ative of -f**5/15 - 2*f**4/3 - 8*f**3/3 - 13*f**2/2 - 5. Let r(g) be the second derivative of p(g). Factor r(n).
-4*(n + 2)**2
Let h be (-45)/(-6)*4/(-3). Let u = h - -12. Factor -5 - 3*k + 2*k**u + 4 + 3*k - k**4.
-(k - 1)**2*(k + 1)**2
Let a(b) be the first derivative of b**6/480 - b**5/240 - 19*b**2/2 - 37. Let d(n) be the second derivative of a(n). Determine p so that d(p) = 0.
0, 1
Let g(a) = a**2 + 17*a + 29. Let x be g(-15). Let t be x/(4 - (1 - -2))*-4. Factor 0*o + 0 + 0*o**2 - 1/2*o**t + 1/2*o**3.
-o**3*(o - 1)/2
Let y be 12/((33 - 15) + -15). Factor 3/11*a**2 + 0 + 3/11*a**y + 8/11*a**3 - 2/11*a.
a*(a + 1)*(a + 2)*(3*a - 1)/11
Let z(q) be the third derivative of q**6/30 - q**5/15 - q**4/3 + 60*q**2 - 1. Factor z(s).
4*s*(s - 2)*(s + 1)
Let c(n) = -n**3 + n**2 + 1. Let l(f) = 4*f**3 + 0 + 3*f**3 - 2 - 5*f**3 - f. Let j be 4/(-2) + (-5 - -4). Let r(x) = j*l(x) - 3*c(x). Factor r(s).
-3*(s - 1)*(s + 1)**2
Factor 22/7*v - 2/7*v**3 + 24/7 - 4/7*v**2.
-2*(v - 3)*(v + 1)*(v + 4)/7
Suppose 20*q = -1 + 81. Let o(x) be the third derivative of -6*x**2 - 3/5*x**3 + 0 - 1/150*x**5 + 1/10*x**q + 0*x. Factor o(s).
-2*(s - 3)**2/5
Let n(z) be the third derivative of z**5/510 + z**4/34 - 9*z**3/17 - 20*z**2 + 12. Factor n(y).
2*(y - 3)*(y + 9)/17
Let b(m) be the first derivative of 0*m**2 + 12 - 5/3*m**3 + 5*m. Let b(q) = 0. What is q?
-1, 1
Factor 4/7*r**3 + 2/7*r**2 - 2/7*r**4 - 4/7*r + 0.
-2*r*(r - 2)*(r - 1)*(r + 1)/7
Let h(u) = -u**3 + 3*u + 4. Let l be h(-2). Factor 5*w**2 - 3*w**3 - w - 2*w**3 + l*w + 18 - 23.
-5*(w - 1)**2*(w + 1)
Let f(g) = 6*g**3 + 12*g**2 + 14*g - 17. Let t(d) = d**3 + d**2 + 2*d - 1. Let k(p) = 4*f(p) - 20*t(p). Suppose k(u) = 0. What is u?
-6, -2, 1
Let q(m) be the first derivative of 3*m**3 - 3/4*m**4 - 47 + 3*m - 9/2*m**2. Let q(h) = 0. Calculate h.
1
Let y = 433/720 - 1/720. Let p(z) be the second derivative of 0 + 0*z**2 - 2/15*z**6 - 2/3*z**4 - y*z**5 + 0*z**3 + z. Factor p(r).
-4*r**2*(r + 1)*(r + 2)
Let c(x) be the second derivative of -x**6/360 - x**5/24 - x**4/4 + 19*x**3/6 + 15*x. Let s(p) be the second derivative of c(p). Suppose s(t) = 0. What is t?
-3, -2
Let v be (-6)/15 + (-896)/(-315) + -2. Find f, given that 2/9*f**2 + 2/9 + v*f = 0.
-1
Let c be (2346/210 + -11)/((-27)/(-42)). Let h(i) be the first derivative of 4*i**2 + 12 - c*i**3 - 20*i. Factor h(r).
-4*(r - 5)**2/5
Suppose -5*n = 2*v + 16, 2*n - 3*v + 7*v + 16 = 0. Let k be (2/3)/(n/(-9)). Let -5*w**2 + 14*w**4 + w**5 - 3*w**k - 13*w**4 + 0*w**2 - 2*w = 0. What is w?
-1, 0, 2
Let k = -19 - -19. Factor k - 8*u + 8 - 5*u**2 + 4*u + u**2.
-4*(u - 1)*(u + 2)
Let g(l) be the third derivative of l**9/12096 + l**8/2016 - l**7/252 - l**6/18 - 2*l**5/5 - 9*l**2. Let t(y) be the third derivative of g(y). Factor t(c).
