e first derivative of k**5/25 - 3*k**4/20 + 2*k**2/5 + 7. Factor o(t).
t*(t - 2)**2*(t + 1)/5
Let v(p) be the first derivative of 3/2*p**2 + 9/2*p**4 + 4*p**3 + 1/2*p**6 + 12/5*p**5 + 0*p - 3. Factor v(o).
3*o*(o + 1)**4
Let y(g) = 25*g**2 + 32*g - 21. Let k(s) = -62*s**2 - 80*s + 52. Let u(h) = 5*k(h) + 12*y(h). Suppose u(n) = 0. Calculate n.
-2, 2/5
Let u(n) = n**2 + n. Let h be -1 - (1 + -2) - -1. Let a(l) = l**3 + 8*l**2 + 9*l + 2. Let q(z) = -2*z. Let c be q(2). Let f(k) = c*u(k) + h*a(k). Factor f(m).
(m + 1)**2*(m + 2)
Let t(q) be the second derivative of 4*q - 8/7*q**2 - 13/3*q**4 - 68/21*q**3 - 21/10*q**5 + 0. Factor t(u).
-2*(3*u + 2)*(7*u + 2)**2/7
What is w in -16*w**3 + w**2 - 9*w**2 + 41*w**2 - 20*w**3 + 36*w - 12 - 21*w**4 = 0?
-2, -1, 2/7, 1
Let v(c) be the first derivative of -c**3/18 + c**2/6 + c/2 - 6. Factor v(k).
-(k - 3)*(k + 1)/6
Suppose 6 = p + 3. Factor 3*s - 3*s**3 - p*s**2 - s**4 + 4*s**4 + 0*s**4.
3*s*(s - 1)**2*(s + 1)
Let z(s) be the third derivative of s**8/84 + s**7/21 + s**6/20 - s**5/30 - s**4/12 + 16*s**2. Solve z(b) = 0.
-1, 0, 1/2
Let z be 608/15*(-5)/(-490). Let n = -2/147 + z. Find g such that -1/5 - 1/5*g**2 + n*g = 0.
1
Let f(g) = -g + 1. Let b(x) = 4*x**2 - 7*x - 5. Let c(u) = -b(u) + 3*f(u). Let c(r) = 0. What is r?
-1, 2
Let u(a) be the first derivative of a**4/18 - a**3/12 - a**2/12 + 8*a + 1. Let s(q) be the first derivative of u(q). Solve s(n) = 0.
-1/4, 1
Let r = 159 - 1429/9. Determine m, given that 2/9*m**4 + r*m**3 - 2/9*m - 2/3*m**2 + 4/9 = 0.
-2, -1, 1
Let a(t) be the third derivative of t**10/75600 - t**8/5600 + t**7/3150 + t**4/8 + 3*t**2. Let i(p) be the second derivative of a(p). Factor i(g).
2*g**2*(g - 1)**2*(g + 2)/5
Let v be (12/(-8))/(10/1648). Let p = v + 248. Factor 2*u + p - 6/5*u**2.
-2*(u - 2)*(3*u + 1)/5
Let l(t) be the second derivative of -t**6/5 + t**5/6 + t**4/6 + t**2 - 2*t. Let k(x) be the first derivative of l(x). Let k(n) = 0. What is n?
-1/4, 0, 2/3
Let w(n) be the second derivative of -n**4/4 - n**3/2 + 3*n**2 + 25*n. Factor w(z).
-3*(z - 1)*(z + 2)
Let k(a) be the third derivative of -a**5/570 - a**4/57 + 5*a**3/57 + 16*a**2 + 1. Suppose k(p) = 0. What is p?
-5, 1
Suppose p + 4 = 0, -p - 8 = s + p. Factor 0 + s*z + 1/2*z**3 - 1/2*z**2.
z**2*(z - 1)/2
Let j(n) = -15*n**2 + 69*n - 42. Let o(k) = 14*k**2 - 69*k + 42. Let r(x) = -5*j(x) - 6*o(x). Determine s, given that r(s) = 0.
2/3, 7
Let l(u) = 14*u**4 - 44*u**3 + 52*u**2 - 26*u + 6. Let t(r) = r**3 - r**2 + 1. Let h(g) = l(g) - 2*t(g). Solve h(c) = 0.
2/7, 1
Let b(v) = 8*v**3 - 5*v**2 - 9*v - 1. Let q = 48 + -27. Let s(k) = -33*k**3 + 21*k**2 + 36*k + 3. Let h(c) = q*b(c) + 5*s(c). Factor h(f).
3*(f - 2)*(f + 1)**2
Suppose -2*s + 42 = 4*s. Let z(w) be the third derivative of 3*w**2 + 1/180*w**5 - 1/72*w**4 + 0 + 0*w + 1/360*w**6 - 1/630*w**s + 0*w**3. Factor z(q).
