27*h**2 - 43*h - 7. Let g(k) = 7*n(k) - 5*y(k). Factor g(j).
-3*j*(j - 4)*(j + 1)
Let o be (20/35)/(12/28). Factor o*l**2 - 2/3*l**4 - 2/3 + 0*l**3 + 0*l.
-2*(l - 1)**2*(l + 1)**2/3
Let w = -356/3 - -4640/39. Determine z so that -w*z - 2/13*z**2 - 2/13 = 0.
-1
Suppose 8*y + 9*y = -7*y. Factor 0*p + y - 2/9*p**2.
-2*p**2/9
Let f be 2/(-11) + (7385/(-2640) - -3). Let m(l) be the second derivative of 0*l**3 + 0 + 1/80*l**5 + f*l**4 + 4*l + 0*l**2. Determine d so that m(d) = 0.
-1, 0
Let x(j) be the first derivative of -1/2*j**4 + j**2 + 1/5*j**5 - 3 + 0*j**3 - j. Factor x(s).
(s - 1)**3*(s + 1)
Let r(l) be the second derivative of -l**5/10 - l**4 - 3*l**3 + 5*l. Determine a so that r(a) = 0.
-3, 0
Suppose 5*j + 15 = -5. Let o = j - -4. Determine t, given that 2/9*t**2 + 0 + 2/9*t**3 + o*t = 0.
-1, 0
Let g be (-28)/(-30) + 33/(-55). Let b(m) be the third derivative of -2*m**2 - g*m**3 + 1/60*m**6 + 0*m + 0 - 1/12*m**4 + 1/30*m**5. Factor b(o).
2*(o - 1)*(o + 1)**2
Let s(f) be the first derivative of 6*f**6 - 24/5*f**5 + 3/2*f**2 - 39/4*f**4 + 9*f**3 - 3*f + 1. Solve s(n) = 0.
-1, -1/3, 1/2, 1
Let i(y) = 2*y**2 + 17*y + 37. Let c be i(-5). Let 4/5 - 6/5*w + 2/5*w**c = 0. Calculate w.
1, 2
Factor -2/3 - 4/3*r**3 + 2/3*r**5 + 4/3*r**2 - 2/3*r**4 + 2/3*r.
2*(r - 1)**3*(r + 1)**2/3
Let s(b) = 17*b**2 - 15*b + 7. Let d(f) = f**2 + f + 1. Let n(i) = 6*d(i) - 2*s(i). Solve n(z) = 0 for z.
2/7, 1
Let g = -18 - 3. Let z be 4/6 + 14/g. Factor 4/7*f**3 + z*f**2 - 4/7*f - 2/7 + 2/7*f**4.
2*(f - 1)*(f + 1)**3/7
Let c(g) be the second derivative of 0*g**2 + 0 + 9*g + 1/15*g**3 - 1/3*g**6 - 11/30*g**4 + 7/10*g**5. Factor c(m).
-2*m*(m - 1)*(5*m - 1)**2/5
Let n be -1 + -3*(-39)/108. Let q(i) be the first derivative of 0*i + n*i**4 - 1/15*i**5 + 4 - 1/18*i**6 + 0*i**2 + 1/9*i**3. Find b such that q(b) = 0.
-1, 0, 1
Let t be 5 + -2 - ((-10)/(-12) + 2). Let d(m) be the first derivative of -2 + 1/3*m**2 + 0*m**3 - t*m**4 + 0*m. Factor d(g).
-2*g*(g - 1)*(g + 1)/3
Let m(l) be the first derivative of -5 + 1/3*l**3 + 0*l**2 + 0*l. Determine u, given that m(u) = 0.
0
Let v(f) = 5*f**5 - 22*f**4 + 21*f**3 + f**2 + f - 3. Let d(u) = -9*u**5 + 44*u**4 - 43*u**3 - 3*u**2 - 3*u + 7. Let l(j) = 3*d(j) + 7*v(j). Factor l(y).
2*y*(y - 1)**3*(4*y + 1)
Let z(i) be the second derivative of i**4/12 + i**3/6 + 4*i. Solve z(m) = 0 for m.
-1, 0
Let r(c) be the first derivative of 4*c**6/3 + 2*c**5 - 3*c**4/2 - 10*c**3/3 - c**2 - 8. Let r(j) = 0. What is j?
-1, -1/4, 0, 1
Let g(i) be the second derivative of i**4/3 - 6*i**3 + 18*i. Determine d so that g(d) = 0.
0, 9
Let f(k) = k - 1. Let j be (2 - 4) + 5 + -2. Let i be f(j). Determine m so that i*m**2 + 0 + 2/5*m**3 + 4/5*m**4 + 0*m + 2/5*m**5 = 0.
