 be the second derivative of 1/27*r**4 - 3*r - 1/30*r**5 + 1/27*r**3 + 0*r**2 + 0. Factor n(k).
-2*k*(k - 1)*(3*k + 1)/9
Let p(g) = 3*g**5 - 11*g**4 - 17*g**3 - 6*g**2 - 20*g + 17. Let l(m) = m**5 - 4*m**4 - 6*m**3 - 2*m**2 - 7*m + 6. Let d(b) = -17*l(b) + 6*p(b). Factor d(s).
s*(s - 1)*(s + 1)**3
Let j(i) be the second derivative of -i**4/18 - 2*i**3/9 + 6*i. Let j(l) = 0. What is l?
-2, 0
Let q(s) be the second derivative of -5*s**4/12 + 5*s**2/2 - 10*s. Factor q(k).
-5*(k - 1)*(k + 1)
Let u = 25 - 23. Let y(n) be the third derivative of 1/12*n**4 + 0*n - 1/60*n**5 - 1/6*n**3 - n**u + 0. Factor y(i).
-(i - 1)**2
Let -5/2 - 10*z - 15/2*z**2 = 0. What is z?
-1, -1/3
Let m be (49/(-14) - -3)/(-2). Find w such that 3/2*w + m*w**2 + 9/4 = 0.
-3
Find d, given that 8*d + 2/3*d**3 - 4*d**2 - 16/3 = 0.
2
Factor 0 - 2/11*l**3 - 12/11*l**2 - 18/11*l.
-2*l*(l + 3)**2/11
Let k(n) be the third derivative of n**8/7840 - n**7/1260 + n**6/1260 - n**4/12 + 2*n**2. Let c(f) be the second derivative of k(f). Let c(r) = 0. Calculate r.
0, 1/3, 2
Suppose z + 119 - 123 = 0. Factor -5/2*w + 3/2*w**2 + 1 + 1/2*w**3 - 1/2*w**z.
-(w - 1)**3*(w + 2)/2
Let u(x) = -x**2 - 2*x. Let l(t) = -8*t**2 - 4*t. Let d(f) = -l(f) + 4*u(f). Factor d(h).
4*h*(h - 1)
Let d = 3797/28 + -515/4. Let 44/7*t**2 - d*t**3 - 40/7*t**4 + 6*t**5 + 6/7*t - 4/7 = 0. Calculate t.
-1, -1/3, 2/7, 1
Suppose -7*p - 3*c = -3*p + 3, -4*p - 4*c = 8. Let h(i) be the third derivative of -1/20*i**5 + 4*i**2 + 0*i + 1/8*i**4 + 0 + 0*i**p. Solve h(o) = 0.
0, 1
Let o = -14 + 20. Let z be (-4)/o*9/(-2). Factor 0*j - z*j - 2*j**2 + 5*j.
-2*j*(j - 1)
Let v = 1231/15 + -82. Let f(j) be the third derivative of 1/48*j**4 + v*j**5 + 1/48*j**6 + 0*j - 1/6*j**3 - j**2 + 0. Factor f(c).
(c + 1)**2*(5*c - 2)/2
Suppose 0 = 5*s - 5. Let a(r) = r**2 - 1. Let t(k) = -3*k**2 + k + 1. Let x(j) = 2*a(j) + t(j). Let h(n) = -2*n**2 - 1. Let o(y) = s*h(y) - 3*x(y). Factor o(q).
(q - 2)*(q - 1)
Suppose -2*y + 3*i + 1 = 4*i, -2*i = 6. Suppose -24*s - 27/2*s**3 + 6 + 63/2*s**y = 0. Calculate s.
2/3, 1
Factor 1/3*a + 0 + a**2.
a*(3*a + 1)/3
Let c(z) be the third derivative of -z**7/420 + z**6/180 - z**3/2 + z**2. Let u(g) be the first derivative of c(g). Factor u(i).
-2*i**2*(i - 1)
Factor -r**3 - 50*r**2 + 61*r**2 - r**3 - 2 + 7*r - 9*r**4 - 5*r**3.
-(r - 1)*(r + 1)**2*(9*r - 2)
Let y(a) = -a - 4. Let n be y(-6). Factor -3*p**2 - 4*p**n + 4*p + p**2 + 4*p**2.
-2*p*(p - 2)
Let b(t) be the second derivative of 0 + 11*t + 0*t**2 + 1/60*t**5 + 0*t**3 + 1/18*t**4. Factor b(g).
g**2*(g + 2)/3
Suppose -7 - 5 = -3*l. Solve -s**l + s**3 + 2*s**5 - 3*s - 3*s**5 + s**2 + 3*s = 0.
-1, 0, 1
Let k(u) be the second derivative of -2/21*u**3 + 1/105*u**6 + 1/35*u**5 - 1/42*u**4 + 0 + 5*u + 0*u**2. What is z in k(z) = 0?
