Let v(z) = 4*z**4 + 5*z**3 + 15*z**2 + 7*z + 5. Let m(f) = -3*f**4 - 5*f**3 - 13*f**2 - 7*f - 4. Let n(c) = 3*m(c) + 2*v(c). Suppose n(w) = 0. Calculate w.
-2, -1
Let z(s) be the second derivative of 3*s**5/80 + 7*s**4/16 + 11*s**3/8 + 15*s**2/8 + s - 19. Factor z(o).
3*(o + 1)**2*(o + 5)/4
Suppose -q - 2 = -21. Let d = q + -15. Factor -5 + 4*x**2 + 0 + d*x - 3.
4*(x - 1)*(x + 2)
Suppose -l + 0*v + 445 = -v, v + 894 = 2*l. Let u = l - 2236/5. Solve 3/5*h**2 - 9/5*h - 3/5 + u*h**3 = 0 for h.
-1, -1/3, 1
Let n(b) = 20*b**4 - b**5 - 16*b**4 - 5*b + 6*b**3 + 0*b - 4*b**2. Let u(a) = a**4 + a**3 - a**2 - a. Let z = -4 + 3. Let l(d) = z*n(d) + 4*u(d). Factor l(t).
t*(t - 1)**2*(t + 1)**2
Let p be (-2)/(-7) - (-832)/28. Let g be (-4)/(-30) - (-56)/p. Find w, given that 8*w + 0*w**2 + g*w**2 - 3*w**2 - 3*w**2 = 0.
0, 2
Let l(s) be the second derivative of -s**7/280 - s**6/60 - s**5/40 - 5*s**3/2 - 5*s. Let h(y) be the second derivative of l(y). Factor h(n).
-3*n*(n + 1)**2
Factor 9*v**3 - 5*v**5 + 12 + 29*v**2 + 14*v**2 + 27*v - 11*v**4 + 13*v.
-(v - 2)*(v + 1)**3*(5*v + 6)
Let l(t) be the first derivative of 3/2*t**4 + 2/5*t**5 + 14 + 0*t + t**2 + 2*t**3. Factor l(k).
2*k*(k + 1)**3
Let h(i) = 2*i**3 - 6*i**2 - 2*i + 6. Suppose -3*u - 3*f = 9, -8*f + 4*f = 3*u + 14. Let n(z) = z**2 - 1. Let s(l) = u*h(l) + 4*n(l). Factor s(y).
4*(y - 2)*(y - 1)*(y + 1)
Let o be 5/1 - (2886/195)/((-18)/(-5)). Factor -40/9*p - 2*p**2 - o.
-2*(p + 2)*(9*p + 2)/9
Let b(t) be the third derivative of t**7/630 - 7*t**6/360 + t**5/30 - 7*t**2 + 1. Factor b(i).
i**2*(i - 6)*(i - 1)/3
Suppose -13*m + 8*m = -1305. Let l = m + -258. Factor 6/5 + 3/5*t - 6/5*t**2 - 3/5*t**l.
-3*(t - 1)*(t + 1)*(t + 2)/5
Let y(x) be the second derivative of x**6/120 - 89*x**5/80 + 337*x**4/8 - 220*x**3/3 - 484*x**2 + 2*x + 86. Let y(j) = 0. What is j?
-1, 2, 44
Let d(f) be the first derivative of -1/12*f**3 + 7/8*f**2 - 21 - 3/2*f. Factor d(j).
-(j - 6)*(j - 1)/4
Let m(u) be the first derivative of -2*u**3/3 + 21*u**2 + 44*u - 124. Factor m(d).
-2*(d - 22)*(d + 1)
Solve -2/3*n**5 - 20*n - 58/3*n**3 + 16/3 + 86/3*n**2 + 6*n**4 = 0.
1, 2, 4
Factor 28*w + 5*w + 53*w + 24*w**2 - 2*w**3 + 60.
-2*(w - 15)*(w + 1)*(w + 2)
Let n(a) be the first derivative of -a**6/16 + 9*a**5/20 - 27*a**4/32 - a**3/2 + 9*a**2/4 - 326. Find f, given that n(f) = 0.
-1, 0, 2, 3
Let u(f) = -f**3 + f**2 - f + 1. Suppose 5*c + 10 = 0, -2*c - 7 = -l + 3. Let a(g) = -g**4 - 2*g**3 - 2*g**2 + 2*g - 2. Let x(j) = l*u(j) + 3*a(j). Factor x(n).
-3*n**3*(n + 4)
Let s(v) be the third derivative of -1/4*v**4 + 0*v**3 + 0*v - 3/20*v**5 + 0 - 1/24*v**6 - 17*v**2 - 11/1890*v**7 - 1/3024*v**8. Let s(l) = 0. What is l?
-3, -2, 0
Let f(z) be the first derivative of -z**6/8 - 3*z**5/10 + 9*z**4/16 + 2*z**3 + 3*z**2/2 - 115. Let f(x) = 0. Calculate x.
