20. Let r(l) = -8*l**2 - 7*l + 120. Let u(w) = -4*r(w) + 3*v(w). Factor u(g).
5*(g - 4)*(g + 6)
Let x be 32/(-72) + 672/540. Factor -2/5 - x*g - 2/5*g**2.
-2*(g + 1)**2/5
Let o(w) = 3*w**5 + 5*w**4 + 8*w**3 - 9*w**2 - w - 1. Let l(b) = 8*b**5 + 14*b**4 + 24*b**3 - 26*b**2 - 4*b - 2. Let z(s) = 5*l(s) - 14*o(s). Factor z(f).
-2*(f - 1)**3*(f + 1)*(f + 2)
Factor 7/3 + 2*w - 1/3*w**2.
-(w - 7)*(w + 1)/3
Suppose -2*g + 2*c + 0 = -2, 2*g - 4*c = 0. Suppose -53 + 3*h**g - 16*h + 128 - 14*h = 0. Calculate h.
5
Let q = -22 - -14. Let u(a) = 20*a**3 - 108*a**2 + 280*a - 200. Let h(l) = 7*l**3 - 36*l**2 + 93*l - 67. Let k(p) = q*h(p) + 3*u(p). Solve k(s) = 0.
1, 4
Let n(t) = -27*t**3 + 9*t**2 + 10*t - 2. Let x = 27 - 22. Let u(f) = -27*f**3 + 9*f**2 + 9*f - 3. Let v(i) = x*u(i) - 6*n(i). Find q, given that v(q) = 0.
-1/3, 1
Let i(d) = -39*d**3 + 87*d**2 - 144*d + 18. Let u(r) = 11*r**3 - 25*r**2 + 41*r - 5. Let z(g) = 5*i(g) + 18*u(g). Factor z(o).
3*o*(o - 3)*(o - 2)
Let s(a) be the third derivative of -2/3*a**3 + 0 + 0*a + 0*a**4 + 1/160*a**5 + 1/480*a**6 - a**2. Let x(m) be the first derivative of s(m). Solve x(b) = 0.
-1, 0
Suppose -25 = 5*n, -17 = -4*q + 6*n - 5*n. Solve -74*y - 146*y - 189*y**2 - 45*y**3 - q*y**4 + 73*y = 0.
-7, -1, 0
Let r(u) = 3*u + 74. Let i be r(-23). Suppose -4*h + i*c - 2 = -5, -4*c = -4. Factor -3*t**4 - 3/2*t + 3/2*t**5 + 3*t**h + 0 + 0*t**3.
3*t*(t - 1)**3*(t + 1)/2
Let x(g) be the first derivative of 21*g**4/20 + 17*g**3/5 + 3*g**2/5 - 24*g/5 - 327. Factor x(b).
3*(b + 1)*(b + 2)*(7*b - 4)/5
Let k(o) be the first derivative of -2*o**3/9 + 7*o**2 - 76*o/3 + 216. What is t in k(t) = 0?
2, 19
Suppose 3 = -0*x + 3*x, -2*o + 9 = 3*x. Factor 1/5*d**2 - 1/5*d**4 - 2/5*d + 2/5*d**o + 0.
-d*(d - 2)*(d - 1)*(d + 1)/5
Let s(m) be the third derivative of -1/40*m**6 + 1/60*m**5 + 1/70*m**7 + 0*m + 0*m**3 + 0*m**4 + 9*m**2 - 1/336*m**8 + 0. Solve s(b) = 0.
0, 1
Determine t, given that 21*t**4 - 210*t**2 + 230*t**2 + 5*t**5 - 36*t**4 = 0.
-1, 0, 2
Let x(u) = u**2 + 21. Let t be x(0). Suppose -17*f = -t*f + 32. Factor 5 + f*z - 7 - 3*z**3 - 5*z**3 + 2*z**2.
-2*(z - 1)*(z + 1)*(4*z - 1)
Factor -2/3*a**4 + 64/3*a**2 + 0 + 0*a + 28/3*a**3.
-2*a**2*(a - 16)*(a + 2)/3
Factor -3/8*a**2 + 15/8*a + 9.
-3*(a - 8)*(a + 3)/8
Let p(i) be the first derivative of -2*i**5/65 + 5*i**4/26 + 4*i**3/13 + 21. Factor p(w).
-2*w**2*(w - 6)*(w + 1)/13
Let 554*a - 80*a**4 + 800*a**3 - 554*a + 2*a**5 = 0. Calculate a.
0, 20
Factor 2/9*k**2 + 4 + 22/9*k.
2*(k + 2)*(k + 9)/9
Let s = -5 + 7. Suppose 0 = -2*i + 3*r - 0*r + 4, -2*r = -i + s. Factor -12*f**2 + 12*f**i + 3*f - 2*f - f**3.