-2, -1, 0, 1
Let t(z) be the third derivative of 0*z + 1/60*z**4 - 1/100*z**5 + 0*z**3 - 3*z**2 + 0. Let t(v) = 0. What is v?
0, 2/3
Let m(w) = -5*w**2 - w - 6. Let q(g) = g**2 + 1. Let a(y) = m(y) + 6*q(y). Let p(z) = z**5 - z**3 + z**2 - z. Let r(t) = -3*a(t) + 3*p(t). Factor r(h).
3*h**3*(h - 1)*(h + 1)
Suppose -x = -4*x + 18. Let i be 3/(0 - (-9)/x). Factor 0*l**i + 5*l**2 - l**2 - 2*l**4 - 2.
-2*(l - 1)**2*(l + 1)**2
Let s(n) be the first derivative of n**6/30 - 10. Solve s(r) = 0.
0
Let p(t) be the third derivative of -3/20*t**5 + 1/8*t**4 + 0 + 1/40*t**6 + 0*t**3 + 3/70*t**7 + 0*t - 5*t**2 - 1/56*t**8. Find c such that p(c) = 0.
-1, 0, 1/2, 1
Let k(w) be the second derivative of -w**5/10 + w**4/2 - w**3 + w**2 - 20*w. Suppose k(j) = 0. What is j?
1
Let f(u) be the first derivative of u**7/1680 + 4*u**3/3 - 3. Let z(k) be the third derivative of f(k). Factor z(y).
y**3/2
Let l = 15 + -44/3. Let i(f) = -f**2 - 13*f - 9. Let m be i(-12). Factor -n**m - l*n + 0 - n**2 - 1/3*n**4.
-n*(n + 1)**3/3
Let g(l) be the first derivative of -3*l**5/35 + 3*l**4/14 - l**3/7 - 3. Factor g(x).
-3*x**2*(x - 1)**2/7
Let o = 1 - 2. Let b(f) = -6*f. Let x be b(o). Find q such that -3*q**5 - 8*q**2 - q**2 + 6*q - x*q**2 + 9*q**3 + 3*q**4 = 0.
-2, 0, 1
Let l(i) = 9*i + 247. Let y be l(-27). Factor -5/2*z**2 + 1/2*z**3 - 2 + y*z.
(z - 2)**2*(z - 1)/2
Let z = 275 - 272. Find i such that 0 + 1/5*i**z - 2/5*i + 1/5*i**2 = 0.
-2, 0, 1
Let l = -27 - -33. Suppose -3*u + u + 8 = 0. Let -19*n**3 + 16*n**u - 16*n**3 - n + 3*n**2 + l*n**2 + 11*n**3 = 0. Calculate n.
0, 1/4, 1
Let p = 12 - 9. Let u(d) be the first derivative of -1/6*d**2 + 0*d + 1 + 2/15*d**5 + 1/18*d**6 + 0*d**4 - 2/9*d**p. Factor u(m).
m*(m - 1)*(m + 1)**3/3
Let v(n) be the third derivative of -n**8/784 - 2*n**7/245 + n**6/70 + 11*n**5/70 - 3*n**4/56 - 9*n**3/7 + 17*n**2. What is x in v(x) = 0?
-3, -1, 1, 2
Let y(i) = 4*i**5 + 2*i**4 - 2*i**2 - 2*i - 2. Let j(b) = -b**5 - b**4 - b**3 + b**2 + b + 1. Let u(d) = 2*j(d) + y(d). Determine m, given that u(m) = 0.
-1, 0, 1
Let p(f) = f**2 - 11*f + 4. Let t(q) = q**3 - 5*q**2 - 4*q - 1. Let u be t(6). Let x be p(u). Factor -h**2 + h**3 - 1/2 + 1/2*h**5 + 3/2*h**x - 3/2*h.
(h - 1)*(h + 1)**4/2
Let s(h) = 7*h**3 + h**2 - 7*h + 5. Let q(l) = -6*l**3 - l**2 + 6*l - 4. Suppose 0 = -3*a - 0 + 18. Let x(o) = a*q(o) + 5*s(o). Factor x(u).
-(u - 1)*(u + 1)**2
Let x(d) = d**5 - d**4 - 3*d**3 - 3*d**2 + 4*d - 2. Let b(o) = -o**5 + 2*o**4 + 3*o**3 + 4*o**2 - 5*o + 3. Let u(i) = -2*b(i) - 3*x(i). Factor u(s).
-s*(s - 1)**2*(s + 1)*(s + 2)
Suppose 16 - 6 = 2*c. Determine a so that 4*a - 5/4*a**4 - 41/4*a**3 + 25/4*a**c + 1 + 1/4*a**2 = 0.