-q*(q - 1)**2*(q + 1)/3
Factor -4/5*a**2 + 12/5*a - 8/5.
-4*(a - 2)*(a - 1)/5
Let n(s) be the first derivative of s**7/210 + s**6/30 + s**5/10 + s**4/6 + s**3/6 - s**2/2 - 6. Let d(u) be the second derivative of n(u). Factor d(j).
(j + 1)**4
Let m = 1894 + -37903/20. Let n = m + 7/5. Find t such that 0 + 1/4*t**5 - n*t**4 + 5/4*t**2 - 1/2*t - 3/4*t**3 = 0.
-2, 0, 1
Let o be 10/(-20)*(-1 - -1). Let b(k) be the second derivative of o*k**4 + k + 0*k**3 - 1/75*k**6 + 0 + 0*k**2 + 0*k**5. Factor b(g).
-2*g**4/5
Suppose c + 2 = 2*i, -2*c + 4 = 3*c + 4*i. Determine k so that 4*k - 9*k**4 - k**5 + 5*k**4 - 8 - k**3 + 0*k**5 + c*k**5 + 10*k**2 = 0.
-2, 1
Suppose 29 = 5*s - t, 0 = -s + t + 30 - 21. Suppose 0 + 2/19*z**s + 2/19*z**4 + 0*z + 0*z**2 + 0*z**3 = 0. What is z?
-1, 0
Let f(p) = 2*p - 9*p - 5*p - 11 + p**2. Let y be f(13). Factor -2/3*v**5 + 0*v + 0*v**y + 0*v**3 - 2/3*v**4 + 0.
-2*v**4*(v + 1)/3
Let d(i) be the second derivative of i**9/7560 + i**8/3360 - i**7/1260 - i**6/360 - i**4/4 - i. Let s(g) be the third derivative of d(g). Factor s(z).
2*z*(z - 1)*(z + 1)**2
Let b = -25 - -27. Factor 1/2*q**b - 5/4*q - 1/2 + 5/4*q**3.
(q - 1)*(q + 1)*(5*q + 2)/4
Let j(y) be the first derivative of -y**6/9 + 4*y**5/15 - 4*y**3/9 + y**2/3 - 1. Factor j(k).
-2*k*(k - 1)**3*(k + 1)/3
Let v(p) be the first derivative of -p**3/7 + 9*p**2/14 - 6*p/7 - 1. Factor v(j).
-3*(j - 2)*(j - 1)/7
Let d be 6*1 + -4 + 1. Let v(o) be the second derivative of 2*o + 0 + 0*o**2 - 1/2*o**4 + 1/2*o**d. What is r in v(r) = 0?
0, 1/2
Factor -1/4 - 1/4*q**2 - 1/2*q.
-(q + 1)**2/4
Let q(d) = 7*d**2 + d + 3*d**2 - 7*d**2. Let o be q(1). Suppose 3*t**3 - 7*t + 3*t**3 - 3*t**3 + o*t = 0. What is t?
-1, 0, 1
Let s be -1 - 1 - (-17 + 3). Let f = -32/3 + s. Factor -4/3*v**3 - 2/3*v**5 + 2*v - 2/3 - f*v**2 + 2*v**4.
-2*(v - 1)**4*(v + 1)/3
Let u be 14/(-12)*6/(-21). Factor -u + 1/3*i**2 + 0*i.
(i - 1)*(i + 1)/3
Let m = -79 - -145. Let j = -196/3 + m. Let 0*r + 2/9*r**5 - 2/3*r**4 - 2/9*r**2 + 0 + j*r**3 = 0. What is r?
0, 1
Let j be 2/8*32/24. Determine w so that -2/3 - j*w + 2/3*w**2 + 1/3*w**3 = 0.
-2, -1, 1
Let t(k) = 5*k**4 - k**3 - 5*k**2 + 5*k. Suppose -7*d = -6*d + 3. Let i(s) = -6*s**4 + 6*s**2 - 6*s. Let l(z) = d*t(z) - 2*i(z). Factor l(g).
-3*g*(g - 1)**2*(g + 1)
Suppose 195 = 17*s - 12*s. Let p be (s/(-182))/((-12)/14). Find x, given that 0 + p*x**2 + 1/4*x = 0.
-1, 0
Let c be 12/4 + (-26)/9. Let u(r) be the second derivative of c*r**3 - 1/30*r**5 + 1/90*r**6 - 1/6*r**2 + r + 0 + 0*r**4. Let u(a) = 0. What is a?
-1, 1
Let t = -169/2 + 85. Factor -1/4 + 0*g**2 - t*g**3 + 1/4*g**4 + 1/2*g.
(g - 1)**3*(g + 1)/4
Let z(a) = -4*a**4 - a**3 + 4*a**2 + 6*a. Let r(q) = -q**2 - 5*q + q**4 + 0*q + 4*q. Let c(p) = 5*r(p) + z(p). Let c(t) = 0. What is t?
