Let a(t) = -7*t**4 + 12*t**3 - 26*t**2 + 29*t - 13. Let v(p) = -6*p**4 + 12*p**3 - 26*p**2 + 28*p - 12. Let o(n) = 4*a(n) - 5*v(n). Factor o(q).
2*(q - 2)**2*(q - 1)**2
Suppose 2*b = -3*b - 4*l - 5, 5*b + 2*l - 5 = 0. Let c(i) be the first derivative of 2 - 4/7*i - 2/21*i**b + 3/7*i**2. Determine r so that c(r) = 0.
1, 2
Factor 9*h**3 + 4*h - 10*h**2 + 1/2*h**5 + 0 - 7/2*h**4.
h*(h - 2)**3*(h - 1)/2
Let o = -1274/5 + 256. Factor 0 - 2/5*z + 0*z**2 + o*z**3 + 4/5*z**4.
2*z*(z + 1)**2*(2*z - 1)/5
Factor -27/5*i**3 + 18/5*i**4 + 0*i**2 + 0*i - 3/5*i**5 + 0.
-3*i**3*(i - 3)**2/5
Let x(p) be the first derivative of -2/3*p**2 + 0*p + 2 - 2/15*p**5 - 2/3*p**4 - 10/9*p**3. Factor x(j).
-2*j*(j + 1)**2*(j + 2)/3
Let n(b) = -31*b**2 + 4*b. Let k(i) = -15*i**2 + 2*i. Let l(a) = 13*k(a) - 6*n(a). Factor l(s).
-s*(9*s - 2)
Let b(t) be the first derivative of -5*t**3/3 + 15*t**2 - 45*t + 7. Determine y, given that b(y) = 0.
3
Let c(s) be the first derivative of -s**7/105 + s**6/60 - s**2/2 + 2. Let g(k) be the second derivative of c(k). What is a in g(a) = 0?
0, 1
Let y(c) = -13*c**2. Let d be ((-5)/2)/(-1)*2. Let t(z) = d*z**2 - 5*z**2 - 6*z**2. Let q(f) = -9*t(f) + 4*y(f). Suppose q(x) = 0. What is x?
0
Let z = 1171/735 + 1/147. Find u, given that -6/5*u**3 + 2/5 + 6/5*u + z*u**4 - 2*u**2 = 0.
-1, -1/4, 1
Solve 10/9*b + 0 - 2/9*b**2 = 0 for b.
0, 5
Suppose -w = -5*u - 2, -7*w + 2*w = -4*u + 11. Let f be w - -2*(-26)/(-16). Find k such that 0 + f*k**2 - 1/4*k = 0.
0, 1
Let y = 303/14 + -148/7. What is n in -y*n + 0 + 1/4*n**2 = 0?
0, 2
Suppose -5*q = -0*n - n - 1, -2*n - 3*q = -11. Let b = -4 + n. Factor -2/3*d**2 - 2/3*d + b.
-2*d*(d + 1)/3
Suppose 11 = 2*b + 5. Suppose c - 14 = b*h, c + 3*h + 6 = h. Solve 0 - 4/9*g + 10/9*g**c = 0 for g.
0, 2/5
Let t(q) be the second derivative of -q**4/3 - 8*q**3/3 + 10*q**2 + 13*q. Factor t(l).
-4*(l - 1)*(l + 5)
Let y(a) = 3*a**4 + 22*a**3 + 22*a**2 - 15*a - 18. Let k(c) = c**4 + 7*c**3 + 7*c**2 - 5*c - 6. Let q(s) = 7*k(s) - 2*y(s). Suppose q(r) = 0. Calculate r.
-3, -2, -1, 1
Suppose -13 = f + f - 3*b, 0 = 5*f + b - 10. Let v be (-5)/((-20)/8)*f. Solve -1/2*t + 0 - 1/4*t**3 - 3/4*t**v = 0 for t.
-2, -1, 0
Let c = 56/9 + -50/9. Let i(h) = -h**3 + 6*h**2 - 5*h + 2. Let u be i(5). Factor -2*d**u - 2*d**3 - c*d**4 - 2/3*d + 0.
-2*d*(d + 1)**3/3
Suppose 24 = 3*k + 3*v, 0 = -4*k + 5*v - v - 8. Factor 0 + 0*w**2 - 9*w**4 - 9*w**k + 4/3*w.
-w*(3*w - 1)*(3*w + 2)**2/3
Let w be -2 + 0 - ((-138)/(-36) - 6). Let q(h) be the third derivative of -2*h**2 - w*h**3 + 0*h + 0 - 1/24*h**4 - 1/240*h**5. Factor q(f).
-(f + 2)**2/4
Let u(c) = -c**3 - c**2 - c. Let y(t) = -t**4 - 6*t**3 - 5*t**2 - 6*t. Let g(p) = -6*u(p) + y(p). Solve g(l) = 0.
