 20. Let h(y) = y**2 - 9. Let s be h(3). Factor 2/5*w**4 + 4/5*w**3 + 2/5*w**2 + s*w + o.
2*w**2*(w + 1)**2/5
Let j = 31 + -28. Let s(i) be the third derivative of 41/540*i**6 - 1/63*i**7 + 0*i + 1/27*i**4 - j*i**2 + 0 - 4/45*i**5 + 0*i**3. Let s(h) = 0. What is h?
0, 1/3, 2/5, 2
Let t be (-16)/(-28)*(3 - 2/3). Find o, given that t + 2/3*o**2 + 2*o = 0.
-2, -1
Let q = -4 + 10. Let u be 4 + 2*(-3)/q. Factor -2*r**2 + 0*r**u - 2*r**3 + 3*r**3.
r**2*(r - 2)
Let c(s) be the third derivative of -s**7/210 + s**6/60 + s**5/60 - s**4/12 - 3*s**2 - 4. Determine l, given that c(l) = 0.
-1, 0, 1, 2
Let v(t) = -4*t - 4. Let d(c) = c**2 + 8*c + 7. Let n(o) = 4*d(o) + 7*v(o). Determine b, given that n(b) = 0.
-1, 0
Let m = -2/361 - -744/3971. Find w such that m*w**3 + 0 - 2/11*w**2 + 0*w = 0.
0, 1
Let i(b) be the third derivative of -1/24*b**4 + b**2 - 1/24*b**5 + 0*b**3 + 0*b - 1/420*b**7 + 0 - 1/60*b**6. Solve i(d) = 0.
-2, -1, 0
Factor -2/9*y + 2/9*y**2 - 4/9.
2*(y - 2)*(y + 1)/9
Let f(i) be the second derivative of i**5/90 + i**4/27 + i**3/27 - 7*i. Find d such that f(d) = 0.
-1, 0
Let j(g) = g**2 - 4*g + 2. Let b be j(3). Let p(i) = -16*i**2 - 44*i - 64. Let y(d) = -d**2 - d. Let h(m) = b*p(m) + 12*y(m). Suppose h(o) = 0. What is o?
-4
Suppose f + 0*f = 6. Suppose -5*l = -f - 4. Determine p, given that 0*p + 3*p**l - p**2 + 2*p = 0.
-1, 0
Let b(o) be the third derivative of o**7/420 - o**6/90 - 2*o**3/3 + o**2. Let w(m) be the first derivative of b(m). Suppose w(z) = 0. Calculate z.
0, 2
Let w(v) be the third derivative of 0 + 0*v + 0*v**4 + 0*v**3 + 1/420*v**6 - 1/210*v**5 - 2*v**2. Determine l so that w(l) = 0.
0, 1
Suppose 6*j - 25 = j. Solve 4*u**2 - 2*u - u**2 + 14*u - j*u**2 - 18 = 0.
3
Suppose -16 = -n - 14. Let o be (-1)/n + 3/3. Let -1/2*v**2 - v**3 + 0 + 0*v - o*v**4 = 0. Calculate v.
-1, 0
Let d(a) = a**4 + 2*a**3 + 2*a**2 - 2*a + 3. Let s(v) = v**3 + v**2 - v + 1. Let k be (-2 - -1)*(0 + 3). Let u(m) = k*s(m) + d(m). Find l such that u(l) = 0.
-1, 0, 1
Suppose 0 = 2*u - 3 - 3. Let n be (-1)/(u/(-18)) - 2. Factor -5*o - 3*o**2 + 2*o**3 + 3*o + 2*o**n + o**4.
o*(o - 1)*(o + 1)*(3*o + 2)
Let f(k) = -k - 3. Let s be f(-3). What is b in s - 1/2*b**5 - 2*b**4 - 3*b**3 - 1/2*b - 2*b**2 = 0?
-1, 0
Let x be ((-33)/21 - -4) + -1. Factor 2/7*r**2 - x*r**3 + 0 + 0*r.
-2*r**2*(5*r - 1)/7
Suppose -4*b + 3 = -5. Factor 2/3*z**b + 4/3 - 2*z.
2*(z - 2)*(z - 1)/3
Suppose -2*y + 4 = -4*k, -6 = -2*y - y. Let l(o) be the second derivative of -1/9*o**7 + 0 + 1/5*o**6 + 0*o**3 - o + k*o**2 - 1/15*o**5 + 0*o**4. Factor l(r).
