i). Let p be m(3). Factor k + 2*k**2 - k**5 + p*k**3 + 3*k**4 + 0*k**3 - 5*k**4.
-k*(k - 1)*(k + 1)**3
Determine n, given that -2/3 - 4*n**2 - 2/3*n**4 + 8/3*n**3 + 8/3*n = 0.
1
Let t(b) = -3*b**2 + 3*b + 4. Let v(m) = -13*m**2 + 13*m + 15. Let w(l) = -9*t(l) + 2*v(l). Factor w(f).
(f - 3)*(f + 2)
Let j(a) = a**4 - a**3 + a**2 - 1. Let w(h) = -2*h**5 + 7*h**4 - h**3 + h**2 - 2*h - 3. Let m(x) = -10*j(x) + 2*w(x). Factor m(r).
-4*(r - 1)**3*(r + 1)**2
Let r(p) be the third derivative of 625*p**8/672 + 25*p**7/42 - 35*p**6/6 + 26*p**5/3 - 19*p**4/3 + 8*p**3/3 - 2*p**2 + 8*p. Find g, given that r(g) = 0.
-2, 2/5
Determine u, given that 0 + 51/2*u**3 + 24*u**2 + 15/2*u**4 + 6*u = 0.
-2, -1, -2/5, 0
Let r(y) be the first derivative of -5*y**5/4 - 5*y**4 - 7*y**3/2 - y**2 - 2*y + 4. Let u(p) be the first derivative of r(p). Find d such that u(d) = 0.
-2, -1/5
Suppose 0 = -z - 1 + 3. Let 2*x**5 - 11*x**z - 2*x**3 + 22*x**2 + 2*x**4 - 13*x**2 = 0. What is x?
-1, 0, 1
Find h, given that 1/2*h**2 + 0 + 0*h = 0.
0
Let a(k) = 6*k**2 + 9*k. Let f(o) = o. Let g(t) = -a(t) + 6*f(t). Determine s, given that g(s) = 0.
-1/2, 0
Factor 4/11*i + 0 + 2/11*i**2.
2*i*(i + 2)/11
Let m(b) = 4*b - 1. Let d = 6 - 5. Let l be m(d). Determine o so that 3*o**3 - 3*o - 2 + 5 - 2*o**l - 5 = 0.
-1, 2
Suppose -q - 4 = -3*q. Solve 0 - 1/3*m**q + 1/3*m = 0 for m.
0, 1
Suppose -5 = -4*t - 5*l, 0 = 3*t + 2*l + 2*l - 4. Let -2/13*x**2 + t*x + 2/13 = 0. Calculate x.
-1, 1
Let 1/4*r**3 - 1/2*r**2 + 1/4*r + 0 = 0. What is r?
0, 1
Let 2*y**5 + 3*y**5 + 151*y**3 - 4*y**5 - 155*y**3 = 0. What is y?
-2, 0, 2
Let r(y) be the second derivative of y**7/21 + 2*y**6/15 - y**5/5 - 2*y**4/3 + y**3/3 + 2*y**2 - 2*y. Solve r(a) = 0.
-2, -1, 1
Let p(g) be the third derivative of -5*g**8/336 - g**7/21 + g**6/12 + 2*g**5/3 + 35*g**4/24 + 5*g**3/3 - 12*g**2. Factor p(k).
-5*(k - 2)*(k + 1)**4
Let y = -14/19 - -136/133. Factor 2/7*d**2 - y*d + 0.
2*d*(d - 1)/7
Let l(n) be the first derivative of -4 - 2/3*n**3 - 2*n**2 - 2*n. Let l(r) = 0. Calculate r.
-1
Let i = -5 - 0. Let m = i + 7. Factor j - j**5 - 9*j**2 - 4*j**4 - 2*j + 5*j**m - 6*j**3.
-j*(j + 1)**4
Let l(w) be the second derivative of 0 + 1/6*w**3 + w + 1/40*w**5 - 1/12*w**4 + 0*w**2 - 1/360*w**6. Let b(y) be the second derivative of l(y). Factor b(v).
-(v - 2)*(v - 1)
Let c be ((-1)/2)/((-5)/10). Let x(z) be the first derivative of -c + 1/6*z**3 + 0*z**2 - 1/2*z. Factor x(b).
(b - 1)*(b + 1)/2
Let c(l) be the third derivative of -l**6/30 + l**5/10 - l**4/8 + l**3/6 + 3*l**2. Let i(v) be the first derivative of c(v). Solve i(h) = 0.
1/2
Let b(u) = -u. Let q(g) = -g**2 + 8*g + 4. Let p(j) = -44*b(j) - 4*q(j). Factor p(k).
4*(k - 1)*(k + 4)
Let s = -6 + -2. Let t = 13 + s. Let 2*b**5 + 2*b**3 + 2*b**4 + 2*b**4 + 0*b**t = 0. What is b?