-2, -1, 0, 2
Let r be (-4 - -2)*1/(-1). Suppose -4*g + 4 = 0, r*g = 2*a - g - 11. Factor 4 - 12*o**3 + 18*o**2 + 6*o**2 - 20*o + a*o**2 - 3*o**2.
-4*(o - 1)**2*(3*o - 1)
Let q = -41 + 45. Factor 4*g**2 + 2*g - q*g**2 + 3*g**2 - 5*g**2.
-2*g*(g - 1)
Factor -79*s**2 + 313*s**2 + 2496 - 9126*s - 10681 - 2*s**3 + 78449 + 48374.
-2*(s - 39)**3
Let i = -88 - -157. Let a = 71 - i. Factor 0*s**a + 0 - 22/5*s**5 + 0*s + 4/5*s**4 + 0*s**3.
-2*s**4*(11*s - 2)/5
What is l in 14*l - l**2 - 638 + 0*l**2 + 638 = 0?
0, 14
Suppose 0 - 70/3*v - 2/3*v**2 = 0. What is v?
-35, 0
Let p(t) be the first derivative of -7 + 4*t - 3*t**2 - 5/4*t**4 - 7/3*t**3. Let j(s) = -4*s**3 - 6*s**2 - 5*s + 3. Let v(x) = 4*j(x) - 3*p(x). Factor v(y).
-y*(y + 1)*(y + 2)
Suppose 0 - l - 18*l**3 - 2*l**2 - 1 + 3*l**2 + 19*l**3 = 0. What is l?
-1, 1
Find i such that 7/3*i**2 - 13/3*i + 2 = 0.
6/7, 1
Let o be -21*((2 + 3 - 5) + -55). Let g = 19641/17 - o. Factor 22/17*c + g*c**2 + 12/17.
2*(c + 3)*(3*c + 2)/17
Suppose 12 = -0*z + 3*z. Suppose -8 = -z*d - 0. Factor -6 + 3 - u - 1 - d*u**2 + 7*u.
-2*(u - 2)*(u - 1)
Let v(h) = -5*h**3 - h**2 + 2*h + 7. Let d(j) be the third derivative of -j**6/20 + j**4/12 + 4*j**3/3 + 5*j**2. Let b(x) = 3*d(x) - 4*v(x). Factor b(u).
2*(u - 1)*(u + 1)*(u + 2)
Let c(t) = -25 + 3 + t - 1. Let g be c(23). Factor 6/7*k - 4/7*k**2 + g - 2/7*k**3.
-2*k*(k - 1)*(k + 3)/7
Let l(d) be the first derivative of -39 - 15/2*d**2 + 0*d + 5/3*d**3. Suppose l(u) = 0. Calculate u.
0, 3
Let l = 81 - 71. Let a be -2*(-12)/(-60)*l/(-8). Factor -1/2*t**2 - a + t.
-(t - 1)**2/2
Let w(k) be the third derivative of k**7/2520 - k**6/360 + k**5/120 + k**4/4 - 16*k**2. Let u(j) be the second derivative of w(j). Suppose u(n) = 0. What is n?
1
Let w(z) be the first derivative of z**3/12 + 7*z**2/4 - 15*z/4 + 38. Factor w(u).
(u - 1)*(u + 15)/4
Let f(y) be the second derivative of 20/3*y**3 + 0 - 50*y**2 - 15*y - 1/3*y**4. Let f(d) = 0. Calculate d.
5
Let i(k) be the second derivative of k**7/168 + k**6/36 - k**5/8 + k**3/3 + 17*k**2/2 + 14*k. Let a(c) be the second derivative of i(c). Factor a(l).
5*l*(l - 1)*(l + 3)
Let g(q) = -q**2. Let o(n) = -5*n**2 + 8*n - 16. Let u(h) = -8 - 11 - h + 3 - 1. Let b be u(-16). Let l(i) = b*o(i) + 4*g(i). What is z in l(z) = 0?
4
Suppose -3*p = 5*f - 17, f - 4 = -3*f. Let q be p/6 + 4 + 4/(-6). Factor 0 + 1/5*l**q + 0*l**3 + 2/5*l - 3/5*l**2.
l*(l - 1)**2*(l + 2)/5
Suppose 23 + 43 = 22*d. Let p(h) be the first derivative of 0*h + 5 + 0*h**d + h**4 - 4/5*h**5 + 0*h**2. Determine f so that p(f) = 0.
0, 1
Let a be (-2 - -12)/(-2)*3/(-5). Let t = 2 - -1. Solve 3 + a*r + 7*r**3 + 2*r**t - 15*r**2 + 0*r**3 = 0 for r.