-1, 0
Let l(d) be the second derivative of d**6/720 + d**3/2 + d. Let b(t) be the second derivative of l(t). Let b(z) = 0. Calculate z.
0
Let u(p) be the second derivative of p**6/195 + 2*p**5/65 + p**4/13 + 4*p**3/39 + p**2/13 + 3*p. Factor u(h).
2*(h + 1)**4/13
Let g(j) = j**2 - 2*j - 6. Let s be g(4). Let r be ((-9)/(-3))/6*0. Factor 4/7*f**3 + 2/7*f**4 + 0*f + r + 2/7*f**s.
2*f**2*(f + 1)**2/7
Let o(l) be the first derivative of 6*l**5/35 + 3*l**4/14 - 6*l**3/7 - 15*l**2/7 - 12*l/7 - 18. Factor o(s).
6*(s - 2)*(s + 1)**3/7
Factor -9/7 + 3/7*w**3 + 3*w - 15/7*w**2.
3*(w - 3)*(w - 1)**2/7
Suppose 4*c = -2*a + 24, 2*a + 3*c - 13 = 7. Suppose -2*r = -4*q + 16, -1 = -2*r + a*r - q. Determine u so that 3*u**2 - 4*u - 3*u**2 + 2*u**2 + r = 0.
1
Let r(o) be the first derivative of -o**4/8 - o**3/2 - 17. Find v such that r(v) = 0.
-3, 0
Factor -448*y**2 - 30*y**3 + 28 + 4*y + 28*y**3 - 62*y**3.
-4*(y + 7)*(4*y - 1)*(4*y + 1)
Let p = -7 + 7. Let m(a) be the third derivative of p*a**5 + 0*a + 0*a**4 + 0*a**3 - a**2 + 1/300*a**6 + 0. Solve m(f) = 0 for f.
0
Let q(r) be the first derivative of -r**4/3 + 16*r**3/3 - 32*r**2 + 4*r + 11. Let m(b) be the first derivative of q(b). Factor m(o).
-4*(o - 4)**2
Factor 0*p**2 - 1/5*p**5 + 0 + 2/5*p**3 - 1/5*p + 0*p**4.
-p*(p - 1)**2*(p + 1)**2/5
Let m(z) = 20*z**4 + 7*z**3 - 23*z**2 - z. Let o(q) = -220*q**4 - 76*q**3 + 252*q**2 + 12*q. Let t(c) = -32*m(c) - 3*o(c). Factor t(k).
4*k*(k - 1)*(k + 1)*(5*k + 1)
Let k = 6 - 2. Let v be -1 + k - (9 - 6). Factor v*h**3 + 4/5*h**5 + 0*h + 6/5*h**4 - 2/5*h**2 + 0.
2*h**2*(h + 1)**2*(2*h - 1)/5
Let q = 20 - 14. Let 2*b**3 + 0*b**3 + 0*b**2 - q*b**2 - 2 + 6*b = 0. What is b?
1
Let m(f) be the first derivative of -f**2 + 1/9*f**3 + 3*f + 5. Determine x, given that m(x) = 0.
3
Let k(f) be the second derivative of f**6/15 - 2*f**5/5 + f**4/6 + 2*f**3 + 25*f. Solve k(l) = 0 for l.
-1, 0, 2, 3
Let t(h) = h**2 + 1. Let d(n) = 2 - n**2 + 10*n**2 + 8*n + 1 + 0. Let p(b) = -2*d(b) + 22*t(b). Solve p(l) = 0 for l.
2
Factor 0*l + 0 - 2/3*l**5 - 2/3*l**2 - 2*l**4 - 2*l**3.
-2*l**2*(l + 1)**3/3
Let v be 2/(-3)*3/(-12). Let s(z) be the second derivative of 0*z**2 + v*z**3 + 0 + 2*z + 1/20*z**5 + 1/6*z**4. Solve s(k) = 0 for k.
-1, 0
Let a(x) be the third derivative of x**8/336 - x**6/40 - x**5/30 + 2*x**2 - 1. Find k such that a(k) = 0.
-1, 0, 2
Let m(h) be the third derivative of h**5/20 - h**4 + 7*h**3/2 + 4*h**2 - 7*h. Suppose m(a) = 0. What is a?
1, 7
Let u(n) be the second derivative of n**6/240 - 3*n**5/160 + n**4/96 + n**3/16 - n**2/8 + 4*n. Suppose u(s) = 0. Calculate s.
-1, 1, 2
Let p(y) = -2*y**5 + 7*y**4 + 9*y**3 + y**2 - 7*y + 7. Let s(c) = c**4 + c**3 + c**2 - c + 1. Let o(b) = -p(b) + 5*s(b). Factor o(a).
2*(a - 1)**3*(a + 1)**2
Factor 21*u**2 + 4*u**3 + 250 - 6*u**3 + u**2 + 8*u**2 - 150*u.