-2*r**3*(r - 1)*(7*r - 2)/3
Let k(b) be the third derivative of -b**8/26880 + b**7/3360 + b**6/320 - 7*b**5/60 - 6*b**2. Let i(s) be the third derivative of k(s). Factor i(x).
-3*(x - 3)*(x + 1)/4
Let h(m) be the third derivative of 2*m**7/735 - 13*m**6/840 + 11*m**5/420 - m**4/84 - 7*m**2. Find a, given that h(a) = 0.
0, 1/4, 1, 2
Let m be 26/7 - 8/(-28). Determine b so that 5*b**2 - 5*b**m + 0*b**5 - b + 0*b + b**5 + 3*b**5 - 3*b**3 = 0.
-1, 0, 1/4, 1
Let v(m) be the second derivative of 1/6*m**3 - m**2 - 1/12*m**4 + 1/60*m**5 + 0 + 3*m. Let r(l) be the first derivative of v(l). Suppose r(s) = 0. Calculate s.
1
Let z(o) be the first derivative of -o**7/15 + 3*o**6/25 + o**5/10 - 3*o**4/10 + 2*o**3/15 + 3*o - 1. Let h(n) be the first derivative of z(n). Solve h(v) = 0.
-1, 0, 2/7, 1
Let x = 100/3 - 32. Factor -2/3*t**2 - x*t - 2/3.
-2*(t + 1)**2/3
Let k(l) be the third derivative of l**6/200 + 3*l**5/100 + l**4/20 - 3*l**2. Find x such that k(x) = 0.
-2, -1, 0
Let j(h) be the second derivative of 2*h + 0*h**4 + 1/2*h**2 + 0 + 0*h**3 - 1/180*h**5. Let g(i) be the first derivative of j(i). Solve g(w) = 0.
0
Suppose 2*n - 12 = -0*n. Let c = 8 - n. Solve -7 - 6*w**c - 9*w**3 + 7 = 0 for w.
-2/3, 0
Let j(t) be the second derivative of 9/100*t**5 + 0*t**2 - 2/35*t**7 - 1/10*t**3 + 1/10*t**4 + 0 - 2/25*t**6 + t. Find f such that j(f) = 0.
-1, 0, 1/2
Let i be (-10)/(-60) - (-11)/6. Let x(b) be the second derivative of -1/60*b**6 + 0*b**3 + 0*b**i + 0 - b + 1/24*b**4 - 1/40*b**5 + 1/84*b**7. Factor x(d).
d**2*(d - 1)**2*(d + 1)/2
Let c(x) be the third derivative of -x**7/420 - x**6/80 - x**5/40 - x**4/48 + 7*x**2. Factor c(b).
-b*(b + 1)**3/2
Let l = 91 + -89. Let w(m) be the first derivative of 2 + 1/30*m**5 + 0*m + 1/36*m**6 + 0*m**4 + 0*m**3 + 0*m**l. Factor w(d).
d**4*(d + 1)/6
Let y = -201 - -5428/27. Let z(a) be the second derivative of -y*a**3 + 0 + 0*a**2 - 1/54*a**4 + a. Determine b so that z(b) = 0.
-1, 0
Let s(t) be the second derivative of -t**6/180 + t**5/30 - t**4/18 - 2*t**2 + 2*t. Let o(f) be the first derivative of s(f). Let o(p) = 0. Calculate p.
0, 1, 2
Let y(s) be the first derivative of 3*s**5/20 - 5*s**4/16 - s**3/3 + s**2/2 - 11. Let y(u) = 0. What is u?
-1, 0, 2/3, 2
Let p(n) = n**2 - 14*n - 4. Let a(f) = f**2 - 13*f - 4. Let w(i) = -6*a(i) + 5*p(i). Let j be w(8). What is o in 3*o + 0*o - o + 2*o**2 - j*o = 0?
0, 1
Let w(c) = 2*c**2 + 4. Let d(l) be the second derivative of l**4/6 - l**3/6 + 5*l**2/2 + 2*l. Let u(q) = -4*d(q) + 5*w(q). Factor u(z).
2*z*(z + 2)
Let j(x) be the first derivative of 3*x**5/10 - 3*x**4 - 4*x**3 + 72*x**2 + 216*x - 18. Find f such that j(f) = 0.
-2, 6
Let m = -273/5 - -55. Factor -4/5*r**3 - 4/5*r**2 + 2/5*r + m*r**4 + 2/5*r**5 + 2/5.
2*(r - 1)**2*(r + 1)**3/5
Let r = -10 + 10. Let d(p) be the second derivative of 0*p**4 + 0*p**3 - 1/20*p**5 + r + 2*p + 0*p**2. Factor d(f).