-1, -2/5, 1
Let p(i) be the second derivative of i**7/3360 - i**6/960 + 5*i**4/6 - 8*i. Let b(k) be the third derivative of p(k). Let b(y) = 0. Calculate y.
0, 1
Let a(b) be the first derivative of 2*b**3/3 + b**2 - 14. Factor a(x).
2*x*(x + 1)
Let p(u) = 10*u - 2. Let g be p(2). Suppose -1 - 7 = -f. Let 2 - 4*k**3 - 18*k**2 - f*k**4 - 3*k - g*k**3 + k = 0. Calculate k.
-1, 1/4
Let v be (-130)/(-845) - 16/(-65). Factor v*l**3 - 6/5*l**2 + 0 + 4/5*l.
2*l*(l - 2)*(l - 1)/5
Let n(d) = d**3 + 9*d**2 + 6*d - 11. Let u = 8 + -16. Let x be n(u). Suppose -5/2*l**4 - x*l**3 - 1/2*l**5 - 1/2 - 5*l**2 - 5/2*l = 0. What is l?
-1
Let s(w) be the third derivative of -1/48*w**4 + 0*w - 1/60*w**5 + 0*w**3 - 1/240*w**6 + 0 - 4*w**2. Factor s(u).
-u*(u + 1)**2/2
Suppose x - 9*x = -x. Let -2/9*o**2 + 2/9*o + x = 0. Calculate o.
0, 1
Let b(i) be the third derivative of -1/12*i**4 - 1/3*i**3 + 0 + 0*i - 1/120*i**5 - 3*i**2. Factor b(x).
-(x + 2)**2/2
Let f = -1 - 0. Let y(q) = -2*q**3 + 24*q**2 - 54*q + 48. Let s(w) = 3 + 1 - 5 + w**2. Let a(o) = f*y(o) + 6*s(o). Factor a(z).
2*(z - 3)**3
Let f(b) = -9*b**3 + 9*b**2 - 3*b - 9. Let q(c) = 26*c**3 - 27*c**2 + 8*c + 27. Let n(m) = 17*f(m) + 6*q(m). Determine h so that n(h) = 0.
-1, 1, 3
Suppose 131 = 5*q - 39. Let p = q + -30. Factor -4/5*n**2 + 0*n**3 + 0 + 1/5*n**5 + 0*n + 3/5*n**p.
n**2*(n - 1)*(n + 2)**2/5
Let k(p) be the second derivative of p**6/90 + p**5/40 - p**4/24 + p**3/2 + p. Let v(a) be the second derivative of k(a). Factor v(h).
(h + 1)*(4*h - 1)
Let v(i) = i**2 - 3*i - 2. Let b be v(4). Solve -10*t**2 - 6*t**2 + 14*t**b = 0.
0
Suppose 33*w - w**2 - 62*w + 32*w - 2 = 0. What is w?
1, 2
Let o(s) be the second derivative of s**4/24 - s**3/3 + s**2 + 5*s. Let o(z) = 0. Calculate z.
2
Suppose 8 = 4*f + 3*j, -4*j = -7*f + 4*f + 6. Suppose 16 = 17*m - 13*m. Determine s so that -5*s**f - 3 + 0*s**2 + m*s**2 + 1 + 3*s = 0.
1, 2
Let u(q) = 2*q - 5. Let n be u(4). Suppose 2 - 5*o**2 + 6*o - n + 29*o**2 - 3 + 14*o**3 = 0. Calculate o.
-1, 2/7
Let z(d) be the first derivative of -d**6/9 + 5*d**4/6 - 4*d**2/3 - 23. Let z(l) = 0. What is l?
-2, -1, 0, 1, 2
Let b = -219/2 - -112. Suppose -b*u**2 + u + 3/2*u**3 + 0 = 0. Calculate u.
0, 2/3, 1
Let o(k) = k**2 - 2*k - 4. Let s be o(4). Let x(w) be the third derivative of 1/60*w**5 - w**2 + 0 + 1/24*w**s + 0*w**3 + 0*w. Let x(b) = 0. Calculate b.
-1, 0
Let h(w) be the first derivative of -2*w**5/15 - w**4/3 + 2*w**3/9 + 2*w**2/3 + 40. Factor h(p).
-2*p*(p - 1)*(p + 1)*(p + 2)/3
Let y(m) be the first derivative of m**8/6720 - m**6/720 + m**4/96 - m**3 - 2. Let i(o) be the third derivative of y(o). Factor i(g).
(g - 1)**2*(g + 1)**2/4
Let l(n) be the first derivative of -5/3*n**3 - 1/5*n**5 + 4 + n**4 + 0*n + n**2. Solve l(u) = 0.
0, 1, 2
Factor -1 + 5*m**