21). Let l(a) be the second derivative of 1/24*a**4 + 1/4*a**3 + a + 0*a**2 + j. Factor l(y).
y*(y + 3)/2
Let x(i) = i**3 + i**2 - 2*i - 2. Let p(j) = 2*j - 8. Let u(g) = -g + 7. Let n(b) = 4*p(b) + 5*u(b). Let k(w) = 2*n(w) + 3*x(w). Solve k(t) = 0 for t.
-1, 0
Suppose -35 - 43 = -13*q. Let v(n) be the second derivative of 3*n + 0 + 1/10*n**5 + 0*n**2 - 1/30*n**q + 0*n**3 - 1/12*n**4. Factor v(m).
-m**2*(m - 1)**2
Let l(p) = -p**3 - 6*p**2 - 4*p - 13. Let h be l(-6). Suppose -4*y = -16, -4*g + 3*g + h = 2*y. Let 35*n**g - 10*n + 2 - 3/2*n**2 + 49/2*n**4 = 0. What is n?
-1, 2/7
Let d(k) = -k**5 - k**4 - k**3 + k. Let v(n) = -n - 14*n**4 + 4*n - 2*n**3 - 17*n**5 + n + n. Let x(r) = -5*d(r) + v(r). Factor x(u).
-3*u**3*(u + 1)*(4*u - 1)
Let c(u) be the second derivative of -u**6/3060 - u**5/510 - u**4/204 - 11*u**3/6 - 6*u. Let g(r) be the second derivative of c(r). Solve g(z) = 0 for z.
-1
Let n(y) be the third derivative of 7*y**8/1440 - y**7/60 + y**6/40 + 7*y**5/60 - 5*y**2. Let t(w) be the third derivative of n(w). Solve t(b) = 0.
3/7
Let p(f) be the second derivative of -45*f + 0 - 32*f**2 + 8/3*f**3 - 1/12*f**4. Solve p(k) = 0.
8
Let c(d) be the third derivative of -1/16*d**4 - 43*d**2 + 0*d**3 + 0 - 1/40*d**5 + 0*d. Let c(h) = 0. Calculate h.
-1, 0
Let y(g) = 14*g**2 + 100*g - 254. Let s(c) = 4*c**2 + 33*c - 85. Let f(m) = 10*s(m) - 3*y(m). Factor f(h).
-2*(h - 11)*(h - 4)
Let k be -8 + 17/((-17)/(-10)). Factor 2/3*b**k - 2/3*b - 2/3 + 2/3*b**3.
2*(b - 1)*(b + 1)**2/3
Let h(n) = n + 1. Let x be h(3). Suppose x = 4*m + 2*c, 5*m = -0*m - 3*c + 3. Factor 4 - 21*t**2 + 10*t + 23/2*t**m - 2*t**4.
-(t - 2)**3*(4*t + 1)/2
Let m = 113 + -110. Let k = 150 - 748/5. Factor 2/5*v**2 + v**m - v - k.
(v - 1)*(v + 1)*(5*v + 2)/5
Let k(l) = -l + 5. Suppose 6*a - 35 + 23 = 0. Let w be k(a). Solve w*n**2 + 9/2*n**3 + 0 + 0*n - 3*n**4 = 0.
-1/2, 0, 2
Let t be 52/20 + (-6)/10 + 0. Factor -2*y**3 + 26*y**2 + 8 - 7*y**3 + 4*y**4 - 28*y - 11*y**3 + 10*y**t.
4*(y - 2)*(y - 1)**3
Suppose v + 21 = -0*v + 3*b, -5*v - 3*b = 69. Let o = -1 - v. Determine z, given that -4*z**3 - 4*z**2 - 8*z**3 + 6*z**4 - o*z**4 = 0.
-1, -1/2, 0
Let k(o) be the second derivative of o**7/21 + 8*o**6/3 + 101*o**5/2 + 805*o**4/3 - 4900*o**3/3 + 2744*o**2 - 22*o + 1. Factor k(z).
2*(z - 1)**2*(z + 14)**3
Let l(j) be the first derivative of 2*j**5/5 + 3*j**4/2 - 8*j**3/3 + 101. Factor l(f).
2*f**2*(f - 1)*(f + 4)
Suppose 31*o + 330 = 19*o + 34*o. Factor 0 + 12*z - 6*z**2 - o*z**3 - 9/2*z**4.
-3*z*(z + 2)**2*(3*z - 2)/2
Let v(c) be the first derivative of -c**7/5880 + c**6/1260 - c**3 + 13. Let z(i) be the third derivative of v(i). Suppose z(g) = 0. What is g?
0, 2
Let u(r) = r**3 - 69*r**2 + 257*r + 197. Let j be u(65). Find f such that 2/5*f**3 + 0*f + 6*f**j + 0 = 0.