-1, 0
Let n(f) be the second derivative of f**4/114 + f**3/57 - 3*f. Determine u so that n(u) = 0.
-1, 0
Let y(g) = -g + 19. Suppose -2 + 16 = q. Let h be y(q). Determine p, given that -2/3*p**h + 0 + 0*p + 2/3*p**2 + 2/3*p**3 - 2/3*p**4 = 0.
-1, 0, 1
Let y be -2*(9/6)/1. Let h be (y/2)/(2/(-4)). Factor -g**3 - g**2 + g + 3*g**4 - 2*g**3 - 2*g**4 + 2*g**h.
g*(g - 1)**2*(g + 1)
Let m(t) be the first derivative of -t**5/10 - t**4/8 - 4. Find v such that m(v) = 0.
-1, 0
Let t(w) be the second derivative of -w**7/84 + w**6/180 + w**5/40 - w**4/72 - 7*w. Determine p, given that t(p) = 0.
-1, 0, 1/3, 1
Let i(a) = -3*a**4 + 9*a**3 + 3*a**2 + 15*a. Let s(j) = -j**3 - j. Let q(d) = i(d) + 12*s(d). Find t such that q(t) = 0.
-1, 0, 1
Let d(f) be the second derivative of f**6/10 + 3*f**5/5 + 5*f**4/4 + f**3 - 16*f. Factor d(a).
3*a*(a + 1)**2*(a + 2)
Let o(u) be the first derivative of -u**4/4 - 2*u**3 + 15*u**2/2 - 8*u + 11. Factor o(j).
-(j - 1)**2*(j + 8)
Factor -4*l**2 + 2*l**2 + 2*l**3 - 2*l**4 - 6*l**3.
-2*l**2*(l + 1)**2
Let s(l) = l**3 - l**2 + l - 1. Let c(x) = 5*x**3 - 3*x**2 - 21*x - 35. Let a(f) = c(f) - 3*s(f). Let a(v) = 0. Calculate v.
-2, 4
Suppose -6 = -z - 2*u, 5*z - 8 - 4 = -u. Suppose 8 = 3*r - 1. Solve 0*p**z - 2*p**5 + p**2 + p**2 - 6*p**r + 6*p**4 = 0 for p.
0, 1
Let y(t) be the second derivative of -1/36*t**4 + 0 + 0*t**3 + 2*t + 0*t**2. Determine b, given that y(b) = 0.
0
Find j, given that 0*j**3 - 2/9*j**4 + 2/3 + 4/3*j**2 + 16/9*j = 0.
-1, 3
Let a(f) = f**3 + f**2 + f. Let q(z) = 14*z**5 - 4*z**4 + 18*z**2 + 14*z. Let t(i) = -28*a(i) + 2*q(i). Find n, given that t(n) = 0.
-1, 0, 2/7, 1
Suppose -3*p = -9 - 3. Factor -4*v**2 - p*v**2 - 2*v - 5*v**3 + 2*v**2 - v**3 - 2*v**4.
-2*v*(v + 1)**3
Let t(l) be the second derivative of 0*l**2 - 4*l + 1/100*l**5 + 3/10*l**3 + 0 + 1/10*l**4. Determine a, given that t(a) = 0.
-3, 0
Let v(r) = -6 + 3*r**2 - r**2 + r**2 + 9*r**4 - 9*r + 3*r + 6*r**3. Let a(c) = c**4 + c**2 - 1. Let n(h) = 6*a(h) - v(h). Solve n(z) = 0.
-2, -1, 0, 1
Let n(o) = o**3 - 5*o**2 - 5*o - 2. Let a be n(6). Suppose 6*z = -a*p + 3*z + 15, 5*p - 5 = -z. Find k such that 1/5*k**3 + 0*k + p*k**2 + 0 = 0.
0
Let s(m) be the third derivative of -m**5/150 + m**4/15 - 4*m**3/15 + 2*m**2. Factor s(x).
-2*(x - 2)**2/5
Let x(v) be the third derivative of -v**7/105 + 11*v**6/60 - 6*v**5/5 + 4*v**4/3 + 64*v**3/3 - 12*v**2. Suppose x(r) = 0. Calculate r.
-1, 4
Let u(y) = -y**3 - 3*y**2 + 3*y + 4. Let q be u(-4). Let a = q + -6. Determine k so that -2*k + 6*k - 4*k**2 - 2 + 2*k**a = 0.
1
Let t(h) = 4*h**4 - 8*h**3 + 8*h**2 - 2. Let l(s) = 17*s**4 - 33*s**3 + 33*s**2 + s - 9. Let i(z) = 2*l(z) - 9*t(z). Suppose i(b) = 0. What is b?
