 0
Let l(p) be the third derivative of p**6/480 - p**5/24 - 23*p**4/96 - p**3/2 + 2*p**2 + 61. Factor l(x).
(x - 12)*(x + 1)**2/4
Let f(a) = -3*a**2 - 15*a + 12. Let g(l) = l**2 + l. Let o = -4 - -9. Let m(r) = o*g(r) + f(r). Factor m(y).
2*(y - 3)*(y - 2)
Let b be 3/(0 - (-3)/2). Let s(l) = -l**3 - l**2 + l. Let r(h) = -h + 2. Let y be r(6). Let f(x) = x**4 - 2*x**2 - 1. Let q(c) = b*f(c) + y*s(c). Factor q(u).
2*(u - 1)*(u + 1)**3
Let n = -1 - -4. Factor -45*v**3 - 6*v**4 - 29*v**4 + 20*v**5 + 55*v**n + 5*v**2.
5*v**2*(v - 1)**2*(4*v + 1)
Let s(u) = 120*u**2 - 100*u - 65. Let h(y) = -11*y**2 + 9*y + 6. Let i(x) = -65*h(x) - 6*s(x). Let i(n) = 0. What is n?
0, 3
Let u be (2 + -2)/(3 + -2). Let s(p) be the third derivative of 1/24*p**4 - 1/120*p**6 + 2*p**2 + 0*p + 0 + 0*p**3 + u*p**5. Factor s(f).
-f*(f - 1)*(f + 1)
Let a be (2/4)/((-2)/(-8)). Let p be (1/a)/(4/152). Determine m so that 31*m**2 + p*m + 5 + 21*m + 49*m**2 = 0.
-1/4
Let t(j) = -j**2 + 4*j - 3. Let d be t(2). Let n = -1/3 + d. Factor 0 + n*l - 1/3*l**2.
-l*(l - 2)/3
Let b(o) be the second derivative of 0*o**2 + 5/3*o**4 + 0 + 5/6*o**3 + 2/3*o**6 + 5/42*o**7 - 4*o + 3/2*o**5. Suppose b(l) = 0. What is l?
-1, 0
Determine q so that -283*q**2 - 355*q - 192 - 51*q**3 - 170*q - 3*q**4 + 4*q**2 - 102 = 0.
-7, -2, -1
Let k(l) = l**2 + 1. Suppose 4*w = 5*w + 1. Let b(o) = -8*o**2 - 6 - 3*o - 2*o + 3*o. Let n(j) = w*b(j) - 6*k(j). Factor n(s).
2*s*(s + 1)
Let l(x) be the second derivative of -4*x**2 + 0 + 1/3*x**4 + 30*x - 2/3*x**3. Suppose l(q) = 0. What is q?
-1, 2
Let l be -1*6*1*5/(-10). Factor 9 - 15*s + l*s**2 + 47*s**3 + 47*s**3 - 91*s**3.
3*(s - 1)**2*(s + 3)
Let a be -4 - (-55 + 6)/1. Suppose 3*p = -o + 2*p + 189, -2*p = o - 194. Factor -a*y**4 - 69*y**4 + 36*y**5 + 36*y - 120*y**2 - 18*y**4 - 4 + o*y**3.
4*(y - 1)**3*(3*y - 1)**2
Let d be 426/30 - (-1)/(-5). Suppose -2*t - 5*t + d = 0. Suppose -8/11*h**t + 4/11 + 6/11*h**3 - 2/11*h = 0. What is h?
-2/3, 1
Let i(p) = 25*p**2 + 9205*p + 355845. Let d(n) = -2*n**2 - 767*n - 29654. Let a(m) = 35*d(m) + 3*i(m). Factor a(t).
5*(t + 77)**2
Let k(x) be the third derivative of x**8/168 + 2*x**7/21 + 11*x**6/20 + 4*x**5/3 + 4*x**4/3 + 94*x**2 + 1. Suppose k(i) = 0. What is i?
-4, -1, 0
Let x(z) = z**3 - 35*z**2 - 35*z - 34. Let y be x(36). Factor y*f - 2/3*f**2 - 4/3.
-2*(f - 2)*(f - 1)/3
Let r = -474 - -476. Let m be 10/9*6/30. Suppose 0 - 2/9*f - m*f**r = 0. Calculate f.
-1, 0
Let h = -29 + 33. Solve -6*m - 18*m**2 + 0*m**5 - 2*m**5 + 8*m**3 + 22*m**2 - h = 0 for m.
-1, 1, 2
Let u(f) = -105*f**2 - 10*f. Let j(c) be the first derivative of 35*c**3 + 5*c**2 + 18. Let s(q) = -3*j(q) - 2*u(q). Factor s(x).