-1, 0, 1
Let f(y) be the third derivative of -2*y**7/105 + y**6/30 + y**5/5 - 5*y**4/6 + 4*y**3/3 - 15*y**2. Factor f(h).
-4*(h - 1)**3*(h + 2)
Let l(b) be the third derivative of -b**7/1680 + b**5/80 - b**4/24 + b**3/16 + 2*b**2 - 6. Determine n so that l(n) = 0.
-3, 1
Factor -337*f**4 - 458*f**2 - 8 - 113*f**4 + 780*f**3 + 110*f - 6*f.
-2*(3*f - 2)**2*(5*f - 1)**2
Let h(o) = -o**4 - o**3. Let t(k) = 343*k**5 - 295*k**4 - 260*k**3 + 286*k**2 - 84*k + 8. Let m(s) = h(s) - t(s). Factor m(p).
-(p - 1)*(p + 1)*(7*p - 2)**3
Suppose -5*w + 25 = -0*w. Let 0*p**3 - 1/2*p + 1/2*p**w + p**2 + 0 - p**4 = 0. Calculate p.
-1, 0, 1
Let m(f) be the first derivative of 0*f + 3 + 0*f**2 + 0*f**3 - 1/4*f**4. Factor m(x).
-x**3
Let l be (-42)/(-30) + (1 - 2). Suppose 3*r - 5*r = 0. Find q, given that 0 + 2/5*q - l*q**3 + r*q**2 = 0.
-1, 0, 1
Let t(s) be the first derivative of -13/2*s**2 - 3*s - 4/3*s**3 - 6. Factor t(x).
-(x + 3)*(4*x + 1)
Suppose 9*f**5 + 21*f - 14*f**4 + 6*f**2 - 5*f**5 - 32*f**3 + 10 - 2*f**2 + 7*f = 0. What is f?
-1, -1/2, 1, 5
Let y(z) be the first derivative of 4*z**3/3 - 15*z**2/2 - 4*z - 17. What is i in y(i) = 0?
-1/4, 4
Let b(h) = -7*h**2 + 0*h - 3*h - 4*h. Let y = -6 - 1. Let w(a) = 8*a**2 + 8*a. Let x(r) = y*b(r) - 6*w(r). What is q in x(q) = 0?
-1, 0
Let n(z) = -4*z**2 - 4*z. Let u(w) = -w**3 - 17*w**2 - 16*w. Let p(v) = -9*n(v) + 2*u(v). Factor p(r).
-2*r*(r - 2)*(r + 1)
Let j(u) = -u**2 - 10*u - 5. Let p be j(-9). Let q(l) be the second derivative of 0 + 7/6*l**p - 4*l**2 - l - l**5 + 4/3*l**3 + 1/5*l**6. What is k in q(k) = 0?
-2/3, 1, 2
Let p = -74 + 379/5. Factor p + 1/5*h**2 + 6/5*h.
(h + 3)**2/5
Let u(x) be the third derivative of -x**7/42 + x**5/12 - 16*x**2. Factor u(s).
-5*s**2*(s - 1)*(s + 1)
Let t be 3/(-6) - 3378/(-28). Let k = t - 119. Factor -k*m - 2/7*m**3 + 0 + 8/7*m**2.
-2*m*(m - 2)**2/7
Let c(x) be the first derivative of 0*x - 14/3*x**3 - 2*x**2 + 4. Suppose c(m) = 0. What is m?
-2/7, 0
Let p(u) = u**2 + 11*u + 20. Let y be p(-9). Let o(z) be the first derivative of 3 - 5/4*z**4 + 2/3*z**3 - 2*z + 5/2*z**y. Factor o(v).
-(v - 1)*(v + 1)*(5*v - 2)
Let i(j) = 7*j**4 + 7*j**3 - 7*j**2 - 7*j. Let l(z) = 190*z**4 + 190*z**3 - 190*z**2 - 190*z. Let d(h) = -55*i(h) + 2*l(h). Find w such that d(w) = 0.
-1, 0, 1
Let c = 37 - 35. Let s = -218 - -667/3. Factor 4/3 + 1/3*d**4 - 4*d - 2*d**3 + s*d**c.
(d - 2)**2*(d - 1)**2/3
Let a(h) = h**2 + 3*h + 4. Let t be a(-3). Factor 6 + 1 - t - 3*s**2.
-3*(s - 1)*(s + 1)
Let q(z) = -z**3 - 22*z**2 - 23*z - 39. Let l be q(-21). Factor 2/3*h**l + 0 + 2/3*h**2 + 0*h.
2*h**2*(h + 1)/3
Let j(h) = 75*h**4 - 175*h**3 + 105*h**2 - 25*h + 10. Let g(t) = 25*t**4 - 58*t**3 + 35*t**2 - 8*t + 3. Let w(c) = 10*g(c) - 3*j(c). Solve w(s) = 0.