-f*(f - 1)*(f + 1)
Let f(m) be the first derivative of -2*m**6/3 + 24*m**5/5 - 12*m**4 + 32*m**3/3 + 159. Factor f(w).
-4*w**2*(w - 2)**3
Let s be (178/(-6))/(17/(-3876)). Let h = 34228/5 - s. Factor 68*i**3 - 72/5 + h*i - 698/5*i**2 - 10*i**4.
-2*(i - 3)**2*(5*i - 2)**2/5
Let g(s) = s**3 - 5*s**2 + 6*s - 1. Let o(f) = -f**2 + f + 1. Suppose 22*l - 19*l = -3. Let h(m) = l*g(m) + o(m). Determine d so that h(d) = 0.
1, 2
Let i(g) be the first derivative of -3*g**5/5 - 3*g**4/4 + g**3 + 3*g**2/2 - 486. Factor i(s).
-3*s*(s - 1)*(s + 1)**2
Solve -26*o + 25*o + o**4 - 2*o**4 + o**3 + o**2 = 0 for o.
-1, 0, 1
What is j in -39*j**2 - j**3 + 739*j + 1024 - 24*j**2 - 1699*j = 0?
-32, 1
Let l = -15188/5 - -3038. Let -2/5*y**3 + l*y + 0 + 0*y**2 = 0. What is y?
-1, 0, 1
Let l(i) = -9*i + 20. Let q be l(2). Let p(g) be the first derivative of -5/3*g**q - 14/9*g**3 + 4/3*g + 4. Factor p(f).
-2*(f + 1)*(7*f - 2)/3
Let f = 1 + 8. Suppose -4*q = -f*q. Suppose 0 - 3*k**3 - 3*k + 6 + 6*k + q - 6*k**2 = 0. Calculate k.
-2, -1, 1
Let w = -3 + -8. Let z be 4/(-22) + (-35)/w. What is c in c**4 + 14 + 2*c**z - 14 = 0?
-2, 0
Factor -39/2*t**4 - 3/2*t**5 + 0 + 0*t + 147/2*t**2 - 105/2*t**3.
-3*t**2*(t - 1)*(t + 7)**2/2
Let s(n) be the first derivative of 0*n**4 + 0*n - 8 + 1/27*n**6 + 4/27*n**3 - 1/9*n**2 - 4/45*n**5. Solve s(q) = 0.
-1, 0, 1
Let w be (11 + (-296)/16)/(-2 - 3 - -2). Solve -w*p**2 - 2 - 1/2*p**3 - 4*p = 0 for p.
-2, -1
Let v(s) = -s**2 + 7*s + 2. Let g(c) = -c - 1. Let u(h) = -11*h - 6. Let q(b) = -4*g(b) + u(b). Let z(m) = 4*q(m) + 3*v(m). Find y, given that z(y) = 0.
-2, -1/3
Let a(l) = 11*l**3 + 29*l**2 + 25*l + 7. Let x(s) = 87*s - 12*s**3 + 66*s**2 + 51*s**3 + 24 + 36*s**2. Let j(v) = 18*a(v) - 5*x(v). Factor j(m).
3*(m + 1)**2*(m + 2)
Let r be (((-60)/275)/(-6))/(7/35). Factor 24/11*d - r*d**2 - 72/11.
-2*(d - 6)**2/11
Let j(c) be the first derivative of c**4/14 + 22*c**3/21 + 24*c**2/7 - 72*c/7 - 36. Factor j(f).
2*(f - 1)*(f + 6)**2/7
Let r(x) be the second derivative of -9*x**5/130 + 8*x**4/39 + 4*x**3/39 + 124*x + 2. What is i in r(i) = 0?
-2/9, 0, 2
Let v(p) = 9*p + 63. Let s be v(-13). Let z be ((-12)/27)/(60/s). Factor 2/5*a**2 + 0 + z*a.
2*a*(a + 1)/5
Let o(f) be the first derivative of 6 - 5/2*f**2 - 15/4*f**4 + 0*f + 5*f**3 + f**5. Factor o(l).
5*l*(l - 1)**3
Factor -6/5*s**3 - 2/5*s + 2/5*s**4 + 0 + 6/5*s**2.
2*s*(s - 1)**3/5
Let s(c) = 2*c**4 + 82*c**3 - 171*c**2 + 88*c - 1. Let f(y) = -y**4 + y**3 + y - 1. Let v(n) = f(n) - s(n). Find a such that v(a) = 0.
-29, 0, 1
Let x(k) be the first derivative of -k**4/12 - 139*k**3/9 + 367. Let x(w) = 0. What is w?
-139, 0
Factor 2/13*c**2 + 2/13*c**4 + 4/13*c**3 + 0 + 0*c.
2*c**2*(c + 1)**2/13
Let z(n) be the second derivative of 0*n**6 + 0 - 1/13*n**3 - 3/65*n**5 + 1/273*n**7 + 4/39*n**4 + 0*n**2 + 25*n. What is v in z(v) = 0?