-15, 0
Suppose -3*l = 8 + 1, 3*l = 4*t - 17. Let x(s) be the second derivative of 0*s**t + 2/9*s**3 + 5*s + 0 - 1/18*s**4. Find i, given that x(i) = 0.
0, 2
Let q(t) be the first derivative of 4/3*t**3 + 3*t**4 + 11 - 4*t**2 + 0*t. Factor q(r).
4*r*(r + 1)*(3*r - 2)
Let o(l) be the third derivative of 2*l**7/105 + 3*l**6/10 - l**5/15 - 3*l**4/2 + 36*l**2. Let o(u) = 0. What is u?
-9, -1, 0, 1
Determine k so that -764*k**3 + 781*k**3 + 14*k - 32*k - 34*k + 24*k**2 + 16 - 5*k**4 = 0.
-2, 2/5, 1, 4
Let i = -138 + 138. Let q(u) be the third derivative of -1/48*u**4 + i - 7/240*u**5 + 0*u + 0*u**3 - 5*u**2. Find p such that q(p) = 0.
-2/7, 0
Suppose 30/13*q**2 + 14/13*q**3 + 0 + 4/13*q = 0. What is q?
-2, -1/7, 0
Determine r, given that -3/5*r**3 - 21/5*r**2 + 81/5 + 63/5*r = 0.
-9, -1, 3
Let n = 3 - -17. Suppose -3*h + 2*g - 10 = -0*g, 4*g = n. Factor 0 + 1/2*q**2 + h*q.
q**2/2
Let z be (54/48)/((-510)/(-544)). Factor -2*t - 4/5*t**2 + z.
-2*(t + 3)*(2*t - 1)/5
Factor 17*a**3 - 3*a**4 + 55*a**2 - 2*a**3 - 67*a**2.
-3*a**2*(a - 4)*(a - 1)
Let u be (-4)/(-9) - 2806/8784. Let j(s) be the second derivative of 0 + 0*s**2 - 1/40*s**5 - 9*s - 1/6*s**3 - u*s**4. Let j(d) = 0. What is d?
-2, -1, 0
Let g(a) be the third derivative of 0 - 3*a**2 - 3/2*a**3 + 0*a - 1/70*a**7 - 5/4*a**4 - 3/20*a**6 - 3/5*a**5. Factor g(m).
-3*(m + 1)**3*(m + 3)
Let v(y) be the third derivative of y**8/168 + y**7/30 - 11*y**6/120 - 7*y**5/60 + 3*y**4/8 + y**2 - 10*y. Factor v(b).
b*(b - 1)**2*(b + 1)*(2*b + 9)
Let x(q) = -q**2 + 11*q + 4. Let a be x(11). Let p(u) be the second derivative of 0 + 2/27*u**3 - 1/54*u**a - 1/9*u**2 - 5*u. Factor p(w).
-2*(w - 1)**2/9
Let a(h) be the second derivative of 15*h + 0 - 1/40*h**5 - 1/12*h**4 + 0*h**2 + 1/4*h**3. Suppose a(d) = 0. What is d?
-3, 0, 1
Let a(r) be the second derivative of r**5/4 - 5*r**4/3 - 25*r**3/6 + 115*r. Factor a(q).
5*q*(q - 5)*(q + 1)
Let h(o) be the first derivative of -3*o**2/2 - 93*o - 57. Let c be h(-31). Find m such that 0 + c*m + 6/5*m**3 - 1/5*m**4 - 9/5*m**2 = 0.
0, 3
Let x(b) = -3*b - 49. Let y be x(-17). Suppose -2 + 12*l - 5*l**3 + 9*l**3 - 22*l**4 - 12*l**5 - 4*l + 24*l**y = 0. What is l?
-1, 1/6, 1
Suppose a = 4 - 3. Let c(x) = 16*x**2 - 1 - 11*x**2 + 0 - 4*x**2. Let y(p) = -12*p**3 + 7*p**2 + 2*p + 3. Let s(k) = a*y(k) + 4*c(k). Let s(i) = 0. Calculate i.
-1/3, 1/4, 1
Let m(h) be the second derivative of 1/48*h**4 - 1/24*h**3 - 3/4*h**2 + 0 + h. Suppose m(k) = 0. What is k?
-2, 3
Let k(b) be the second derivative of -b**5/70 - 4*b**4/21 - b**3 - 18*b**2/7 - 74*b. Factor k(d).
-2*(d + 2)*(d + 3)**2/7
Let o be 2/10*15/1. Factor -15/2*g**2 + 0 + 9/2*g**3 + o*g.