-2*(u - 5)**3
Suppose s + 0 = 2. Factor -2/9 - 4/9*n - 2/9*n**s.
-2*(n + 1)**2/9
Let q(j) = -j**2 + 1. Let m be q(0). Let w be (m/3)/((-3)/(-27)). Factor 0*i - i**3 + 0*i + w*i**3.
2*i**3
Let v(a) be the first derivative of -2*a**4 - 26*a**3/3 - 3*a**2 + 11. Factor v(w).
-2*w*(w + 3)*(4*w + 1)
Let s = 340/3 + -113. Factor 1/3*v**2 - 1/3*v**4 - 1/3*v**3 + s*v**5 + 0*v + 0.
v**2*(v - 1)**2*(v + 1)/3
Let a(g) be the third derivative of g**6/200 + 2*g**5/25 - 26*g**2. Suppose a(w) = 0. What is w?
-8, 0
Suppose 8*q = 5*q + 54. Determine h, given that -h**2 + 3*h**2 - h**2 + q + h**2 + 12*h = 0.
-3
Let n(d) be the second derivative of 3/50*d**5 + 2/75*d**6 + 1/210*d**7 - d + 1/30*d**3 + 0*d**2 + 0 + 1/15*d**4. Let n(m) = 0. What is m?
-1, 0
Let v(u) be the second derivative of 0 + 1/12*u**4 + 0*u**2 + 0*u**3 + u. Factor v(r).
r**2
Factor 5/2*k - 5/2 + 5/2*k**2 - 5/2*k**3.
-5*(k - 1)**2*(k + 1)/2
Let x(l) = 19*l - 2. Let v be x(1). Factor 24*s - 41*s - s**2 + v*s.
-s**2
Let v be ((-2)/(-4))/(18/4). Let w(p) be the third derivative of -1/180*p**6 + 0*p + 1/90*p**5 - v*p**3 + 0 - p**2 + 1/36*p**4. Find b such that w(b) = 0.
-1, 1
Let u be ((2 - 0) + -2)/(-2). Let m(t) = t - 6. Let j be m(8). Solve u*y**j + 1/4*y**3 + 0*y**4 - 1/4*y**5 + 0*y + 0 = 0.
-1, 0, 1
Let r = 9 - -4. Suppose -r = -2*b - 5. Solve -1/4*g**b + 0 + 0*g + 0*g**2 + 0*g**3 = 0 for g.
0
Solve 4*q**3 - 239*q**2 + 239*q**2 - 4*q**4 = 0.
0, 1
Solve -54*i**2 - 11*i**5 + 6*i**2 - 17*i**5 + 48*i**4 - 16*i + 44*i**3 + 0*i**5 = 0.
-1, -2/7, 0, 1, 2
Let s(a) be the third derivative of 0*a**5 + 0*a + 0*a**3 + 0*a**4 - 2/945*a**7 + 1/540*a**6 + 1/1512*a**8 + 0 - 2*a**2. Factor s(u).
2*u**3*(u - 1)**2/9
Let i = -1/4 + 9/20. Factor 1/5*m**3 + i*m + 2/5*m**2 + 0.
m*(m + 1)**2/5
Factor -3*v**2 - 4*v**2 - 16 + 3*v**2 + 4*v**4 + 4*v**5 - 20*v**3 + 0*v**2 + 32*v.
4*(v - 1)**3*(v + 2)**2
Suppose -3*u = -u - k + 2, -4*k - 7 = -3*u. Let b = 5 + u. Solve 80*n - 34*n**b - 8 + 524*n**3 - 154*n**3 - 226*n**2 - 14*n**2 - 168*n**4 = 0 for n.
1/4, 2/7, 2/3, 1
Let c(w) be the third derivative of w**7/1155 - w**6/330 - w**5/110 + 3*w**2. What is u in c(u) = 0?
-1, 0, 3
Let a(y) be the third derivative of 1/30*y**5 + 9*y**2 + 0*y + y**3 + 0 + 1/3*y**4. Let a(o) = 0. Calculate o.
-3, -1
Suppose -3*n = -12 - 33. Let x be (-2)/10 + 3/n. Factor 2/3*y**2 + 0 + 8/3*y**4 + 10/3*y**3 + x*y.
2*y**2*(y + 1)*(4*y + 1)/3
Let z(u) be the first derivative of 0*u + 0*u**4 - 4/3*u**3 + 4/5*u**5 - u**2 + 1/3*u**6 - 2. Suppose z(j) = 0. What is j?
-1, 0, 1
Let y = 481/18 + -49/2. Find t, given that -4/3*t**3 + 2/9*t**4 - y*t + 2/3 + 8/3*t**2 = 0.
1, 3
Let g(b) be the second derivative of b**6/70 + 8*b. Factor g(h).
3*h**