 6*q**2 + 3*q + 12. Let d be l(6). Factor d*u + 26 + 2*u**2 + 25 - 6 + 3*u**2.
5*(u + 3)**2
Suppose -2*a - 25 = -17. Let i be 2 + 0 + -1*(-5)/a. Factor 9/4*g - i*g**2 - 3/2.
-3*(g - 2)*(g - 1)/4
Let h be 12/24 + 76/8 + -6. Solve 1/5*v**h + 4/5*v**3 + 0 + v**2 + 2/5*v = 0 for v.
-2, -1, 0
Let a(q) = -4*q**2 + 11*q - 10. Let r(w) = -5*w**2 + 11*w - 10. Let l(x) = -7*a(x) + 6*r(x). Let k be l(-6). Factor 4*j**2 + 0 + j + 21/4*j**3 + 9/4*j**k.
j*(j + 1)*(3*j + 2)**2/4
Let q = 1594 + -1594. Factor q - 4/11*b**3 - 2/11*b**2 + 2/11*b.
-2*b*(b + 1)*(2*b - 1)/11
Let n be (-30)/12*(-36)/(-20) - -5. Let g(q) be the first derivative of -5 + n*q + 1/8*q**4 + 3/4*q**2 + 1/2*q**3. Factor g(f).
(f + 1)**3/2
Let w(s) be the first derivative of s**6/480 - s**5/40 - 3*s**4/8 + s**3/3 + 5*s + 53. Let o(q) be the third derivative of w(q). Find j, given that o(j) = 0.
-2, 6
Factor 2/7*b**2 - 8/7*b + 8/7.
2*(b - 2)**2/7
Let o(h) be the first derivative of 5*h**4/4 + 25*h**3/3 + 15*h**2/2 + 7*h - 12. Let u(i) be the first derivative of o(i). Factor u(b).
5*(b + 3)*(3*b + 1)
Let g(h) be the second derivative of 1/6*h**4 + 1/21*h**7 + 0*h**2 + 7*h + 0*h**3 - 1/15*h**6 - 1/10*h**5 + 0. Find x, given that g(x) = 0.
-1, 0, 1
Find t such that 4/3*t**4 + 0*t**2 - 10/3*t**3 - 4/3 + 10/3*t = 0.
-1, 1/2, 1, 2
Let n be (-3)/15 + 15459/31395. Let l = n - 2/299. Determine b, given that 2/7*b**4 - 2/7*b + 4/7 + l*b**3 - 6/7*b**2 = 0.
-2, -1, 1
Let y = -4055 + 20276/5. Factor 1/5*p**4 + y*p**2 - 2/5*p**3 + 0 + 0*p.
p**2*(p - 1)**2/5
Suppose 4*d = 7*d. Suppose -2*m + f + 16 = d, 0 = -5*f + 2*f + 12. Factor m*j - 2*j**3 + 0*j**3 + 6 - 15*j**2 + 17*j**2.
-2*(j - 3)*(j + 1)**2
Let p(h) be the first derivative of h**3/3 - 6*h**2 + 15*h - 4. Let f be p(11). Determine x, given that f*x**3 - x**2 - 4*x**3 + 3*x - 4*x + x**3 + 1 = 0.
-1, 1
Let x(i) = -i**4 + i**2 - i - 1. Let q(d) = -4*d**4 - 116*d**3 + 208*d**2 - 60*d - 20. Let c(k) = q(k) - 20*x(k). Factor c(g).
4*g*(g - 5)*(g - 2)*(4*g - 1)
Let v(m) be the first derivative of -3 - 1/9*m**3 + 1/3*m**2 - 1/3*m. Factor v(n).
-(n - 1)**2/3
Let d(r) be the third derivative of -r**6/240 - 3*r**5/20 - 11*r**4/16 - 4*r**3/3 - 650*r**2. Factor d(y).
-(y + 1)**2*(y + 16)/2
Let l = -13 + 10. Let k(s) = s**3 + 3*s**2 + 6*s - 2. Let x(b) = 3*b**3 + 9*b**2 + 17*b - 5. Let p(q) = l*x(q) + 8*k(q). Factor p(m).
-(m + 1)**3
Let t = 868 - 867. Let i(l) be the first derivative of 0*l - 4/3*l**3 - l**4 + 4*l**2 + t. Solve i(d) = 0 for d.
-2, 0, 1
Let s(y) = 10*y - 266. Let o be s(27). Let k(l) be the first derivative of -5 - 2/3*l**2 + 2/3*l**3 + 0*l - 1/6*l**o. Factor k(j).
