2
Let t(l) be the second derivative of 1/8*l**2 - 5/4*l**3 + 8*l + 25/4*l**4 + 0 - 25/2*l**5. Factor t(z).
-(10*z - 1)**3/4
Suppose 5*q + 0*q + 5 = -5*j, -4 = -5*j - 2*q. Let o(a) = -16*a**2 - 2*a - 7. Let x(m) = -5*m**2 - m - 2. Let l(g) = j*o(g) - 7*x(g). Let l(d) = 0. What is d?
-1, 0
Let w(d) = -76*d**4 + 176*d**3 + 188*d**2 - 32. Let n(q) = -7*q**4 + 16*q**3 + 17*q**2 - 3. Let j(g) = -32*n(g) + 3*w(g). Factor j(l).
-4*l**2*(l - 5)*(l + 1)
Solve -14*y - 5 - 1 - 2*y**3 + 453*y**2 - 463*y**2 = 0 for y.
-3, -1
Factor -17*c + 4*c**2 + 2*c**3 + 6*c**3 - 7*c - 4*c**3.
4*c*(c - 2)*(c + 3)
Suppose -9/4*s**2 - 1 - 3*s = 0. Calculate s.
-2/3
Let u(x) = 9*x**3 + 7*x**2 + 25*x - 19. Let p(i) = 5*i**3 + 4*i**2 + 13*i - 10. Let b(c) = 11*p(c) - 6*u(c). Suppose b(y) = 0. What is y?
-4, 1
Let b(z) be the third derivative of 0*z + 0 - 1/60*z**5 - 2*z**2 + 1/24*z**4 + 0*z**3. Suppose b(p) = 0. Calculate p.
0, 1
Factor 100/3*y**2 - 4/3*y**5 - 76/3*y**3 + 28/3*y**4 + 16/3 - 64/3*y.
-4*(y - 2)**2*(y - 1)**3/3
Let f(o) be the third derivative of 0*o - 1/10*o**4 - 3*o**2 - 1/15*o**3 - 1/75*o**6 - 3/50*o**5 + 0. Let f(r) = 0. What is r?
-1, -1/4
Let g = 2 + 0. Suppose 2 = q - 1. Factor 10*j**4 - 10*j**g - 4*j + 7 - 7 + 4*j**q.
2*j*(j - 1)*(j + 1)*(5*j + 2)
Suppose -19*a - a - 122*a**3 + 12*a**3 - 50*a**4 - 4*a + 112*a**2 = 0. What is a?
-3, 0, 2/5
Let n = 313 - 935/3. Let 2*h + 2/3*h**4 + 2/3*h**2 - 2*h**3 - n = 0. What is h?
-1, 1, 2
Factor -93*a + a**2 + 75 + 2*a**2 + 63*a.
3*(a - 5)**2
Let t(p) be the second derivative of -4/7*p**2 + 1/10*p**5 + 1/5*p**6 + 0 - 4*p - 16/21*p**3 - 17/42*p**4 + 3/49*p**7. Suppose t(f) = 0. What is f?
-1, -2/3, 1
Let c = 0 + 0. Suppose -p = c, 3*k - 5*p = 5*k - 6. Solve 0*v + 4*v**2 + 3*v**k - 5*v**3 - 2*v = 0.
0, 1
Determine j, given that 6*j**2 - 7*j**2 - 3*j**2 = 0.
0
Factor 0 - 3/5*u + 6/5*u**3 - 3/5*u**5 + 0*u**2 + 0*u**4.
-3*u*(u - 1)**2*(u + 1)**2/5
Let x be 5 - (6 + -5 + 2). Find d such that 3 - 8*d**2 + 9*d**x + 3 - 4*d**2 - 3*d = 0.
-2, 1
Determine k so that 12*k - 2*k**2 + 2*k**4 + 8*k**2 - 6*k**3 - 14*k = 0.
0, 1
Let a(p) be the first derivative of -5*p**4 + 32*p**3/3 - 2*p**2 - 8*p + 2. Factor a(y).
-4*(y - 1)**2*(5*y + 2)
Find c, given that -6/11*c - 6/11*c**4 + 2/11*c**5 + 2/11 + 4/11*c**3 + 4/11*c**2 = 0.
-1, 1
Let r(a) = 6*a - 7*a**2 + 0*a**2 + 3 - a**3 - 2*a**3 + 4*a**3. Let d be r(6). Solve 8/3 + b**d + 14/3*b**2 + 20/3*b = 0 for b.
-2, -2/3
Suppose -2*k + 26 = 20. Let o(m) be the second derivative of -1/135*m**6 + 0 + 0*m**4 - 2/27*m**k + 1/9*m**2 + 1/45*m**5 + 2*m. Factor o(b).