-3, 0, 1
Let l(n) be the third derivative of n**8/15680 + n**7/5880 - n**6/1680 + n**5/6 + 11*n**2. Let x(j) be the third derivative of l(j). What is r in x(r) = 0?
-1, 1/3
Let d(i) be the first derivative of 28*i**3/3 + 122*i**2 - 72*i - 79. Determine j so that d(j) = 0.
-9, 2/7
Let u(c) be the second derivative of c**6/30 + c**5/5 - c**4/12 - 2*c**3/3 + 60*c. Solve u(q) = 0 for q.
-4, -1, 0, 1
Let d be (-2 + 1)*(0 + 0). Let s = -93 + 104. Determine o, given that s + 17 + d*o + 18*o - 1 + 3*o**2 = 0.
-3
Let z be (-66)/(-9) - 4/(-6). Suppose -18 = -z*y + 5*y. Suppose 0*f**2 - 3*f**2 + 9*f - y + 2*f**2 - 2*f**2 = 0. What is f?
1, 2
Let w(d) be the third derivative of 0*d - 1/2415*d**7 - 4*d**2 + 1/69*d**4 - 1/460*d**6 + 0*d**3 + 0 + 0*d**5. Factor w(j).
-2*j*(j - 1)*(j + 2)**2/23
Let w(g) = -9*g**3 - 12*g**2 - g + 6. Suppose 7 + 0 = s. Let m = 6 - s. Let r(a) = -a. Let j(t) = m*w(t) + 4*r(t). Solve j(k) = 0.
-1, 2/3
Let d be 13/(-26)*((-4)/(-42) - 6/9). Solve 2/7*y + 2/7*y**5 - 4/7*y**3 - 4/7*y**2 + 2/7*y**4 + d = 0 for y.
-1, 1
Let v(c) be the first derivative of c**5/45 - c**3/9 + c**2/9 + 45. Factor v(k).
k*(k - 1)**2*(k + 2)/9
Let c = 63911/19176 + 3/6392. Solve -2/3*w**2 - 8/3*w + c = 0.
-5, 1
Let s = 2407/900 - 7/900. Solve 4/3*j - s - 125/3*j**3 + 70/3*j**2 + 73/3*j**4 - 14/3*j**5 = 0.
-2/7, 1/2, 1, 2
Let f(z) = -z**2 - 11*z - 25. Let t be 2 - 4/16*0 - 7. Let h be f(t). Find b such that 12/5*b**4 + 0 + 12/5*b**2 + 18/5*b**3 + 3/5*b**h + 3/5*b = 0.
-1, 0
Let l(t) be the second derivative of 17*t + 75/2*t**2 + 5*t**3 + 0 + 1/4*t**4. Factor l(h).
3*(h + 5)**2
Let x = -205 + 208. Let c(b) be the first derivative of 3/4*b**4 + 3/5*b**5 - 5 + 0*b + 1/6*b**6 + 1/3*b**x + 0*b**2. Factor c(a).
a**2*(a + 1)**3
Let o(w) be the first derivative of -5*w**3/3 - 40*w**2 - 140*w - 108. Solve o(g) = 0.
-14, -2
Let d(t) = 90*t**2 + 353*t - 24. Let j be d(-4). Find y, given that -5/3*y**3 + 0 + 2/3*y**2 + 8/3*y + 1/3*y**j = 0.
-1, 0, 2, 4
Suppose -242*m = -250*m. Let u(x) be the second derivative of 3*x + 0*x**3 + m - 1/105*x**6 + 0*x**5 + 1/21*x**4 - 1/7*x**2. Factor u(o).
-2*(o - 1)**2*(o + 1)**2/7
Let i = -2145 + 19337/9. Factor -2/9*c**2 - i*c - 128/9.
-2*(c + 8)**2/9
Factor 119*s - 289/7 + 190/7*s**3 + 1/7*s**5 - 766/7*s**2 + 31/7*s**4.
(s - 1)**3*(s + 17)**2/7
Find w, given that -3/2*w**3 - 21/2 - 45/2*w - 27/2*w**2 = 0.
-7, -1
Let u(p) be the first derivative of -2*p**5/85 + 3*p**4/34 + 32*p**3/51 + 12*p**2/17 - 117. Find q such that u(q) = 0.
-2, -1, 0, 6
Suppose 8 = 2*g - 5*i, g - 7 = -0*i + i. Let h(w) be the first derivative of 0*w**4 + g*w + 12*w**2 - 3/5*w**5 + 6*w**3 - 3. Let h(t) = 0. Calculate t.
-1, 3
Let l(i) be the third derivative of -i**5/20 + 11*i**4/12 - 121*i**3/18 + 18*i**2. Solve l(s) = 0.
11