0, 1/5, 1
Let n = 89 + -62. Suppose 4*r + 3*y - 26 = 0, 0 = -5*r + 2*y + n - 6. Factor -7*c - 4*c**4 - 5 + r - 1 - 13*c**3 - 11*c**2 - 4*c**2.
-(c + 1)**3*(4*c + 1)
Let u be 4*2/8 - -3. Suppose i = -2*i - u*m + 6, 4*i - 5*m - 8 = 0. Factor -2/9 + 2/9*o + 2/9*o**i - 2/9*o**3.
-2*(o - 1)**2*(o + 1)/9
Factor -2*n**4 + 2*n**2 - 3*n**2 - 5*n**4 + 8*n**4.
n**2*(n - 1)*(n + 1)
Let p = 73/2 + -35. Factor -p*t**2 - 4*t - 2.
-(t + 2)*(3*t + 2)/2
Let d(g) = g**2 - 9*g + 8. Let n be d(7). Let w be (n/3)/(2/(-3)). Factor 0 + 0*k + 2/3*k**w + 2/3*k**5 + 0*k**2 + 4/3*k**4.
2*k**3*(k + 1)**2/3
Let f(n) be the second derivative of -1/2*n**4 + 0 - 5/3*n**3 + 2*n**2 + 3*n. Factor f(k).
-2*(k + 2)*(3*k - 1)
Let 4*x**3 + 6*x**5 - 6*x**3 - 4*x**5 = 0. Calculate x.
-1, 0, 1
Let h(b) be the first derivative of -1/4*b - 1/12*b**3 - 1 - 1/4*b**2. Factor h(q).
-(q + 1)**2/4
Let s(z) be the first derivative of -z**4/2 - 4*z**3/21 + 4*z**2 + 16*z/7 + 6. Determine r so that s(r) = 0.
-2, -2/7, 2
Let s(c) be the first derivative of 2*c**5/25 - 2*c**4/5 + 4*c**3/5 - 4*c**2/5 + 2*c/5 - 1. Factor s(x).
2*(x - 1)**4/5
Let w(v) be the third derivative of -v**6/6 - 7*v**5/15 - v**4/3 - 3*v**2. Factor w(p).
-4*p*(p + 1)*(5*p + 2)
Suppose -4*w = -3*w - 8. Let k = w - 5. Find m such that -2*m + m + m - m + 1 - m**2 + m**k = 0.
-1, 1
Let p(u) be the third derivative of u**9/45360 - u**8/5040 + u**7/1512 - u**6/1080 - u**4/24 + 3*u**2. Let v(z) be the second derivative of p(z). Factor v(g).
g*(g - 2)*(g - 1)**2/3
Let q(a) = a**2 + 5. Let l be q(4). Let x = l + -21. Factor 4/5*t**2 + 0 - 4/5*t**4 + 2/5*t + x*t**3 - 2/5*t**5.
-2*t*(t - 1)*(t + 1)**3/5
Let o(d) be the first derivative of 49*d**3/9 - 7*d**2 + 3*d - 2. Factor o(a).
(7*a - 3)**2/3
Suppose -2*h = h - 183. Let j = -425/7 + h. Solve 0*c - 2/7*c**3 + 0 + 2/7*c**4 + j*c**5 - 2/7*c**2 = 0.
-1, 0, 1
Let s(n) = n**2 - 7*n + 6. Let w be s(6). Let d(j) be the first derivative of 1/5*j**4 + 2/15*j**3 + 2/25*j**5 + w*j**2 + 0*j - 2. What is p in d(p) = 0?
-1, 0
Let g = 18 - 18. Let k(t) be the second derivative of 1/21*t**7 + 0*t**2 + 0*t**4 + 0*t**5 - 2*t + 0 + g*t**3 - 1/15*t**6. Factor k(z).
2*z**4*(z - 1)
Let i(g) = -3*g**2 - 4*g + 8. Let c(f) = -2*f**2 - 4*f + 7. Let h(o) = -4*c(o) + 3*i(o). Factor h(y).
-(y - 2)**2
Suppose 7/4*z**3 + 1/2*z**2 + 1/2*z**4 + 0 + 0*z - 3/4*z**5 = 0. What is z?
-1, -1/3, 0, 2
Let k(o) be the third derivative of o**8/560 + o**7/350 - 3*o**6/200 - o**5/20 - o**4/20 + o**2. Let k(m) = 0. What is m?
-1, 0, 2
Suppose 3*j - 14 = 7. Let b be (-4 + j)/((-1)/(-3)). Factor -1 + b*m - 8*m - m**3 + m**2 + 0.
-(m - 1)**2*(m + 1)
Let s(l) be the second derivative of -l**6/660 + l**4/132 + 3*l**2/2 - l. Let d(i) be the first derivative of s(i). Factor d(h).
-2*h*(h - 1)*(h + 1)/11
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