-1, 0, 1
Solve -8/7*i**2 + 4/7*i + 4/7*i**3 + 0 = 0.
0, 1
Let u be 12/(-294)*-7 - 12/(-42). Determine f so that 4/7*f + 1/7*f**5 - 3/7*f**3 + 0 + u*f**2 - 2/7*f**4 = 0.
-1, 0, 2
Factor 0 + 1/2*c - 1/2*c**3 + 1/4*c**4 - 1/4*c**2.
c*(c - 2)*(c - 1)*(c + 1)/4
Let w(k) be the second derivative of -k**5/90 + 2*k**4/9 - 16*k**3/9 + 64*k**2/9 + 6*k. Factor w(g).
-2*(g - 4)**3/9
Let q be -5*1/(-3)*30/75. Find d, given that -5/3*d - d**2 - q = 0.
-1, -2/3
Let m = 217/3 - 209/3. Factor -4*x**3 - m*x**2 + 0 - 2/3*x - 2/3*x**5 - 8/3*x**4.
-2*x*(x + 1)**4/3
Let v be (5/40)/((-10)/(-344)). Let l = 381/70 - v. Factor 2/7*i + 10/7*i**2 + l*i**3 + 0.
2*i*(i + 1)*(4*i + 1)/7
Let b = 71/2 + -851/24. Let r(w) be the third derivative of w**2 + b*w**4 + 0*w**6 + 0*w**3 + 0 - 1/40*w**5 + 0*w + 1/420*w**7. Factor r(d).
d*(d - 1)**2*(d + 2)/2
Let c(j) be the first derivative of -3*j**4/32 - j**3/4 + 9*j**2/16 - 28. Let c(a) = 0. Calculate a.
-3, 0, 1
Let p(q) = 10*q**3 + 25*q**2 + 25*q - 5. Let k(o) = 5*o**3 + 13*o**2 + 12*o - 2. Let y(c) = 5*k(c) - 2*p(c). Factor y(h).
5*h*(h + 1)*(h + 2)
Let v(y) = -12*y**4 - 12*y**3 - 19*y**2 - 10*y - 13. Let x(q) = -q**4 - q**3 - 2*q**2 - q - 1. Let u(s) = -2*v(s) + 22*x(s). Solve u(g) = 0 for g.
-2, -1, 1
Factor -6*n**4 + 10*n**5 - 3*n**2 - 9*n**5 + 13*n**3 + 4*n - 9*n**2.
n*(n - 2)**2*(n - 1)**2
Let y(f) be the second derivative of -f**6/6 + 3*f**5/4 - 5*f**4/12 - 5*f**3/2 + 5*f**2 + 3*f. Determine w so that y(w) = 0.
-1, 1, 2
Find d such that 23*d**3 + 2*d**3 - 10 + 15*d**2 - 5*d**2 - 5*d - 20*d = 0.
-1, -2/5, 1
Let j(a) be the third derivative of -10*a**7/21 + 3*a**6/2 - 8*a**5/5 + 2*a**4/3 + 6*a**2. Suppose j(y) = 0. Calculate y.
0, 2/5, 1
Let l(t) be the first derivative of -2/7*t**5 + 0*t**2 + 0*t - 1/7*t**4 - 1 + 0*t**3. Find h such that l(h) = 0.
-2/5, 0
Suppose 2*n = 2*g + n - 7, -5*n = 15. Suppose -5*q - 10 = 3*a, 2*a = -g*a + q + 2. Solve a*v - 4/3*v**3 - 2/3 + 2*v**2 = 0 for v.
-1/2, 1
Factor 8*d + 8*d + 5*d**5 - 5*d**4 - 16*d.
5*d**4*(d - 1)
Let k be (11 + 1)*2/4. Suppose 3*n + 8 = 5*m, -2*m + 14 = n + 2. Factor -2*w + w**2 + 3*w - k + m.
(w - 1)*(w + 2)
Suppose -5*u + 2*d = -10, -3*u + 3*d = -0*u - 15. Factor -2/5*w + u - 4/5*w**4 + 4/5*w**2 + 0*w**3 + 2/5*w**5.
2*w*(w - 1)**3*(w + 1)/5
Factor -4/3 - 4/3*o + o**2.
(o - 2)*(3*o + 2)/3
Let w(f) be the first derivative of -1/9*f**6 + 1/6*f**2 + 1/9*f**3 + 4 - 1/4*f**4 - 1/3*f**5 + 0*f. Factor w(l).
-l*(l + 1)**3*(2*l - 1)/3
Let c be 12 + (1 - 1) + 2. Let p = c + -2. Factor -p*a - 4 - 4*a - 32*a**2 + 2.
-2*(4*a + 1)**2
Let j(l) be the second derivative of l**5/5 - 3*l. Fac