0, 1
Suppose 4*b - 3*k = -6, k + 2 = b + 2*k. Let r(c) be the first derivative of -3 + b*c**2 + 1/3*c**3 + 0*c. Find w such that r(w) = 0.
0
Let m(t) be the third derivative of t**8/168 - t**6/60 + 6*t**2. Solve m(v) = 0 for v.
-1, 0, 1
Let u = 2423/5 + -483. Let m = -76/85 + 22/17. Factor u*o + m*o**2 + 8/5.
2*(o + 2)**2/5
What is p in -2/5*p**2 + 0*p - 2/5*p**4 + 4/5*p**3 + 0 = 0?
0, 1
Solve 2/13*j**5 - 2/13*j**4 - 2/13 + 4/13*j**2 + 2/13*j - 4/13*j**3 = 0 for j.
-1, 1
Let m(l) = -5 + 6*l - 2 - 5*l. Let o be m(7). Suppose -2/3*g**3 + 4/3*g - 2/3*g**2 + o = 0. What is g?
-2, 0, 1
Let b be ((-32)/120)/(20/(-6)). Let y = 36/175 + b. Suppose 0 + 0*w**4 + 0*w**2 + 2/7*w**5 - 4/7*w**3 + y*w = 0. What is w?
-1, 0, 1
Let s be 4/(-26) + 170/936. Let b(r) be the third derivative of 0*r - 1/90*r**5 + 0 + 0*r**3 - s*r**4 + 2*r**2. Suppose b(m) = 0. Calculate m.
-1, 0
Suppose 5*f = -3*k + 8, 0*f + k = 3*f - 16. Let z(q) be the first derivative of -f*q**2 + 2*q + 8/3*q**3 + 2. Factor z(v).
2*(2*v - 1)**2
Let x be 242/120 + 2*(-5)/5. Let d(m) be the third derivative of 1/300*m**6 + 1/150*m**5 + 0*m**3 - 1/525*m**7 - x*m**4 + 0*m + 0 - m**2. Solve d(g) = 0 for g.
-1, 0, 1
Let g(l) = 20*l**4 - 8*l**3 - 5*l**2 - 5*l + 5. Let q(m) = -10*m**4 + 4*m**3 + 3*m**2 + 3*m - 3. Let k(y) = 6*g(y) + 10*q(y). Factor k(n).
4*n**3*(5*n - 2)
Let p be (-12)/(-54) + 6/(-27). Let n(t) be the first derivative of p*t**2 + 4/15*t**5 + 0*t**3 + 1/6*t**4 + 0*t + 1/9*t**6 + 2. Factor n(i).
2*i**3*(i + 1)**2/3
Suppose 0*c + 12 = 3*c. Let r = 2 + 2. Find t, given that 14*t**3 - 2*t**4 - t**c - 4*t**4 - 4*t**2 - 3*t**r = 0.
0, 2/5, 1
Suppose -4*a = -a. Let q be a/((-2)/(0 + -2)). Factor -1/4*p**2 + 0*p + q.
-p**2/4
Let x be (((-99)/(-24))/3)/((-2)/(-56)). Factor -49/2*t**3 - x*t**2 - 2 - 16*t.
-(t + 1)*(7*t + 2)**2/2
Let n = 148/443 - 1/1329. Let z(j) = -j**3 - 4*j**2 - 5*j - 2. Let x be z(-3). Factor 2/3 + n*r**x - r**2 + 1/3*r - 1/3*r**3.
(r - 2)*(r - 1)*(r + 1)**2/3
Suppose -5*k + 322 = -98. What is t in -3*t - k*t**4 + 119*t**2 - 6 + 3*t**3 - 29*t**2 + t**3 - t**3 = 0?
-1, -1/4, 2/7, 1
Let i(n) = n + 9. Let l be i(-7). Suppose 0 = -l*z + 8, 0*t + 11 = 5*t - z. Let 0*w + 4/3*w**t + 0 - 2/3*w**2 - 2/3*w**4 = 0. Calculate w.
0, 1
Solve -k**2 + 3*k**3 + 5*k**2 + 2*k**4 - 4*k**4 - k**5 - 4*k + 0*k**2 = 0.
-2, 0, 1
Let z(u) be the third derivative of u**5/90 + 5*u**4/36 + 4*u**3/9 - 61*u**2. Factor z(h).
2*(h + 1)*(h + 4)/3
Let w be 2 - ((-2)/60 - -2). Let q(x) be the second derivative of 0*x**2 + 1/9*x**3 + 1/18*x**4 - w*x**5 + 0 - x - 1/45*x**6. Determine i so that q(i) = 0.
-1, 0, 1
Solve 2*j - 4*j**2 + 0*j + 0*j**5 + 4*j**4 - 2*j**5 = 0.
-1, 0, 1
Factor -3/5*q**5 - 21/5*q**4 - 66/5*q**2 - 39/5*q - 54/5*q**3 - 9/5.
-3