5*(c - 2)*(c + 2)**2
Let s(i) be the second derivative of i**6/45 - 2*i**5/15 + i**4/6 - i + 330. Determine x so that s(x) = 0.
0, 1, 3
Let s(f) be the first derivative of 0*f + 17 + f**4 + 6*f**2 + 16/3*f**3. Factor s(n).
4*n*(n + 1)*(n + 3)
Let a(y) be the first derivative of -y**6/2 - 6*y**5/5 + 6*y**4 - 2*y**3 - 21*y**2/2 + 12*y + 153. Suppose a(c) = 0. Calculate c.
-4, -1, 1
Let g(v) be the first derivative of -1/3*v**3 + 38 + 5/2*v**2 + 0*v. Suppose g(u) = 0. Calculate u.
0, 5
Let g(m) = m**5 + m**4 - m**3 - 2*m**2 + m. Let f(t) = -5*t**5 + 12*t**4 - 19*t**3 - 25*t**2 + 21*t + 16. Let x(k) = 5*f(k) + 15*g(k). What is z in x(z) = 0?
-1, -1/2, 1, 4
Let o(v) be the first derivative of -2*v**3/27 + 14*v**2/9 - 26*v/9 + 55. Determine x so that o(x) = 0.
1, 13
Let q = 19555 + -19553. Factor 6/11*r**q + 0 + 10/11*r**3 + 0*r - 2/11*r**5 + 2/11*r**4.
-2*r**2*(r - 3)*(r + 1)**2/11
Let g(w) be the second derivative of w**6/540 - w**3 - 10*w. Let h(v) be the second derivative of g(v). Let h(i) = 0. What is i?
0
Let q(b) = -b**2 + 1. Let d(c) = -8*c**2 - 4*c + 13. Suppose -6 - 1 = -t. Suppose t - 19 = 3*i. Let k(y) = i*d(y) + 36*q(y). Factor k(a).
-4*(a - 2)**2
Factor 3*l**2 + 489*l**3 - 485*l**3 - 7*l**2 + 8*l**4.
4*l**2*(l + 1)*(2*l - 1)
Let u(x) be the first derivative of 4*x + 1 - 2/3*x**3 + x**2. Factor u(y).
-2*(y - 2)*(y + 1)
Let a be -11 + 13 + 7 + -6. Factor 9/4*s - 3/4*s**a + 0*s**2 - 3/2.
-3*(s - 1)**2*(s + 2)/4
Let w(k) be the third derivative of -6*k**2 + 0*k**4 + 0*k + 1/18*k**3 - 1/180*k**5 + 0. Solve w(p) = 0 for p.
-1, 1
Let a(w) be the first derivative of 18*w**5/5 + 21*w**4/4 + 2*w**3 + 714. Factor a(g).
3*g**2*(2*g + 1)*(3*g + 2)
Let f(g) be the second derivative of g**5/8 - 5*g**3/12 + 46*g. Factor f(b).
5*b*(b - 1)*(b + 1)/2
Factor 2/9*h**2 + 0 + 2/3*h.
2*h*(h + 3)/9
Let r(s) = 5*s**4 - 10*s**3 - 9*s**2 + 110*s + 110. Let q(m) = -7*m**4 + 11*m**3 + 9*m**2 - 111*m - 111. Let i(d) = -2*q(d) - 3*r(d). Factor i(g).
-(g - 6)**2*(g + 1)*(g + 3)
Let b(y) be the second derivative of 14*y + 1/80*y**5 + 0*y**2 - 1/240*y**6 - 1/24*y**3 + 0 + 1/96*y**4. Factor b(j).
-j*(j - 2)*(j - 1)*(j + 1)/8
Let z(m) = m**2 - m. Let a(s) = 8*s**2 + 17*s + 15. Let r(b) = a(b) - 3*z(b). Determine q, given that r(q) = 0.
-3, -1
Suppose 5 - 14 = -3*s + 5*m, -2*m - 15 = -5*s. Factor 3/4*l**2 + 9/4*l - s.
3*(l - 1)*(l + 4)/4
Let z(w) be the first derivative of -w**5/5 + 2*w**3/3 - 35*w - 26. Let v(q) be the first derivative of z(q). Factor v(f).
-4*f*(f - 1)*(f + 1)
Let i(f) = -3*f**2 + 19*f + 42. Let m(h) = 21*h**2 - 135*h - 294. Let x(g) = -15*i(g) - 2*m(g). Factor x(d).
3*(d - 7)*(d + 2)
Determine x so that 4317*x**3 + 89864*x**2 - 952*x**3 + 338*x**4 + 26880*x + 2048 + 7555*x**3 = 0.
