r 2*n**b - 2*n**3 + 4*n**3 - 4*n**4 + 4*n**4 - 4*n**4.
2*n**3*(n - 1)**2
Let k(p) = 2*p**2 - 3*p - 19. Let b(f) = -6*f**2 + 8*f + 56. Let t(h) = 5*b(h) + 16*k(h). Find i such that t(i) = 0.
-2, 6
Let w(t) be the second derivative of -t**8/5040 + t**7/1260 - t**5/180 + t**4/72 + 2*t**3/3 - 4*t. Let l(c) be the second derivative of w(c). Factor l(z).
-(z - 1)**3*(z + 1)/3
Let j(g) = -20*g**4 + 88*g**3 - 168*g**2 + 128*g - 28. Let m(z) = 8*z**4 - 35*z**3 + 67*z**2 - 51*z + 11. Let w(f) = 5*j(f) + 12*m(f). Solve w(k) = 0.
1, 2
Let u = 0 + 3. Factor 10*w**u - 4*w**2 + 0*w**5 + 8*w**3 - 8*w**4 + 10*w**5 - 16*w**4.
2*w**2*(w - 1)**2*(5*w - 2)
Let b = -17 - -19. Factor 8/7*x + 20*x**4 - 40/7*x**b + 0 + 14*x**5 - 6/7*x**3.
2*x*(x + 1)**2*(7*x - 2)**2/7
Let h(j) be the second derivative of j**7/105 + j**6/25 + 3*j**5/50 + j**4/30 - 5*j - 3. Factor h(s).
2*s**2*(s + 1)**3/5
Let d(n) be the second derivative of -n**8/20160 + n**7/1890 - n**6/432 + n**5/180 + n**4/6 - n. Let u(v) be the third derivative of d(v). Factor u(q).
-(q - 2)*(q - 1)**2/3
Let r(f) be the third derivative of 7*f**6/300 - 8*f**5/75 + f**4/15 + 25*f**2. Solve r(y) = 0 for y.
0, 2/7, 2
Let d(l) be the second derivative of 243*l**7/140 - 27*l**6/10 + 9*l**5/5 - 2*l**4/3 - l**3/6 + l. Let o(i) be the second derivative of d(i). Factor o(m).
2*(9*m - 2)**3
Let z(b) be the third derivative of -b**5/20 + b**3/2 - 9*b**2. Factor z(g).
-3*(g - 1)*(g + 1)
Let w(t) = -t**2 - 10*t + 4. Let c be w(-5). Suppose -5*k - 21 = 2*g, -5*k - c = -3*g + g. Factor 0*s + 2/5*s**4 + 0*s**3 - 4/5*s**g + 2/5.
2*(s - 1)**2*(s + 1)**2/5
Let a = 2049/5 + -409. Solve a*l - 2/5*l**2 + 6/5 = 0 for l.
-1, 3
Solve 7/4*i**2 + 9/4*i + 1/2 = 0.
-1, -2/7
Let c = 32/259 + 6/37. Let 0 + 0*p**2 + 0*p + 4/7*p**4 + 2/7*p**5 + c*p**3 = 0. What is p?
-1, 0
Factor 52*a + 8 + 9*a**3 - 32 + 19*a**3 + 46*a**2 + 58*a**2.
4*(a + 1)*(a + 3)*(7*a - 2)
Suppose -8*m - 5 = -3*m. Let f be 4*(m - 12/(-9)). Solve f*h + 2/3*h**2 + 2/3 = 0.
-1
Let v(z) be the first derivative of 4*z**7/273 + 4*z**6/195 + z**5/130 + 5*z + 2. Let b(j) be the first derivative of v(j). Find a such that b(a) = 0.
-1/2, 0
Suppose -4*p - 32 = -4*s, 3*p - 52 = -3*s - p. Let h be (-40)/(-99) - s/66. Find m, given that 2/9 + h*m**4 - 8/9*m - 8/9*m**3 + 4/3*m**2 = 0.
1
Let d(a) be the first derivative of -a**4/14 + 2*a**3/21 + 15. Determine x, given that d(x) = 0.
0, 1
Let r(d) be the third derivative of d**8/336 - d**7/42 + 7*d**6/120 - d**5/20 + 11*d**2. Solve r(k) = 0 for k.
0, 1, 3
Let 18*c**3 - 14*c**3 - 16*c + 4*c**2 - 8 - 8 = 0. What is c?
-2, -1, 2
Let j(c) be the first derivative of -2*c**3/39 + 40*c**2/13 - 800*c/13 - 17. Let j(d) = 0. Calculate d.
20
Suppose 4*t + 3*q = 1 + 10, -1 = -q. Factor -6*h + 3*h**t - 5*h + 12 - h.
