r 80/11*k**3 + 20/11*k + 6*k**2 + 2/11 + 32/11*k**4.
2*(k + 1)**2*(4*k + 1)**2/11
Let t(x) = 6*x**2 + 12*x. Let f(q) = -q**2 - 1. Let u(v) = 9*f(v) + t(v). Factor u(z).
-3*(z - 3)*(z - 1)
Suppose 2*u = 3*d - 3*u - 198, 0 = 3*d + u - 198. Let l be (8/5)/(d/55). Factor -2/3*z**5 + 0*z**3 - l*z**2 + 2/3*z + 0 + 4/3*z**4.
-2*z*(z - 1)**3*(z + 1)/3
Let d be -4*(-1)/12 + (-1)/12. Factor -1/4*g + 0 + d*g**2.
g*(g - 1)/4
Factor 16*l**4 + 8*l**2 + 4 - 8*l**3 - 4*l**5 + 2*l**4 - 30*l**4 + 12*l.
-4*(l - 1)*(l + 1)**4
Let d(s) be the second derivative of -s**4/30 + 2*s**3/45 + 6*s. Find h, given that d(h) = 0.
0, 2/3
Factor 2/5*f**5 + 0 - 2/5*f + 4/5*f**2 + 0*f**3 - 4/5*f**4.
2*f*(f - 1)**3*(f + 1)/5
Factor -1/6*m**3 + 0*m - 1/6*m**4 + 1/6*m**5 + 0 + 1/6*m**2.
m**2*(m - 1)**2*(m + 1)/6
Let l(z) be the first derivative of -2*z**3/15 + 2*z**2/5 - 2. Factor l(t).
-2*t*(t - 2)/5
Let g = -44 + 142/3. Factor 8/3*p**2 + 2/3*p**3 + 4/3 + g*p.
2*(p + 1)**2*(p + 2)/3
Let j(u) be the second derivative of 9*u**5/4 - 125*u**4/12 - 5*u**3 + u - 5. What is f in j(f) = 0?
-2/9, 0, 3
Let h be ((-24)/(-20))/(6/15). Let w be (6/2)/(h/2). Find f, given that 35/3*f**w + 1/3 + 25/3*f**3 + 11/3*f = 0.
-1, -1/5
Let a(i) = 32*i**3 + 460*i**2 + 2860*i + 2432. Let w(u) = 13*u**3 + 184*u**2 + 1144*u + 973. Let r(j) = 5*a(j) - 12*w(j). Let r(z) = 0. What is z?
-11, -1
Let x(m) be the second derivative of 2*m**6/105 - m**5/14 + m**4/14 + m**3/21 - m**2/7 + 29*m. Factor x(h).
2*(h - 1)**3*(2*h + 1)/7
Let f(q) = q**2 + q - 2. Let x be f(-4). Suppose 36*p**2 + 11*p**4 + 40*p**3 + x*p + 1 + 0*p + 5*p**4 - 3*p**2 = 0. Calculate p.
-1, -1/4
Let j = 631/2 - 4415/14. Factor -1/7*u**4 + j - 2/7*u**3 + 0*u**2 + 2/7*u.
-(u - 1)*(u + 1)**3/7
Let n(a) be the first derivative of -a**5/80 + a**4/48 + 3*a + 1. Let s(c) be the first derivative of n(c). Factor s(l).
-l**2*(l - 1)/4
Suppose 2*v = -4*n - 230, -3*n + 2*n + 5*v - 41 = 0. Let i be 2*2*(-42)/n. Find p, given that -2/9*p**2 + 2/9*p - 2/3*p**i + 4/9*p**5 + 0 + 2/9*p**4 = 0.
-1, 0, 1/2, 1
Let b(o) be the second derivative of -o**4/12 - o**3/3 + 3*o**2/2 - 12*o. Factor b(q).
-(q - 1)*(q + 3)
Let x(l) be the first derivative of -l**6/240 + l**4/16 + l**3/6 + 2*l**2 + 3. Let s(r) be the second derivative of x(r). Suppose s(u) = 0. Calculate u.
-1, 2
Let f(r) = -r**2 + 6*r + 6. Let b be f(6). Suppose 0 = d + d - b. Solve 0*h**2 + 3 - 3*h + d*h**2 - 5 - h**3 + 3 = 0 for h.
1
Factor -195*z**3 + 25*z**2 - 5 + 20 - 35*z + 190*z**3.
-5*(z - 3)*(z - 1)**2
Let m(b) be the third derivative of 1/180*b**6 - 4/135*b**5 + 0 - 2/27*b**3 + 7/108*b**4 + 0*b - b**2. Let m(z) = 0. Calculate z.
2/3, 1
Let v be (-3)/(-15) - (-132)/15. Let a be (-6)/v - 44/(-48). Factor 0*x + 0 + a*x**3 - 1/4*x**5 + 0*x**2 + 0*x**4.