-16, -2/13
Let f(n) be the first derivative of n**3/3 + 3*n**2/2 + 10*n - 3. Let w be f(-4). Let -4*a**3 + 4*a**5 - 8*a**3 - 6*a**2 + w*a**2 = 0. Calculate a.
-2, 0, 1
Let g(m) be the second derivative of m**7/1680 - m**5/20 - 7*m**4/6 - 11*m. Let w(t) be the third derivative of g(t). Find s such that w(s) = 0.
-2, 2
Suppose 3*g + 4*g = 168. Factor -15*a - 9*a**2 + g*a**2 - 5*a**4 + 5*a.
-5*a*(a - 1)**2*(a + 2)
Let f = -1107299/300 - -3691. Let a(m) be the third derivative of 0*m**3 + 0*m + 0 - 1/300*m**6 + 1/60*m**4 - 1/1050*m**7 + 6*m**2 + f*m**5. Factor a(u).
-u*(u - 1)*(u + 1)*(u + 2)/5
Suppose 6/11*h**2 + 0*h - 8/11*h**3 + 2/11*h**4 + 0 = 0. What is h?
0, 1, 3
Let u(c) be the first derivative of 0*c - 5/3*c**3 - 6 + 10*c**2. Factor u(m).
-5*m*(m - 4)
Let z(s) be the first derivative of -s**4/2 + 26*s**3/3 - 35*s**2 - 98*s + 88. Factor z(p).
-2*(p - 7)**2*(p + 1)
Let p(r) be the first derivative of 2 + 0*r - 1/480*r**6 + r**2 - 1/96*r**4 + 0*r**3 + 1/120*r**5. Let z(b) be the second derivative of p(b). Factor z(x).
-x*(x - 1)**2/4
Let h(d) be the second derivative of d**8/5600 + d**7/2100 + 17*d**4/12 - 12*d. Let x(k) be the third derivative of h(k). Factor x(s).
6*s**2*(s + 1)/5
Let k be (-4)/48 - (-203)/420. Let f(l) be the first derivative of 0*l**2 - k*l - 4/5*l**4 + 6/25*l**5 + 7 + 4/5*l**3. What is v in f(v) = 0?
-1/3, 1
Let a(s) = 5*s**5 + 6*s**4 + 4*s**3 - 6*s**2 + 6*s - 3. Let g(v) = 22*v**5 + 25*v**4 + 17*v**3 - 25*v**2 + 26*v - 13. Let h(b) = -26*a(b) + 6*g(b). Factor h(x).
2*x**2*(x - 3)*(x - 1)*(x + 1)
Let t(a) be the second derivative of -a**3/6 + a**2/2 + 2*a. Let j be t(-2). Factor -15*p**3 + 12 + 6*p**2 - j*p**5 + 12*p**4 - 12.
-3*p**2*(p - 2)*(p - 1)**2
Let 3/8*t**3 - 15/2 + 3*t + 33/8*t**2 = 0. What is t?
-10, -2, 1
Find b, given that 15/7*b**4 + 0*b**2 - 12/7*b**3 - 3/7*b**5 + 0*b + 0 = 0.
0, 1, 4
Factor 0 - 120/11*d + 6/11*d**2.
6*d*(d - 20)/11
Let j be (-4)/(-5) - 6/9. Let i be (1/(-4))/(-1*(5040/(-256))/(-21)). Find c such that -i*c - j - 2/15*c**2 = 0.
-1
Let t(g) be the first derivative of 2*g**6/15 + 2*g**5/5 - 4*g**4/3 - 4*g**3/3 + 6*g**2 - 13*g - 41. Let n(i) be the first derivative of t(i). Factor n(b).
4*(b - 1)**2*(b + 1)*(b + 3)
Suppose -2*k + 2 = 0, 2*z + 3 = z + 3*k. Let n be (z*(-3)/6)/(5 + -6). Let n + 2/5*p - 2/5*p**2 = 0. What is p?
0, 1
Let a(h) = -h**3 - h**2 - h + 1. Let d(x) = -2*x**3 + 2*x**2 - x + 1. Let y(m) = -4*a(m) + 4*d(m). Solve y(k) = 0.
0, 3
Factor 4/3*m**2 + 28*m + 80/3.
4*(m + 1)*(m + 20)/3
Let x(g) be the first derivative of -g**3/5 - 24*g**2/5 - 9*g - 84. Solve x(u) = 0.
-15, -1
Suppose 8 = 2*h - 6. Let w(b) = b**2 - 5*b - 7. Let g be w(h). Factor -g - 20*l**3 + 48*l - 7 + 5 - 7 - 12*l**2.
-4*(l - 1)*(l + 2)*(5*l - 