3*g*(g - 1)*(3*g - 2)/2
Let c be (33/(-3))/44 + 13/4. Let l(v) be the first derivative of 36/5*v**2 + 27/10*v**4 + 20/3*v**c - 2 + 16/5*v + 2/5*v**5. Let l(s) = 0. Calculate s.
-2, -1, -2/5
Let y be ((-448)/12)/(-16) + 1/(-3). Factor 2/3*q**y + 0 + 0*q + 4/3*q**3 + 2/3*q**4.
2*q**2*(q + 1)**2/3
Factor 3*b**3 - 7782 + 7*b**4 - 6*b + 17*b**2 - b**5 + 7782 - 20*b**3.
-b*(b - 3)*(b - 2)*(b - 1)**2
Let m = -12 - -37. Factor 20*s**2 - 10*s - 50*s**2 + m*s**2.
-5*s*(s + 2)
Let v(c) be the first derivative of 25*c**3/3 + 115*c**2 + 205*c + 97. Solve v(o) = 0.
-41/5, -1
Let o(f) be the first derivative of 3*f**5/20 - 3*f**3/2 - 3*f**2 - 7*f - 15. Let g(d) be the first derivative of o(d). Factor g(w).
3*(w - 2)*(w + 1)**2
Let l(c) be the first derivative of 1/8*c**4 - 11 - 5/16*c**2 - 1/10*c**5 + 1/48*c**6 + 1/4*c + 1/12*c**3. Factor l(s).
(s - 2)*(s - 1)**3*(s + 1)/8
Let a = -88 + 98. Solve -20*z**4 - 11*z**3 - 14*z**3 - 5*z**5 + 0*z - a*z**2 + 0*z = 0.
-2, -1, 0
Let q be ((-32)/3)/(2/(-258)). Let l be (-8)/(-20) - q/(-10). Find n such that -168*n**4 + 180*n**3 + 2 - l*n**2 - 5 + 36*n + 93*n**4 = 0.
1/5, 1
Find f such that 0*f + 0 - 2/7*f**2 - 2/7*f**4 - 4/7*f**3 = 0.
-1, 0
Suppose 5*g + 8 - 3 = 0, 0 = 5*z + 4*g + 4. Let x be (-296)/22 + 18 + -4. Find k such that z*k + 0 + x*k**3 - 2/11*k**2 + 2/11*k**5 - 6/11*k**4 = 0.
0, 1
Let s(q) be the first derivative of q**5/20 + q**4/4 - 3*q**3/2 - 8*q**2 - 25. Let a(t) be the second derivative of s(t). Find o, given that a(o) = 0.
-3, 1
Let z(y) = -y. Let a(l) = -2*l**2 - 109*l - 212. Let c(b) = a(b) + z(b). Factor c(x).
-2*(x + 2)*(x + 53)
Find n, given that -8/9*n + 2/9*n**3 - 2/9*n**4 - 16/9 + 4/3*n**2 = 0.
-2, -1, 2
Suppose 6*z = -4*w + 11*z, 0 = -3*w + 3*z. Factor 2/3*s**4 + w*s - 4/9*s**3 - 2/9*s**2 + 0.
2*s**2*(s - 1)*(3*s + 1)/9
Suppose 4*g = 8*g - 20. Let d = -142178 - -995248/7. Determine s, given that 6/7*s**g + d*s**2 + 2/7*s**3 + 0 + 0*s - 10/7*s**4 = 0.
-1/3, 0, 1
Let a(r) be the third derivative of r**6/90 + 13*r**5/150 - r**4/5 + 3*r**3/2 + 8*r**2. Let x(z) be the first derivative of a(z). Find c, given that x(c) = 0.
-3, 2/5
Let f(j) be the first derivative of -j**8/252 - 5*j**7/504 - j**6/216 - 4*j**3 - 4. Let r(x) be the third derivative of f(x). Factor r(z).
-5*z**2*(z + 1)*(4*z + 1)/3
Factor -1/2*o**2 - 2*o - 3/2.
-(o + 1)*(o + 3)/2
Let y(s) be the third derivative of -s**6/40 - 3*s**5/20 + s**4/2 - 27*s**2 - 3*s. Solve y(t) = 0 for t.
-4, 0, 1
Suppose -77 = 4*j - 15*j. Suppose j = 2*p + 1. Suppose 0 - 3/2*h**p - 3/2*h - 3*h**2 = 0. Calculate h.
-1, 0
Let o = -30/91 - -332/455. Let -1/5*k**4 - 1/5*k**2 + 0 + 0*k + o*k**3 = 0. Calculate k.
0, 1
Factor 16/7*y**2 + 34/7*y + 20/7 + 2/7*y**3.
2*(y + 1)*(y + 2)*(y + 5)/7
Let u be (-2)/(-5)*(2 - (-179)/(-12)). Let m = 29/3 + u.