(y - 3)**2*(y - 1)**2
Suppose 0 = -5*k + 4*x + 32, -2*x - 22 = -5*k + 4. Determine f, given that 0*f**2 - 1 - 2 + 2*f**2 - 3*f**2 + k*f = 0.
1, 3
Let h(g) be the third derivative of -g**10/30240 + g**9/5040 - g**7/630 + g**4/8 + g**3/2 - 9*g**2 - 4. Let s(c) be the second derivative of h(c). Factor s(w).
-w**2*(w - 2)**2*(w + 1)
Let 2*n**4 - 69*n**2 + 38*n - 54*n**3 + 16*n**3 + 67*n**2 = 0. Calculate n.
-1, 0, 1, 19
Let l(k) = 2*k - 7*k**3 + 2*k**3 + k**3. Let r(p) = 1144*p - 1142*p + 1 - p**2 + 0*p**2 - 5*p**3. Let w(a) = -3*l(a) + 2*r(a). Factor w(b).
2*(b - 1)**2*(b + 1)
Let b = 331/12 - 82/3. Let y(g) be the second derivative of 3*g - b*g**2 - 1/2*g**4 + 1/4*g**5 - 1/20*g**6 + 1/2*g**3 + 0. Factor y(r).
-(r - 1)**3*(3*r - 1)/2
Let f(l) = 3*l**4 + 35*l**3 + 45*l**2 + 13*l + 7. Let g(s) = -4*s**4 - 36*s**3 - 44*s**2 - 12*s - 6. Let a(j) = 6*f(j) + 7*g(j). Find o, given that a(o) = 0.
-3, -1, -1/5, 0
Let h(b) be the third derivative of -b**5/330 - 3*b**4/44 + 2*b**3/3 - 330*b**2. Let h(y) = 0. What is y?
-11, 2
Let k(d) = -d**2 + 10*d - 1. Let u be k(8). Suppose i = -10*w + 8*w + 6, 4*i - 5*w + u = 0. Factor 2*r**2 - 2/3*r**4 + 0 + i*r + 4/3*r**3.
-2*r**2*(r - 3)*(r + 1)/3
Suppose -10*v = -5*v - 8*v. Let w(s) be the second derivative of 1/120*s**6 + 0*s**3 + 1/8*s**2 - 3*s + v*s**5 - 1/24*s**4 + 0. Factor w(u).
(u - 1)**2*(u + 1)**2/4
Let o = -56048/7 - -8007. Suppose 23/7*f**2 + 12/7 - 8/7*f**3 + o*f**4 - 4*f = 0. What is f?
1, 2, 3
Suppose -4*r + 5*s = -10, -r + s - 12 = -3*r. Suppose 5*f - 20 = 5*q, -r*f + 21 = -f + q. Factor f*b**5 + b**3 - b**5 - 4*b**5 - b**5.
-b**3*(b - 1)*(b + 1)
Let y(q) be the first derivative of 5*q**9/3024 - q**7/42 + q**6/36 + q**5/8 - 5*q**4/12 - q**3 + 13. Let f(i) be the third derivative of y(i). Solve f(n) = 0.
-2, -1, 1
Let o(s) = s**3 + 10*s**2 + 18*s + 52. Let g be o(-8). Let t be (8/g*-6)/((-6)/9). Factor t*f + 2401/8*f**5 + 0 + 147*f**3 - 343*f**4 - 28*f**2.
f*(7*f - 2)**4/8
Let d(a) = 3*a**3 - 39*a**2 + 69*a + 105. Let p(z) = 3*z**3 - 37*z**2 + 70*z + 106. Let r(t) = -2*d(t) + 3*p(t). What is f in r(f) = 0?
-1, 6
Let v(p) = -p**3 - p**2 - 10*p - 4. Let d(o) = 84*o - 11*o + 27 - 4*o + 4*o**3 + 2*o**3 + 6*o**2. Let y(x) = -4*d(x) - 27*v(x). Factor y(m).
3*m*(m - 1)*(m + 2)
Suppose 3*w = 3, 5 + 1 = 5*t - 4*w. Factor -a**4 + 3*a**t - 2*a**3 + 7 - 7.
-a**2*(a - 1)*(a + 3)
Let n be (-63)/(-21) - (-40)/(-15). Let r(k) be the first derivative of 2/3*k + n*k**4 + 8/9*k**3 + 10/9*k**2 + 2/45*k**5 + 5. Factor r(j).
2*(j + 1)**3*(j + 3)/9
Let x(u) be the third derivative of -u**6/360 - u**5/36 - u**4/9 - 2*u**3/9 - 39*u**2. Solve x(k) = 0 for k.
-2, -1
Solve 34/7*o - 2/7*o**4 + 6/7*o**2 - 10/7*o**3 + 20/7 = 0 for o.