-2*j*(j - 2)*(j - 1)/3
Let w(b) = -b**2 - 22*b - 103. Let y be w(-7). Factor 0*a + 4/3*a**y + 0 - 2/3*a**4 + 2/3*a**3.
-2*a**2*(a - 2)*(a + 1)/3
Let d(h) be the third derivative of h**6/240 - 73*h**4/48 - 6*h**3 + 591*h**2. Solve d(k) = 0.
-8, -1, 9
Suppose -3*k = -3*l + l - 16, 5*l + 25 = 0. Let x(n) be the third derivative of 0*n - 1/15*n**5 - 7*n**k + 0 + 4/3*n**3 + 1/6*n**4. Find v, given that x(v) = 0.
-1, 2
Let l = 4 + 0. Let n be ((-104)/572)/(-3 + (-64)/(-22)). Factor 0 + 0*s - 2/3*s**3 - 2/3*s**l + 4/3*s**n.
-2*s**2*(s - 1)*(s + 2)/3
Let f(v) = v**3 - 4*v + 8. Let d be f(2). Factor 10*c - d*c + 3*c**2 - 11*c.
3*c*(c - 3)
Suppose 4*m - j - 5 = 0, -3*m - 15 = 2*m + 3*j. Let t(d) be the second derivative of 1/66*d**4 + 0 + m*d**2 - 1/33*d**3 - 2*d. Determine q, given that t(q) = 0.
0, 1
Let j(k) = k**2 - 7*k + 8. Let g(f) = f**3 + 8*f**2 + 4*f - 15. Let r be g(-7). Let t be j(r). Let -41*d - 10 - 16*d**t + 4*d**3 + 61*d + 2 = 0. Calculate d.
1, 2
Let f be 32/88*66/12. Let m(x) be the second derivative of 0 + 1/40*x**5 + 1/2*x**f + 10*x - 1/8*x**4 - 1/12*x**3 + 1/60*x**6. Factor m(u).
(u - 1)**2*(u + 1)*(u + 2)/2
Let m(x) be the third derivative of x**11/997920 - x**9/181440 + x**5/12 - 8*x**2. Let w(q) be the third derivative of m(q). Suppose w(f) = 0. Calculate f.
-1, 0, 1
Let p(j) be the third derivative of 10*j**2 + 1/32*j**5 + 0 + 0*j + 1/8*j**3 - 7/64*j**4. Factor p(o).
3*(o - 1)*(5*o - 2)/8
Let a(g) be the second derivative of -g**6/180 + g**5/45 - 17*g**2/2 + 15*g. Let l(f) be the first derivative of a(f). Factor l(t).
-2*t**2*(t - 2)/3
Let r be (-21 + 165/9)/(0 + 0 - 2). Factor r + 2/3*t - 2/3*t**2.
-2*(t - 2)*(t + 1)/3
Let b(r) = 7*r**3 - 33*r**2 - 24*r - 11. Let t(l) = l**3 + l**2 + l + 1. Suppose 8*h - 396 = -3*h. Let f(x) = h*t(x) + 4*b(x). Factor f(m).
4*(m - 2)*(4*m + 1)**2
Let g(j) be the third derivative of j**6/40 - 36*j**5/5 + 864*j**4 - 55296*j**3 + 251*j**2. Factor g(n).
3*(n - 48)**3
Suppose -218 = -2*m - 2*u, 7*u - 11*u + 326 = 3*m. Let n be (-9 + 1005/m)/(3/4). Let -2/11*b**3 + 2/11*b**2 + 0 + n*b - 2/11*b**4 = 0. What is b?
-1, 0, 1
Let h(p) be the second derivative of 23/15*p**5 + 5/21*p**7 + 0 + 2/3*p**2 - 46/45*p**6 - 2/3*p**4 - 5/9*p**3 + 7*p. Determine b so that h(b) = 0.
-1/3, 2/5, 1
Let s = 2941/5 - 587. Let k(j) be the first derivative of 8 + 2/15*j**3 + 18/5*j - s*j**2. Determine c, given that k(c) = 0.
3
Let z(v) = v**3 + 6*v**2 - 16*v - 10. Let y be z(-10). Let n = -250 - y. Let n*o + 8/13*o**4 + 4/13*o**2 - 2/13*o**5 - 10/13*o**3 + 0 = 0. What is o?
0, 1, 2
Let f(z) be the first derivative of 1/3*z**4 - 4/3*z + 1/15*z**5 - 2/3*z**2 + 1/3*z**3 + 49. Factor f(a).
(a - 1)*(a + 1)*(a + 2)**2/3
Let j(d) be the first derivative of 2*d**3/3 + 40*d**2 + 78*d + 125. Factor j(z).