-2*(b - 1)**3*(b + 1)/9
Let m = -11 + 16. Suppose -3*b - 1 - m = -5*h, -3*b = 2*h - 15. Find j such that -2*j + j**2 - 4*j + j**b + 5*j - 1 = 0.
-1, 1
Suppose 0 = -21*x + 12*x. Factor -2/11*i**2 + x + 2/11*i**3 - 4/11*i.
2*i*(i - 2)*(i + 1)/11
Let u(d) be the third derivative of -d**8/168 - d**7/105 + d**6/12 + d**5/30 - 2*d**4/3 + 4*d**3/3 - 15*d**2 - 2*d. Factor u(y).
-2*(y - 1)**3*(y + 2)**2
Let k(g) = 5*g**3 - g**2 - 8. Suppose -2*o = -4*z - 22, -3*o + 7*o = 20. Let r(a) = -4*a**3 + 7. Let d(w) = z*k(w) - 4*r(w). Factor d(s).
(s - 1)*(s + 2)**2
Let w(i) = -i**3 + 8*i**2 + 11*i - 11. Let s be w(9). Factor -3*g**4 + 2*g + 4*g - 4*g**2 + s*g**2 - 6*g**3.
-3*g*(g - 1)*(g + 1)*(g + 2)
Suppose -3*t - 2*t = -10. Factor 4*q**2 + 1 + 2*q - q**t - 2*q**2 + 0.
(q + 1)**2
Let j(f) be the first derivative of f**8/960 + f**7/280 + f**6/480 - f**5/240 - f**3 + 1. Let p(l) be the third derivative of j(l). Factor p(s).
s*(s + 1)**2*(7*s - 2)/4
Factor -w + 7*w + 2*w**3 - 6*w + 4 - 4*w**2 - 2*w.
2*(w - 2)*(w - 1)*(w + 1)
Let x(m) be the first derivative of -m**7/120 - m**6/96 + m**5/120 - 2*m**2 - 3. Let a(y) be the second derivative of x(y). Let a(n) = 0. Calculate n.
-1, 0, 2/7
Let q = 947/2070 - 3/230. Let t be 8/4*(-5)/(-15). Let 0 + 4/9*p - t*p**2 + 2/3*p**4 - q*p**3 = 0. Calculate p.
-1, 0, 2/3, 1
Let x(l) = l**2 + 18*l. Let h be x(-18). Let c(f) be the second derivative of 0*f**3 + 2*f + 0 + 0*f**2 - 1/60*f**5 + h*f**4. Let c(p) = 0. Calculate p.
0
Let o be (2/5)/((-1)/(-10)). Find d such that -o*d + d**2 + 2*d + 0*d + 4*d = 0.
-2, 0
Let -8*u**4 - 7*u**4 + 75*u**3 + 24*u**2 + 24*u**4 = 0. Calculate u.
-8, -1/3, 0
Let 0*q - q**2 + 4/3 - 1/3*q**3 = 0. Calculate q.
-2, 1
Let c(a) be the second derivative of a**5/30 - a**4/12 - a**3/6 + a**2/3 + 3*a. Factor c(x).
(x - 2)*(x + 1)*(2*x - 1)/3
Let f be 5/(-1) + (-5 - -6). Let s = 0 - f. Factor -d**5 - 4*d**2 + s*d**4 + 2*d - d**5 + 0*d**4.
-2*d*(d - 1)**3*(d + 1)
Find m, given that -12*m + 13*m + 12*m**4 - m**2 - 11*m**4 - m**3 = 0.
-1, 0, 1
Factor 2*i + 11*i + 5*i**2 + i + 5*i + 12.
(i + 3)*(5*i + 4)
Let b be ((-5)/20)/((-90)/4). Let m(d) be the third derivative of 0*d - 1/9*d**3 + 0 - b*d**5 + 2*d**2 - 1/18*d**4. Find h, given that m(h) = 0.
-1
Find b, given that 40*b + 3*b**2 + 31*b - 131*b + 57 = 0.
1, 19
Let l(n) be the second derivative of n**10/105840 - n**9/17640 + n**8/7840 - n**7/8820 - n**4/6 + 3*n. Let w(k) be the third derivative of l(k). Factor w(s).
2*s**2*(s - 1)**3/7
Let i(a) be the second derivative of a**5/10 - a**4/3 + a**3/3 + 7*a. Factor i(z).
2*z*(z - 1)**2
Let z(d) be the second derivative of -1/78*d**4 + 2*d + 1/130*d**5 + 0*d**2 - 2/39*d**3 + 0. Solve z(w) = 0.
-1, 0, 2
Let w(i) be the second derivative of i**2 - i - 1/2*i**3 + 1/12*i**4 + 0. Factor w(z).
(z - 2)*(z - 1)
Let c(s) = -9*s - 3. Let i be c(-2). Suppose l = 3*z + 15, 0*z + i = -5*l - 3*z. What is f in -2/11*f + l + 2/11*f**2 = 0?