3*(h - 2)**2
Let i(f) = -f**3 - 3*f**2 + 4*f. Let q be i(-4). Let j(y) be the second derivative of q + y + 0*y**2 + 1/21*y**3 + 1/14*y**4. Find s such that j(s) = 0.
-1/3, 0
Let h be ((-3)/(-44))/((-27)/(-747)). Let p = -18/11 + h. Solve -1/4*x - p*x**2 + 1/2 = 0.
-2, 1
Let t(u) be the first derivative of -u**6/10 - 3*u**5/20 + u**4/4 + u**3/2 - 6*u - 4. Let s(m) be the first derivative of t(m). Factor s(h).
-3*h*(h - 1)*(h + 1)**2
Let j(c) be the third derivative of 5*c**7/126 - c**6/72 - 4*c**5/45 - c**4/18 + 7*c**2. Factor j(y).
y*(y - 1)*(5*y + 2)**2/3
Let b(m) be the first derivative of -m**3 - 3*m**2 + 1. Factor b(u).
-3*u*(u + 2)
Let c(f) = -f**4 - f + 1. Let q(l) = -11*l**4 + 10*l**2 - 6*l + 1. Let k(y) = -6*c(y) + q(y). Factor k(n).
-5*(n - 1)**2*(n + 1)**2
Let x be (2/(-20))/((-21)/35 - 0). Factor 2/3*p**3 + 0*p + 0 + 5/6*p**4 + 1/3*p**5 + x*p**2.
p**2*(p + 1)**2*(2*p + 1)/6
Let u = -13 - -12. Let d(s) = -s**4 - s**3 - s**2 - s - 1. Let i(l) = -7*l**4 - 3*l**3 - 4*l**2 - 4*l - 4. Let g(x) = u*i(x) + 4*d(x). Factor g(a).
a**3*(3*a - 1)
Let r(l) = l**4 + l**3 - 2*l**2 - 3. Let d(w) = -w**4 - 3*w**3 + 4*w**2 + 5. Let a(j) = 3*d(j) + 5*r(j). What is c in a(c) = 0?
0, 1
Let u(w) = -w**3 + 2*w**2 + 2. Let h be u(2). Suppose -5*o + 2*o - 5*n + 3 = 0, o = 4*n + 18. Factor 3*y**3 - o*y**3 - y**2 + h*y**3.
-y**2*(y + 1)
Let g = 3 + 0. Solve 0*w**2 + 4*w**2 + g - 1 - 6*w = 0.
1/2, 1
Let n be -2 - ((-44)/28 - 1). Let u(p) be the first derivative of -2/7*p**4 + 3 - 4/7*p**2 + 2/7*p + 2/35*p**5 + n*p**3. Factor u(i).
2*(i - 1)**4/7
Let i(z) = 22*z**4 - 2*z**3 - 28*z**2 + 14*z. Let a(d) = 45*d**4 - 5*d**3 - 56*d**2 + 27*d. Let l(c) = 6*a(c) - 11*i(c). What is g in l(g) = 0?
-1, 0, 2/7, 1
Let b(f) be the second derivative of f**7/14 + f**6/10 - 9*f**5/20 - f**4/4 + f**3 - 33*f. Let b(u) = 0. What is u?
-2, -1, 0, 1
Suppose 5*k - 15*k = -30. Let a(u) be the second derivative of 1/3*u**4 + 4/15*u**6 + 7/10*u**5 - 1/3*u**k + 2*u + 0*u**2 + 0. Factor a(d).
2*d*(d + 1)**2*(4*d - 1)
Factor 0 + 1/2*k**5 + 0*k**4 + 1/2*k + 0*k**2 - k**3.
k*(k - 1)**2*(k + 1)**2/2
Let q = 64483/66 + -977. Let u(p) be the second derivative of 0*p**2 + 0 - p - 4/165*p**6 - q*p**4 - 2/55*p**5 + 0*p**3. Let u(g) = 0. Calculate g.
-1/2, 0
Let f be (-85)/(-10) + (-2)/4. Suppose 76*t - 8 - 9*t**2 + f*t + 343*t**3 - 285*t**2 = 0. Calculate t.
2/7
Let h(i) be the third derivative of -i**8/11200 - i**7/4200 - i**4/6 - i**2. Let d(k) be the second derivative of h(k). Factor d(q).
-3*q**2*(q + 1)/5
Suppose -1984 = 5*q - h, -4*q - 901 - 679 = h. Let l be (-6426)/q - 3/2. Determine j so that l*j**2 + 8/11 - 72/11*j = 0.
2/9
Let f = -28 - -57/2. Find p such that -1/2*p**2 + 0 - f*p**3 + 0*p = 0.