-5, -1, 2
Let s = -345 + 345. Let x(h) be the third derivative of s - 1/21*h**7 + 2*h**2 + 0*h**4 + 1/42*h**8 + 0*h + 0*h**3 + 1/60*h**6 + 0*h**5. Factor x(k).
2*k**3*(k - 1)*(4*k - 1)
Let a(c) be the first derivative of -5*c**3/18 + 10*c**2 - 120*c - 49. Solve a(s) = 0 for s.
12
Let o(b) = b**2 + b - 3. Let n(z) = 5*z**2 + 20*z + 21. Let c(h) = n(h) - 2*o(h). Factor c(k).
3*(k + 3)**2
Let x(b) be the second derivative of -23*b - 1/4*b**4 - 3/100*b**5 + 0*b**2 + 0 + 3/5*b**3. Determine a so that x(a) = 0.
-6, 0, 1
Let a(y) be the second derivative of 3*y**5/140 + 13*y**4/28 - y**3/14 - 39*y**2/14 + 22*y. Factor a(w).
3*(w - 1)*(w + 1)*(w + 13)/7
Let c = -7042 - -35032/5. Let b = -34 - c. Factor -24/5*t + 26/5*t**2 + 2/5*t**4 - 12/5*t**3 + b.
2*(t - 2)**2*(t - 1)**2/5
Let b(m) be the first derivative of -m**6/30 - 3*m**5/10 - 13*m**4/12 - 2*m**3 - 2*m**2 + 2*m + 39. Let o(w) be the first derivative of b(w). Factor o(i).
-(i + 1)**2*(i + 2)**2
Let q(s) be the first derivative of 3*s**5/5 - 7*s**4/2 - 131*s**3/9 - 18*s**2 - 28*s/3 - 703. Factor q(o).
(o - 7)*(o + 1)*(3*o + 2)**2/3
Let h(x) = 2*x**4 + 6*x**3 + 2*x**2 - 6*x + 5. Let d(u) = -u**4 - 5*u**3 - 2*u**2 + 8*u - 6. Let g(a) = 3*d(a) + 2*h(a). Let g(w) = 0. What is w?
-2, 1, 2
Let i(d) be the first derivative of -3*d**5/5 + 30*d**4 - 546*d**3 + 4056*d**2 - 6591*d - 214. Suppose i(r) = 0. Calculate r.
1, 13
Let v(n) be the first derivative of -n**3/6 - n**2/2 - n/2 - 20. Factor v(p).
-(p + 1)**2/2
Suppose -3*z = 3 + 9. Let x be 30/z*6/(-33) + -1. Suppose 2/11*t**2 + 2/11 + x*t = 0. Calculate t.
-1
Let k(w) = 3*w**3 + w**2 - 3*w - 5. Let v(o) = o**3 - o**2 - o - 1. Let x(z) = k(z) - 2*v(z). Determine f so that x(f) = 0.
-3, -1, 1
Let l(w) be the third derivative of -w**5/300 + 257*w**4/60 - 66049*w**3/30 - 27*w**2 + 2*w. Solve l(a) = 0.
257
Let r(n) be the second derivative of -n**5/100 - n**4/10 + n**3/2 - 4*n**2/5 + 150*n + 1. Factor r(b).
-(b - 1)**2*(b + 8)/5
Let k(j) = 31*j**2 - 3*j - 2. Let t be k(-2). Let i be t/(-56)*1/(-4). Determine s so that 2/7 - 10/7*s**4 + 4/7*s**3 + i*s**5 - 8/7*s + 8/7*s**2 = 0.
-1, 1/2, 1
Let m(x) be the first derivative of -x**6/240 + x**5/60 + 12*x**2 + 8. Let f(t) be the second derivative of m(t). Let f(k) = 0. What is k?
0, 2
Factor -1/6*i**3 - 49/2*i + 7/2*i**2 + 343/6.
-(i - 7)**3/6
Let k(y) be the third derivative of -y**8/23520 + y**7/4410 - y**6/2520 + 13*y**4/24 + 28*y**2. Let b(c) be the second derivative of k(c). Solve b(h) = 0.
0, 1
Let o(g) be the first derivative of 10*g**6/3 + 692*g**5/5 + 425*g**4 + 1148*g**3/3 - 68*g**2 - 256*g + 437. Suppose o(j) = 0. Calculate j.
-32, -1, 2/5
Suppose 54 - 102 = -4*l. Let r = -35 + 37. Let 3/4*h**4 - 12 + l*h + 0*h**r - 3*h**3 = 0. Calculate h.
-2, 2
Let t = -13912/9 - -1546. Factor 0 - t*h - 2/9*h**2.
-2*h*(h + 1)/9
Suppose -18 = -3*z + 3. Let l = 9 - z. Let -1 + 0 - 3*w + 8*w - w**l - 3*w = 0. Calculate w.