-x**3*(x - 1)*(x + 1)/4
Let o(q) be the second derivative of 0*q**2 + 2*q + 1/12*q**4 + 0 + 1/10*q**5 + 1/30*q**6 + 0*q**3. Determine j, given that o(j) = 0.
-1, 0
Solve -2/13 + 2/13*b**2 + 0*b = 0 for b.
-1, 1
Let t = 9/10 - -37/20. Solve 1/2 - t*g**2 - 9/4*g = 0.
-1, 2/11
Let y(z) be the third derivative of -z**6/40 + 7*z**4/8 - 3*z**3 - 39*z**2. Solve y(w) = 0 for w.
-3, 1, 2
Solve -3*v**4 + 5*v**4 - 8*v - 2 - 2*v**5 + 0*v**4 - 10*v**2 + 10*v**3 + 10 = 0.
-2, -1, 1, 2
Let y be ((-36)/48 - (-30)/8) + 1. Factor 0*x + 4/7*x**2 + 0 + 0*x**y - 2/7*x**5 + 6/7*x**3.
-2*x**2*(x - 2)*(x + 1)**2/7
Factor 14*f**3 - 5*f**2 - 9*f**3 - 3*f**2 + 5*f - 2*f**2.
5*f*(f - 1)**2
Let v be 4/6 - 8/12. Suppose -1/2*x**5 + 1/2*x + 0*x**3 - x**2 + x**4 + v = 0. Calculate x.
-1, 0, 1
Let o(x) be the first derivative of -x**7/1050 - x**6/300 + x**5/300 + x**4/60 - x**2 + 1. Let c(q) be the second derivative of o(q). Factor c(d).
-d*(d - 1)*(d + 1)*(d + 2)/5
Let v(f) be the first derivative of -f**5/40 + f**4/24 - 3*f - 2. Let g(u) be the first derivative of v(u). Solve g(a) = 0 for a.
0, 1
Let d(t) be the second derivative of t**5/110 + 14*t**4/33 + 196*t**3/33 - 23*t + 2. Determine b, given that d(b) = 0.
-14, 0
Let c = 234 - 232. Let 2/3 - c*r + 2*r**2 - 2/3*r**3 = 0. Calculate r.
1
Let u(z) = z**3 + 11*z**2 + z + 11. Let x be u(-11). Factor -2*a**2 - 2*a - 3*a**2 + 3*a**2 + x*a**2.
-2*a*(a + 1)
Factor 72/7 + 24/7*z + 2/7*z**2.
2*(z + 6)**2/7
Let b(k) = -k**3 + 9*k**2 + 7*k + 2. Let t be b(10). Let h = 57/2 + t. Factor -1/2*w**3 + 1/2*w**5 + 1/2*w**4 + 0 + 0*w - h*w**2.
w**2*(w - 1)*(w + 1)**2/2
Let i = 11 - 8. Suppose -2*a = i*a - 10. Determine x so that -2/7*x**a - 2/7 - 4/7*x = 0.
-1
Let j(r) = -5*r**3 - 21*r**2 + 8*r. Let q = -4 + 8. Let h = -29 + 20. Let p(u) = -2*u**3 - 10*u**2 + 4*u. Let f(x) = h*p(x) + q*j(x). Solve f(n) = 0 for n.
0, 1, 2
Let x = 4 - 2. Factor 5*k**3 + 2*k**x + 9*k**4 - 5*k**4 + k**5 + 0*k**5.
k**2*(k + 1)**2*(k + 2)
Let v(n) be the third derivative of -n**7/1260 - n**6/180 - n**5/90 + 4*n**3/3 + n**2. Let y(i) be the first derivative of v(i). Factor y(w).
-2*w*(w + 1)*(w + 2)/3
Let f(i) be the third derivative of i**7/11340 + i**6/1080 + i**5/270 + i**4/12 - 3*i**2. Let v(g) be the second derivative of f(g). Factor v(p).
2*(p + 1)*(p + 2)/9
Let w(r) be the first derivative of -r**5/30 - r**4/12 - 33. Determine i, given that w(i) = 0.
-2, 0
Suppose -3*m = -8*m. Let a(r) be the third derivative of 0*r**3 - 1/70*r**6 - 1/1176*r**8 + 2/105*r**5 + 0*r - 1/84*r**4 + m + 4/735*r**7 - 2*r**2. Factor a(g).
-2*g*(g - 1)**4/7
Let w(c) be the first derivative of 1/11*c**4 + 2/11*c - 2/11*c**2 + 0*c**3 + 1 - 2/55*c**5. Factor w(n).
-2*(n - 1)**3*(n + 1)/11
Suppose -5*v = -0*v - 5. Let r be v/(-4) + 26/8. Factor 17*f**4 + 1 - 2*f**5 + 22*f**2 + 0*f**5 - 8*f - 28*f**r - 2*f**5.