0, 1
Let d(q) be the third derivative of -q**5/75 + 2*q**4/15 - 8*q**2 - 4. Factor d(h).
-4*h*(h - 4)/5
Let x(v) be the third derivative of v**5/360 - v**4/144 - v**3/18 - 4*v**2. What is u in x(u) = 0?
-1, 2
Suppose -6 = -2*s - s. What is j in s*j - 3/2*j**2 - 1/2 = 0?
1/3, 1
Suppose -217*m + 20 = -207*m. Let y = 2 + 1. Solve 1/3*b + 1/3 - 5/3*b**y - 2/3*b**4 - b**m = 0 for b.
-1, 1/2
Let r(n) be the second derivative of -n**2 + 2*n + 0 + 1/60*n**5 + 0*n**3 + 0*n**4. Let d(v) be the first derivative of r(v). Factor d(b).
b**2
Let j(u) = u**2 + 13*u - 10. Let v be j(-14). Let k(m) be the first derivative of -1/2*m**v - m**2 + 0*m - 4/3*m**3 + 1. Find r such that k(r) = 0.
-1, 0
Let o be 0 - (-8 - -9 - (-15)/(-11)). Determine j, given that 2/11*j**5 + 2/11*j**3 - o*j**4 + 0*j + 0 + 0*j**2 = 0.
0, 1
Let b(k) be the first derivative of 1/2*k**4 - 2/3*k**2 + 0*k + 2/9*k**3 + 6. Find l, given that b(l) = 0.
-1, 0, 2/3
Let h = 14 - 10. Find q, given that -8*q**3 + 4*q**3 - 2*q**4 + 4*q**h + 2*q + 2*q**5 + 2 - 4*q**2 = 0.
-1, 1
Let u(s) be the third derivative of s**6/20 + 7*s**5/30 - s**4/6 - 2*s**3 + 2*s**2. Let a(y) = y**2 + y - 1. Let v(k) = -4*a(k) + u(k). Factor v(m).
2*(m - 1)*(m + 2)*(3*m + 2)
Let p(r) = 2*r**2 - 2*r - 9. Let b(o) = 3*o**2 - 2*o - 10. Let f(i) = 5*b(i) - 6*p(i). Let d(t) = 2*t**2 + 2*t + 4. Let s(u) = 5*d(u) - 4*f(u). Factor s(w).
-2*(w - 2)*(w + 1)
Let f(s) = -30*s**3 - 60*s**2 - 55*s + 25. Let r(u) = 5*u**3 + 10*u**2 + 9*u - 4. Let q(b) = 4*f(b) + 25*r(b). Factor q(p).
5*p*(p + 1)**2
Factor u**3 + 2/3*u - 1/3*u**4 + 0 + 5/3*u**2 - 1/3*u**5.
-u*(u - 2)*(u + 1)**3/3
Factor 78*g**2 + 7 + 6*g**5 + 1 + 18*g + 44*g**4 + 22*g - 10*g**4 + 74*g**3.
2*(g + 1)**3*(g + 2)*(3*g + 2)
Let h = -396 - -1988/5. Let g(n) be the first derivative of h*n + 1/10*n**4 + 2/3*n**3 + 1 + 8/5*n**2. What is q in g(q) = 0?
-2, -1
Let q(w) be the second derivative of -w**5/110 - w**4/66 + w**3/33 + w**2/11 + 6*w. Factor q(g).
-2*(g - 1)*(g + 1)**2/11
Let l(d) be the second derivative of d**6/50 - 3*d**5/100 - d**4/10 - d. Solve l(o) = 0.
-1, 0, 2
Factor -18*n - 6*n**3 - 33/2*n**2 - 27/4 - 3/4*n**4.
-3*(n + 1)**2*(n + 3)**2/4
Let h(c) be the first derivative of -c**3/5 - 3*c**2/10 + 6*c/5 + 25. Factor h(n).
-3*(n - 1)*(n + 2)/5
Let w(a) = 8*a**2 - 2*a + 6. Let u(t) = 2*t**2 - 2*t + 5 + 5*t**2 + 0*t + 0*t**2. Let i(r) = -6*u(r) + 5*w(r). Suppose i(j) = 0. What is j?
0, 1
Let p = 344 - 5152/15. Factor 2/5 + 2/15*b**2 + p*b.
2*(b + 1)*(b + 3)/15
Let z(l) be the first derivative of 1/18*l**3 + 0*l - 1/72*l**4 - 1/90*l**5 - 2 + 1/2*l**2. Let b(c) be the second derivative of z(c). Factor b(n).
-(n + 1)*(2*n - 1)/3
Let o(r) be the second derivative of -3*r - 1/15*r**6 - 1/10*r**5 + 0 + 0*r**2 + 1/3*r**