-1/3, 1
Let j(f) = -f**3 - 5*f**2 - 6*f - 4. Let k be j(-4). Suppose 4*t - 4*d = 0, -2*t - d = -t - k. Suppose 0*n - 2/3*n**3 + 0 - 4/3*n**t = 0. What is n?
-2, 0
Let j be (-1)/5 + (-187)/(-85). Solve 25/8 - 5/4*m + 1/8*m**j = 0 for m.
5
Let v be (-10)/(-20)*2*(2 - 2). Let y(f) be the third derivative of -5*f**2 + 0*f + 0 - 1/27*f**3 + v*f**4 + 1/270*f**5. Factor y(m).
2*(m - 1)*(m + 1)/9
Let g = 12 + -181. Let v = -335/2 - g. Factor 0*k + 15/2*k**4 + 0 + v*k**2 - 9*k**3.
3*k**2*(k - 1)*(5*k - 1)/2
Let f = 24 - 21. What is a in -2*a**f + 2*a + 5*a**3 + 3 + 13*a - 9 - 12*a**2 = 0?
1, 2
Let z be (-5 - -4)/(1/(-2)). Suppose 8/5*k**3 + 4/5*k**4 - 4/5*k**z + 0 - 8/5*k = 0. What is k?
-2, -1, 0, 1
Let v(i) be the second derivative of i**5/40 - 25*i**4/24 + 14*i**3 - 36*i**2 + 234*i. Factor v(m).
(m - 12)**2*(m - 1)/2
Let q(m) be the third derivative of m**7/945 + 174*m**2. Factor q(a).
2*a**4/9
Let r(h) be the second derivative of h**4/28 + 4*h**3/7 + 3*h**2/2 + 337*h. Factor r(d).
3*(d + 1)*(d + 7)/7
Let c(k) = -k**5 - k**2. Let v(y) = 7*y**5 + 23*y**4 + 20*y**3 - 30*y**2 - 32*y + 16. Let b(r) = -6*c(r) - 3*v(r). Solve b(a) = 0 for a.
-2, 2/5, 1
Suppose -72 = 56*n - 62*n. Suppose 0 = -j + n*j - 22. Factor 1/3*l**j + 3*l + 2/3 - 4*l**3.
-(l - 1)*(3*l + 2)*(4*l + 1)/3
Let c(g) = 11*g**3 + 2*g**2 - 15*g + 6. Let m(j) = -32*j**3 - 7*j**2 + 42*j - 17. Let r(w) = -17*c(w) - 6*m(w). Solve r(b) = 0 for b.
-1, -3/5, 0
Let u(w) = 2*w**2 + 2*w + 24. Let g(a) = a**2 + 2*a + 24. Let r(y) = 3*g(y) - 2*u(y). Factor r(t).
-(t - 6)*(t + 4)
Let w(c) = 2*c**5 - 14*c**4 - 2*c**3 + 10*c**2. Let m(k) = -k**5 + 12*k**4 + 2*k**3 - 9*k**2 - k. Let s(q) = 4*m(q) + 3*w(q). Factor s(r).
2*r*(r - 1)*(r + 1)**2*(r + 2)
Let j(c) = 2*c**2 + 4*c - 11. Let u(b) = 4*b**2 + 8*b - 7. Let i(l) = -3*l**2 - 7*l + 8. Let p(v) = -3*i(v) - 2*u(v). Let t(w) = -4*j(w) + 5*p(w). Factor t(n).
-3*(n - 2)*(n - 1)
Let n(p) = 18*p - 15 + 2*p**2 + p**2 - 8*p**2 - 7*p**2. Let i(b) = b**2 - b + 1. Let q(w) = -2*w + 31. Let t be q(16). Let z(r) = t*n(r) - 15*i(r). Factor z(a).
-3*a*(a + 1)
Let x(j) be the second derivative of 0 + 25/12*j**4 - 5/3*j**3 - 7*j + 25/4*j**5 + 0*j**2. Factor x(g).
5*g*(5*g - 1)*(5*g + 2)
Suppose 0*h - u = h + 12, -48 = 4*h - 4*u. Let v = h - -14. Factor -6 + 8 + o**v - 2*o**2 - o.
-(o - 1)*(o + 2)
Let o(c) be the third derivative of -1/6*c**4 - 7/45*c**5 + 1/30*c**6 + 0 + 2/63*c**7 - 19*c**2 + 4/9*c**3 + 0*c. Determine z so that o(z) = 0.
-1, 2/5, 1
Let k(a) = -a - 1. Let s(x) = -1 + 15*x - 2*x**2 - 8 + 7 - 1. Let r(f) = -5*k(f) - s(f). Let r(z) = 0. What is z?
1, 4
Let w(x) = x**5 + 17*x**4 - 171*x**3 + 284*x**2 + 7. Let s(a) = -a**4 + 2*a**2 + 1. Let m(l) = -14*s(l) + 2*w(l). Suppose m(t) = 0. What is t?
-30, 0, 3
Suppose