-(f - 1)**4*(4*f - 1)
Let b be 10/(-15) - 44/(-62). Let m = 724/465 + b. Determine i, given that -6/5*i**3 + 4/5 - m*i**2 + 2/5*i = 0.
-1, 2/3
Let n(b) = b**2 - 9*b + 8. Let l be n(8). Let c(s) be the first derivative of 3 + 4/9*s**3 + l*s - 1/6*s**4 - 1/3*s**2. Factor c(p).
-2*p*(p - 1)**2/3
Let g(v) = 3*v**2 - 2*v**2 + 0 - 2. Let b be g(2). Factor -7*a - 3*a**2 + 5*a + b*a**2.
-a*(a + 2)
Factor 3*a**4 - 192*a**2 + 428*a + 417*a - 512 - 333*a - 5*a**4 + 32*a**3.
-2*(a - 4)**4
Let k(s) = s**3 + 6*s**2 - 4. Let l(i) = i**3 + 7*i**2 - 5. Let h(c) = 5*k(c) - 4*l(c). Determine n so that h(n) = 0.
-2, 0
Factor i**3 + 60*i**2 - 80*i + 16 + 28*i + 4*i**4 + 2*i**3 - 31*i**3.
4*(i - 4)*(i - 1)**3
Let k = -10 - -14. Suppose -5*d + 7*d = k. Factor -3/5*m**3 + 0*m - 3/5*m**4 + 0*m**d + 0.
-3*m**3*(m + 1)/5
Let t(l) be the second derivative of l**5/100 - l**3/30 - 18*l. Factor t(y).
y*(y - 1)*(y + 1)/5
Let j = -62 + 67. Factor 0*c**2 + 2/7*c**3 + 0*c**4 + 0*c - 2/7*c**j + 0.
-2*c**3*(c - 1)*(c + 1)/7
Let x(a) be the third derivative of a**5/240 - a**4/96 + 5*a**2. Factor x(n).
n*(n - 1)/4
Let q(l) = -l**3 + 6*l**2 - l + 6. Let v be q(6). Factor -2*m**4 + 0*m**4 + 4*m**2 + v*m**4 + 2*m**3.
-2*m**2*(m - 2)*(m + 1)
Let k be (-3)/6 + (-15)/(-2). Let z(u) = u**2 - 8*u + 9. Let c be z(k). Factor 0 + 1/4*a + 1/4*a**c.
a*(a + 1)/4
Suppose 0*t + t - 5 = 0. Find d such that 4*d**4 + 0*d**2 + d**2 + 3*d**2 + d**t + d + 6*d**3 = 0.
-1, 0
Let j = 3 - -1. Let i(b) = b**2 - 4*b + 2. Let p be i(j). Factor -2*l**5 - 6*l**3 + 2*l**2 - 6*l**4 - 6*l**2 + p*l**2.
-2*l**2*(l + 1)**3
Suppose -2*c + 4*c = -2*k + 8, 3*c = -4*k + 14. Find w such that w**3 - 3*w + w**k + 3*w**4 + 3*w - w**5 - 4*w**4 = 0.
-1, 0, 1
Suppose -3*t = -8*t - 5*h + 80, -48 = -3*t - h. Solve -2*q**5 + 17*q**4 - 9*q**4 + 40*q**2 - t*q - 36*q**3 + 6*q**4 = 0.
0, 1, 2
Let g(y) be the third derivative of y**8/1176 - y**7/245 + y**6/210 + y**5/105 - y**4/28 + y**3/21 + 8*y**2. Solve g(s) = 0.
-1, 1
Let b be (-9)/36 + 29/4. Let f be b - 7 - 4/(-10). Let f*r**3 - 2/5 + 6/5*r - 6/5*r**2 = 0. What is r?
1
Let l(u) be the second derivative of -u**7/252 - u**6/90 + u**4/36 + u**3/36 - 2*u. Factor l(j).
-j*(j - 1)*(j + 1)**3/6
Suppose -12 + 20 = 4*k. Let f(m) be the third derivative of 0*m**4 + 0*m**3 - 1/240*m**5 + 0*m + 2*m**k + 0. Determine j so that f(j) = 0.
0
Let m(t) be the third derivative of t**9/3024 + t**8/840 - t**6/180 - t**5/120 + 2*t**3/3 - 4*t**2. Let y(l) be the first derivative of m(l). Factor y(k).
k*(k - 1)*(k + 1)**3
Factor -2 - 3*n**3 - 3 - 5 + 3*n + 6*n**2 + 4.
-3*(n - 2)*(n - 1)*(n + 1)
Let k(y) = y**2 - 1. Let z(t) = 9*t**4 + 25*t**3 + 4*t