-1, 0
Let m = -408 - -2044/5. Let -3/5 - 1/5*o**2 + m*o = 0. Calculate o.
1, 3
Let p(k) be the third derivative of k**6/120 - k**5/45 - k**4/72 + k**3/9 - 21*k**2. Factor p(d).
(d - 1)**2*(3*d + 2)/3
Let n = -345 - -347. Factor 2*h - 4/3 - 2/3*h**n.
-2*(h - 2)*(h - 1)/3
Let w be 66/42 - 8/14. What is r in w - 12*r**2 + 32*r + 76*r**2 + 3 = 0?
-1/4
Let o(w) be the second derivative of -3*w**5/10 - 4*w**4/3 - 4*w**3/3 - 12*w. Factor o(r).
-2*r*(r + 2)*(3*r + 2)
Let c(m) be the third derivative of 0*m + 1/252*m**8 + 0*m**3 - 1/120*m**6 + 0 + 3*m**2 + 1/72*m**4 - 2/315*m**7 + 1/90*m**5. Factor c(k).
k*(k - 1)**2*(2*k + 1)**2/3
Let y(x) be the second derivative of -x**5/4 + 25*x**4/4 - 105*x**3/2 + 245*x**2/2 - 33*x. Let y(u) = 0. Calculate u.
1, 7
Let u = 25/51 - -1/102. Find y such that 3/4*y**5 + 0 + 1/4*y**4 + 0*y - u*y**3 + 0*y**2 = 0.
-1, 0, 2/3
Let u(w) = -w**2 + 4*w - 2. Let s be u(2). Find a, given that -a**2 + 4*a**2 - a - 3*a**s + a**3 = 0.
-1, 0, 1
Let k(w) be the first derivative of w**7/420 + w**6/45 + w**5/12 + w**4/6 - 4*w**3/3 + 4. Let t(s) be the third derivative of k(s). Factor t(g).
2*(g + 1)**2*(g + 2)
Let t = 6 + -2. Factor -4*p**4 + 4*p + 4*p**2 + t*p + 0*p - 4*p - 4*p**3.
-4*p*(p - 1)*(p + 1)**2
Suppose 0 = -5*i + 4 + 16. Suppose -2*g + i*g - 8 = 0, -3*l + 1 = -2*g. Factor -2*r**4 + 7*r - 2 - r + 8*r**l - 12*r**2 + 2*r.
-2*(r - 1)**4
Factor 3181*f**3 + 1464*f**3 + 312*f + 2028*f**2 - 244*f**3 + 16 - 7*f**3.
2*(13*f + 2)**3
Let q(a) be the second derivative of 1/80*a**5 - 4*a + 1/48*a**4 + 0*a**3 + 0*a**2 + 0. Factor q(c).
c**2*(c + 1)/4
Let u(y) be the first derivative of -2*y**5/25 + y**4/10 + 2*y**3/15 - y**2/5 + 31. Factor u(c).
-2*c*(c - 1)**2*(c + 1)/5
Let g(h) = h**3 - 6*h**2 - 7*h. Let r(f) = 6*f**2 + 6*f. Let x(i) = 3*g(i) + 2*r(i). Factor x(b).
3*b*(b - 3)*(b + 1)
Let o(d) be the second derivative of -d**5/270 + d**4/54 - d**2/2 - 4*d. Let i(z) be the first derivative of o(z). Suppose i(n) = 0. What is n?
0, 2
Let k(o) be the first derivative of 49*o**6/51 + 154*o**5/85 + 16*o**4/17 + 8*o**3/51 + 16. Factor k(d).
2*d**2*(d + 1)*(7*d + 2)**2/17
Suppose -4*f + 7*f + 39 = 0. Let i(w) = -w**2 - 14*w - 11. Let j be i(f). Determine d so that -1/2*d**j - 2 + 2*d = 0.
2
Factor -v - 3/4 - 1/4*v**2.
-(v + 1)*(v + 3)/4
Let i(a) be the first derivative of -8*a**3/3 - 11*a**2 - 12*a + 28. Factor i(h).
-2*(h + 2)*(4*h + 3)
Determine b so that -b - 1/4*b**4 + b**3 - 3/4*b**2 + 1 = 0.
-1, 1, 2
Suppose 151 - 155 = -2*z. Factor -1/4*l**3 + 0 - 1/4*l - 1/2*l**z.
-l*(l + 1)**2/4
Let h(v) = 11*v**4 + 6*v**3 - 18*v**2 - 35*v - 12. Let n(x) = 5*x**4 + 3*x**3 - 9*x**2 - 17*x - 6. Let p(i) = -2*h(i) + 5*n(i). Find l such that p(l) = 0.
-1, 2
Factor 6/11*z**3 + 12/11*z + 2*z**2 + 0.
2*z*(z +