-5*x*(21*x + 2)
Let k(n) be the second derivative of n**4/2 - 5*n**3/6 - 3*n**2/2 - 2*n. Let u(h) = 5*h**2 - 4*h - 3. Let i(j) = -3*k(j) + 4*u(j). Factor i(m).
(m + 1)*(2*m - 3)
Let d(z) be the second derivative of 0 - 1/90*z**6 + 0*z**4 + 13*z + 0*z**2 - 1/30*z**5 + 0*z**3. Find u, given that d(u) = 0.
-2, 0
Let v(u) be the third derivative of -u**8/100800 + u**6/3600 - 11*u**5/60 + 3*u**2. Let m(a) be the third derivative of v(a). Factor m(w).
-(w - 1)*(w + 1)/5
Suppose 2*o = 0, -2*o - 1424 = p - 3*p. Factor 26*k**4 - 688*k - 64 - 2520*k**2 - 299*k**3 - 3033*k**3 - p*k**4.
-2*(k + 4)*(7*k + 2)**3
Let y = 10168/5 - 2033. Let -y*j**4 - 3/5*j**3 + 0*j + 0*j**2 + 0 = 0. What is j?
-1, 0
Find c such that 5*c**3 - 5*c**4 + 8*c + c - 14*c**3 - 26 + 7*c**2 + 18 + 6 = 0.
-2, -1, 1/5, 1
Let q(d) be the third derivative of -2*d**7/245 - d**6/30 - d**5/140 + d**4/14 + 2*d**3/21 - d**2 + d. Find u, given that q(u) = 0.
-2, -1/2, 2/3
Factor -72/5*l - 3/5*l**2 - 432/5.
-3*(l + 12)**2/5
Let o(t) = -t**3 + 7*t**2 - 4*t - 9. Suppose 0 = -2*n - 2*n + 24. Let a be o(n). Find i such that 9/5*i**a - 4/5*i**5 + 0*i - 3/5*i**4 - 2/5*i**2 + 0 = 0.
-2, 0, 1/4, 1
Suppose -2*y = 5*q + 383 - 408, 12 = -q + 3*y. Factor 0 - 4/9*x + 16/3*x**q - 44/9*x**2.
4*x*(x - 1)*(12*x + 1)/9
Let r(q) be the second derivative of -q**5/4 + 5*q**4/3 - 5*q**3/6 - 15*q**2 + 30*q. Suppose r(x) = 0. Calculate x.
-1, 2, 3
Factor -11*x**3 - 8*x**3 - 80*x**2 - 1024 + 512*x - 13*x**3 + 42*x**3 - 6*x**3.
4*(x - 8)**2*(x - 4)
Suppose -24 = 15*h - 19*h. Let j = 7 - h. Factor 9*b**2 + 2 + 16*b**2 - j + 10*b + 0*b**2.
(5*b + 1)**2
Let v = 39 + -36. Factor -v*u**2 + 7 - 20*u + 11*u**2 + 1 - 4*u**2 + 8*u**3.
4*(u - 1)*(u + 2)*(2*u - 1)
Let v(h) = 7*h**2 - 3*h. Let r be 6 - (-1 - 12/(-4)). Suppose 24 = -b + r*b. Let u(a) = 11*a**2 - 5*a. Let l(d) = b*v(d) - 5*u(d). Factor l(g).
g*(g + 1)
Let a(k) be the third derivative of k**8/224 - 3*k**7/140 + k**6/80 + 3*k**5/40 - k**4/8 - 2*k**2 + 66. Suppose a(u) = 0. What is u?
-1, 0, 1, 2
Let o(s) be the second derivative of s**7/1470 - s**6/210 + s**5/70 - s**4/42 - s**3/3 + 23*s. Let g(l) be the second derivative of o(l). Factor g(r).
4*(r - 1)**3/7
Let q = -424101/10 + 42450. Let o = q - 79/2. Factor 18/5*n**3 - 2*n + 6/5*n**2 + o.
2*(n + 1)*(3*n - 1)**2/5
Let w = -6 - -14. Solve 2*u**2 + u**2 - 94 + 78 - 4*u**2 - w*u = 0 for u.
-4
Solve -17*i**2 - 30 + 175*i + 75*i**3 - 223*i**2 + 268*i**4 - 248*i**4 = 0 for i.
-6, 1/4, 1
Let j be 2/5*1929/3. Let o = 258 - j. Factor -1/5*v**5 - 1/5*v + 4/5*v**4 + 0 + o*v**2 - 6/5*v**3.
-v*(v - 1)**4/5
Let b be -1*4/(-4)*3. Let z(j) = j**2 + 3*j + 4. Let d be z(-3). Factor f**b + d*f - f - 4*f**3.
-3*f*(f - 1)*(f + 1)
Let x be 9/6*2/15. Factor -3/5*j + 0 + x*j**2.
j*(j - 3)/5
Factor 12*l - 196*l**2 + 391*l**2 + 8 + 6 - 191*l**2 - 6.