1
Let q(l) be the third derivative of 1/180*l**5 + 19*l**2 + 0*l + 1/36*l**4 - 1/360*l**6 + 0 + 0*l**3. Factor q(v).
-v*(v - 2)*(v + 1)/3
Factor -28/3*s**2 + 0*s + 1/3*s**3 + 0.
s**2*(s - 28)/3
Let b(z) be the third derivative of 7*z**6/260 - 4*z**5/195 - z**4/39 + 102*z**2. Factor b(v).
2*v*(3*v - 2)*(7*v + 2)/13
Factor -5/4*k**4 + 0 - 5/2*k**3 + 15*k + 55/4*k**2.
-5*k*(k - 3)*(k + 1)*(k + 4)/4
Let f be (-1 - -1) + (-5)/20 + (-17)/(-4). Factor -8/9*a**f + 4/3*a**3 + 0*a**2 + 0*a - 4/9*a**5 + 0.
-4*a**3*(a - 1)*(a + 3)/9
Let p(h) be the first derivative of 0*h - 4/5*h**5 + 4/3*h**3 + 0*h**2 + 0*h**4 - 27. Solve p(v) = 0.
-1, 0, 1
Suppose -5*g = -2*w - 118, 0 = -2*g - g + w + 71. Factor -4*n**3 - 2*n**2 - 2*n**4 - 29*n - g*n + 53*n.
-2*n**2*(n + 1)**2
Factor 0*x + 184/5*x**2 + 0 + 2/5*x**3.
2*x**2*(x + 92)/5
Let z(c) = c**2 - 4*c + 1. Let x(a) = -a**2 - 4*a + 6. Let u be x(-6). Let m(n) = n - 1. Let f(h) = u*m(h) - 2*z(h). Let f(s) = 0. Calculate s.
-1, 2
Let g(l) be the first derivative of l**6/21 - 2*l**5/7 + 3*l**4/7 + 8*l**3/21 - 8*l**2/7 - 43. Factor g(x).
2*x*(x - 2)**3*(x + 1)/7
Let y(i) be the third derivative of -i**7/1155 - 213*i**2. Factor y(x).
-2*x**4/11
Factor -8/5 - 12*c**2 + 68/5*c.
-4*(c - 1)*(15*c - 2)/5
Let i(z) = z**2 + 3*z + 1. Suppose 31 - 86 = -11*t. Let h(a) = a**2 + 3*a. Let l(f) = t*h(f) - 4*i(f). Factor l(q).
(q - 1)*(q + 4)
Let z(f) be the first derivative of f**6/2 - 18*f**5/5 - 9*f**4/2 + 44*f**3 - 153*f**2/2 + 54*f + 20. Find q, given that z(q) = 0.
-3, 1, 6
Let i(j) = -15*j**3 - 37*j**2 - 53*j - 15. Let r(y) = 5*y**3 + 12*y**2 + 18*y + 5. Let z(x) = -3*i(x) - 8*r(x). Find n, given that z(n) = 0.
-1
Suppose -1/8*z**2 + 3/4 + 5/8*z = 0. What is z?
-1, 6
Let i be (7/3)/(5 + -3 + 15/(-18)). Factor 3/2*o**i + 0*o + 0 - 3/4*o**3 - 3/4*o**4.
-3*o**2*(o - 1)*(o + 2)/4
Let o(z) = -2*z**5 - z**3 + z**2 - z + 1. Let v(y) = 9*y**5 + 2*y**4 + 18*y**3 + 5*y**2 + 5*y - 5. Let n(g) = -5*o(g) - v(g). Let n(p) = 0. What is p?
-2, -1, 0, 5
Suppose 0 = 2*f - 14 - 6. Factor 3*y**5 + 10*y**2 - 2*y**5 - f*y**4 - 5*y + 4*y**5.
5*y*(y - 1)**3*(y + 1)
Let y be (-1)/(-3) - (889/(-105) + 8). Let -3/5*w**4 + 0 + y*w**3 + w**2 - 2/5*w = 0. What is w?
-1, 0, 1/3, 2
Suppose 0 = -a + 5*a - 72. Suppose p - 5*k = a, -p = -0*p + 3*k + 6. Factor 5*g**2 + 5*g**2 + g**p - 9*g**2.
g**2*(g + 1)
Let q be (-264 - -277) + (-280)/22. Solve 1/11*u**3 + q*u**2 + 1/11 + 3/11*u = 0.
-1
Let a = -39 + 42. Suppose -8*x + 7*x + j = -a, -5*x - 2*j = -22. Determine k, given that 0*k**2 - 16/5 - 16/5*k + 1/5*k**x + 4/5*k**3 = 0.
-2, 2
Let b(i) = 11*i**2 - 1866*i + 172992. Let m(u) =