2*(z + 1)*(z + 39)
Let z = -15 + 25. Suppose k + 4*k = z. Determine q so that 5*q**k - q**4 - 8*q**2 + 4*q**2 = 0.
-1, 0, 1
Suppose -5*z - 3*p = 21, -z = p + 1 + 4. Let r be 2*(z + 2)*10/(-65). Factor 0 + 6/13*i**2 + r*i + 2/13*i**3.
2*i*(i + 1)*(i + 2)/13
Let p = -3/4 + 5/6. Let j(w) be the first derivative of -1/6*w**2 + p*w**4 + 2/3*w - 3 + 1/15*w**5 - 1/3*w**3. Suppose j(i) = 0. Calculate i.
-2, -1, 1
Suppose -9/2 + 1/2*h**3 + 5/2*h**2 + 3/2*h = 0. What is h?
-3, 1
Factor 8/5*f - 8/5 + 6/5*f**2 - 2/5*f**4 - 4/5*f**3.
-2*(f - 1)**2*(f + 2)**2/5
Let f(q) = 80*q**3 - 325*q**2. Let d(n) = -n**3 - 5*n**3 + 3*n**3 - 2*n**2 + 14*n**2. Let b(y) = -55*d(y) - 2*f(y). Factor b(m).
5*m**2*(m - 2)
Find a, given that -16*a + 3*a**2 - 1032 + a + 1050 = 0.
2, 3
Let r be 23/((-2530)/(-1000))*8/16. Factor -r*p**3 - 60/11*p**2 + 0 - 18/11*p.
-2*p*(5*p + 3)**2/11
Let d(r) be the second derivative of -7/20*r**4 + 3/25*r**5 + 0 + 22*r + 1/5*r**3 + 3/10*r**2. Factor d(f).
3*(f - 1)**2*(4*f + 1)/5
Let s(a) be the third derivative of a**7/1008 - a**6/720 + 3*a**4/8 - a**3/6 + 21*a**2. Let r(o) be the second derivative of s(o). Let r(w) = 0. What is w?
0, 2/5
Let w(c) be the third derivative of -2*c**6/105 - 13*c**5/105 - 11*c**4/42 - 4*c**3/21 + 2*c**2 + 11*c. Find x, given that w(x) = 0.
-2, -1, -1/4
Suppose 30*k - 38 = 22. Let v(b) be the first derivative of 1/12*b**3 + b + 1/2*b**k - 7. Factor v(n).
(n + 2)**2/4
Let r(b) be the second derivative of -1/48*b**4 + 1/120*b**6 + 0*b**3 - 2 + 0*b**5 + 15*b + 0*b**2. Factor r(z).
z**2*(z - 1)*(z + 1)/4
Suppose -4*u + 72*s - 70*s + 6 = 0, 3*u - 3 = 2*s. Let g(f) be the second derivative of 1/36*f**4 + 25/6*f**2 + 0 - 5/9*f**u - 14*f. Factor g(q).
(q - 5)**2/3
Let n(h) be the first derivative of -h**5/110 - h**4/66 + h**3/33 + h**2/11 - h + 2. Let r(q) be the first derivative of n(q). Suppose r(s) = 0. Calculate s.
-1, 1
Let m(p) be the third derivative of -p**8/161280 - p**7/10080 - p**6/1920 - p**5/12 + 4*p**2. Let b(q) be the third derivative of m(q). Factor b(o).
-(o + 1)*(o + 3)/8
Let n(p) be the second derivative of -p**4/3 - 20*p**3/3 + 78*p**2 + 2*p + 38. Factor n(z).
-4*(z - 3)*(z + 13)
Suppose -5/4*i**4 - 55125 - 365/2*i**3 - 38325*i - 28745/4*i**2 = 0. Calculate i.
-70, -3
Let f(w) = 3*w - 16. Let g be f(6). Let l(p) = p**2 - 6*p - 13. Let h be l(8). Factor -9/2*k**g - 3 + 3/2*k**4 + 3/2*k**h - 15/2*k.
3*(k - 2)*(k + 1)**3/2
Let p(y) be the second derivative of y**6/1080 - y**5/90 - 5*y**4/72 + 10*y**3/3 - 19*y. Let g(f) be the second derivative of p(f). What is h in g(h) = 0?
-1, 5
Let h(m) be the first derivative of 4/3*m**3 + 27 - 4*m + 0*m**2. Factor h(x).
4*(x - 1)*(x + 1)
Let y = 165 + -165. Let u(f) be the second derivative of 1/33*f**3 - 1/11*f**2 + 2*f + y + 1/66*f**4 - 1/110*f**5. Factor u(z).
-2*(z - 1)**2*(z + 1)/11
Let n(h) = h*