4*(l + 1)*(l + 2)
Factor 52/5*k + 2/5*k**2 + 338/5.
2*(k + 13)**2/5
Let a = -76/25 + 106/25. Solve 2/5*t**2 + a*t + 4/5 = 0 for t.
-2, -1
Let u be 6/51 - (-44)/(-374). Let j(p) be the third derivative of -3/11*p**3 + u - 1/22*p**4 - 1/330*p**5 - 5*p**2 + 0*p. Let j(m) = 0. Calculate m.
-3
Suppose -7*t + 5*t + 4 = 4*u, 0 = 5*u + 2*t - 7. Let i(w) be the third derivative of 4/9*w**u + 0*w**4 - 1/30*w**5 + 7*w**2 - 1/180*w**6 + 0*w + 0. Factor i(j).
-2*(j - 1)*(j + 2)**2/3
Let x = 257259/13 - 19789. Solve -6/13*v**4 - x + 4/13*v**3 - 4/13*v + 8/13*v**2 = 0.
-1, -1/3, 1
Let n(h) be the second derivative of -h**4/84 + 43*h**3/42 - 3*h**2 + 11*h. Find l such that n(l) = 0.
1, 42
Let w = -2/1274525 - -406573903/272748350. Let g = 1/107 + w. Let -3/4*k**2 + 9/4*k - g = 0. What is k?
1, 2
Let k(r) be the third derivative of -r**6/360 + 7*r**5/720 - r**4/144 - 3*r**3 - 28*r**2. Let c(h) be the first derivative of k(h). Factor c(y).
-(y - 1)*(6*y - 1)/6
Factor 13/3*p + 22/3 + 1/3*p**2.
(p + 2)*(p + 11)/3
Determine w, given that 1/5*w**2 - 4/5 + 0*w = 0.
-2, 2
Factor -2/5*m**2 - 12/5 - 2*m.
-2*(m + 2)*(m + 3)/5
Let t be (-2)/(1/2*(-8 + 10)). Let c be (-2 + 3)/((-1)/t). Suppose 2/11*d**c + 0 - 4/11*d = 0. Calculate d.
0, 2
Let w(j) = 5*j + 228. Let y be w(-45). Suppose 4*p - 32 = -4*p. Factor -1/3*s**2 - 4/3 + 8/3*s - 5/3*s**y + 1/3*s**5 + 1/3*s**p.
(s - 1)**3*(s + 2)**2/3
Determine t, given that -24/5*t**3 - 18/5 - 56/5*t - 12*t**2 - 2/5*t**4 = 0.
-9, -1
Let v(u) be the first derivative of u**6/180 - u**5/12 + 5*u**3 + 11. Let g(d) be the third derivative of v(d). What is t in g(t) = 0?
0, 5
Let v(m) = -55*m**2 + 21*m + 18. Let c(i) = -55*i**2 + 20*i + 15. Let w(r) = 6*c(r) - 5*v(r). Factor w(s).
-5*s*(11*s - 3)
Let i = 4801/2 - 2398. Find z, given that -z - 1/4*z**5 + 5/4*z**3 - i*z**2 + 2 + 1/2*z**4 = 0.
-2, -1, 1, 2
Let n = -4342 - -4345. Factor 2/3*v**2 - v**n + 0 + 0*v + 1/3*v**4.
v**2*(v - 2)*(v - 1)/3
Factor -128*r + 44476*r**4 + 9*r**3 + 112*r**2 + 11*r**3 - 44480*r**4.
-4*r*(r - 8)*(r - 1)*(r + 4)
Suppose 2*p - 5*p - 2*p = 0. Let n(m) be the first derivative of 9/4*m**4 - m**3 - 9/5*m**5 - 3 + 1/2*m**6 + p*m**2 + 0*m. Factor n(q).
3*q**2*(q - 1)**3
Let w(d) be the first derivative of -d**5/20 + 5*d**4/16 - d**3/6 - d**2 - 72. Factor w(y).
-y*(y - 4)*(y - 2)*(y + 1)/4
Let t(w) be the first derivative of 0*w + 0*w**3 - 1/2*w**4 + 0*w**5 + 1/6*w**6 + 35 + 1/2*w**2. Suppose t(d) = 0. Calculate d.
-1, 0, 1
Let j(g) = 2*g**2 - 2*g. Suppose 2*r - 4 = 4*r. Let l(x) = -x**3 + x. Let z be 8/12 - 24/9. Let o(a) = r*l(a) + z*j(a). Let o(n) = 0. Calculate n.
0, 1
Let n(k) be the second derivative of -k**6/18 - k**5/4 - 5*k**4/12 - 5*k**3/18 - 293*k. Factor n(q).
-5*q*(q + 1)**3/3
Let h be (-531)/(-354)*