9 = 0 for a.
1
Let j(f) be the first derivative of -f**6/45 - 4*f**5/75 + f**4/30 + 4*f**3/45 - 28. Determine o so that j(o) = 0.
-2, -1, 0, 1
Let i(m) be the second derivative of -m**5/300 + m**4/12 - 3*m**3/10 - 15*m**2/2 - 16*m - 1. Let z(t) be the first derivative of i(t). Factor z(s).
-(s - 9)*(s - 1)/5
Let m(u) = -5*u + 4*u + u**2 - 3*u**2 + 3*u**2. Let s(i) = -i**4 - 2*i**3 - 3*i**2 + 6*i. Let z = 7 - 8. Let g(p) = z*s(p) - 4*m(p). Factor g(y).
y*(y - 1)*(y + 1)*(y + 2)
Let r(a) = -6*a**3 - 30*a**2 - 24*a - 8. Let d(i) = 8*i**3 + 31*i**2 + 23*i + 10. Let n(h) = 4*d(h) + 5*r(h). What is k in n(k) = 0?
-1, 0, 14
Let h(c) be the second derivative of -1/30*c**6 - 13*c - 1/3*c**4 - 1/5*c**5 + 0*c**3 + 0 + 0*c**2. Factor h(r).
-r**2*(r + 2)**2
Let 10 + b**5 - 3*b**5 + 18*b**4 + 68*b**2 - 52*b**3 - 691*b + 649*b = 0. What is b?
1, 5
Let c be (0 - 4/1)/(-40). Let -1/10*i + 0 - c*i**2 = 0. What is i?
-1, 0
Let o(x) be the third derivative of -x**8/336 + x**7/168 + x**6/36 - x**3/3 + 15*x**2. Let s(p) be the first derivative of o(p). Solve s(y) = 0 for y.
-1, 0, 2
Let b(t) be the second derivative of -t**7/210 + t**6/45 + t**5/30 - t**4/3 + 4*t**3 + 28*t. Let u(n) be the second derivative of b(n). Solve u(y) = 0 for y.
-1, 1, 2
Solve 5/6*u**5 + 5/3*u**3 - 5/2*u - 15/2 + 35/3*u**2 - 25/6*u**4 = 0 for u.
-1, 1, 3
Let m be (1/4)/(1/12). Suppo