-f**3
Let h(o) = 2*o**2 - 3*o - 5. Let g(n) be the first derivative of 4/3*n**3 - 11*n - 7/2*n**2 + 2. Let v(x) = 4*g(x) - 9*h(x). Factor v(w).
-(w + 1)*(2*w - 1)
Factor 0*c**2 + 12*c**3 + 5*c**4 + 3*c**2 + 6*c**2 + 2*c.
c*(c + 1)**2*(5*c + 2)
Let n(f) = -2*f**3 - 3*f**2 - 2*f + 2. Let h be n(-3). Factor -3*i**2 + 7*i + 32 - h - i.
-3*(i - 1)**2
Let y(w) = 13*w**5 + 15*w**4 + 37*w**3 + 18*w**2 - 3*w. Let x(j) = j**5 - j**4 + j**3 - j. Let t(v) = 14*x(v) - 2*y(v). Suppose t(a) = 0. What is a?
-1, -2/3, 0
Let k(u) = 4*u**3 - 2*u**2 + 2. Let p be ((-4)/(-14))/(10/70). Let l(g) = -17*g**3 + 7*g**2 + g - 9. Let z(c) = p*l(c) + 9*k(c). Let z(b) = 0. What is b?
0, 1
Factor -a**4 + 6*a + 4*a**5 + 5*a**4 - 6*a.
4*a**4*(a + 1)
Let u(t) be the third derivative of t**10/15120 - t**8/3360 - t**4/8 + 3*t**2. Let g(m) be the second derivative of u(m). Find z such that g(z) = 0.
-1, 0, 1
Let c(h) be the second derivative of 1/20*h**5 - 7/90*h**6 - 1/9*h**3 + 0 + h + 0*h**2 + 1/12*h**4 + 1/42*h**7. Factor c(p).
p*(p - 1)**3*(3*p + 2)/3
Let q(u) = u**3 + 8*u**2 + 7*u + 5. Let c be q(-7). Let p(y) = -y + 1. Let d(s) = 4*s**3 - 7*s**2 - 3*s + 6. Let k(f) = c*p(f) - d(f). Factor k(m).
-(m - 1)**2*(4*m + 1)
Let v(g) be the first derivative of 2*g**3/7 + 9*g**2/7 + 12*g/7 + 20. Factor v(d).
6*(d + 1)*(d + 2)/7
Suppose -2*y - 16 = -6*y. Let p(f) be the first derivative of -1 + y*f + 0*f**3 + 3*f**2 + 8*f**2 + 6*f**3. Factor p(k).
2*(k + 1)*(9*k + 2)
Suppose 2*l = 7*l - 20. Factor 13*s**3 - 4*s**l - 3*s**3 - 2*s**3.
-4*s**3*(s - 2)
Let v(q) = q**2 - 2. Let l be v(-2). Let g be (l/6)/(1/3). Factor -g + 2 - 4*z**2 - 2*z + 2*z**2 + 3.
-2*(z - 1)*(z + 2)
Let c = 5 - 9. Let g(w) = w**3 - 2*w**2 + 3. Let u(l) = 2*l**3 - 2*l**2 + 4. Let s(d) = c*g(d) + 3*u(d). Find h, given that s(h) = 0.
-1, 0
Let k(n) be the first derivative of 128*n + 5 - 152/3*n**3 - 128*n**2 - 5*n**4. Factor k(f).
-4*(f + 4)**2*(5*f - 2)
Let c(t) be the second derivative of 5*t**4/12 + 55*t**3/6 + 25*t**2 - 59*t. Factor c(a).
5*(a + 1)*(a + 10)
Let c(d) be the third derivative of 5/27*d**7 + 0*d**3 - 19/54*d**6 - d**2 - 2/27*d**4 + 0 + 0*d + 34/135*d**5. Find f such that c(f) = 0.
0, 2/7, 2/5
Let s(k) be the third derivative of k**9/7560 - k**8/6720 - k**7/1260 + k**6/720 - k**4/6 - 2*k**2. Let i(c) be the second derivative of s(c). Factor i(y).
y*(y - 1)*(y + 1)*(2*y - 1)
Factor -2 - 2*y**2 - 21*y + 13*y + 3*y**2 + 7*y.
(y - 2)*(y + 1)
Let p(j) be the second derivative of -j**7/840 + j**5/80 + j**4/48 - j**2 - 2*j. Let q(h) be the first derivative of p(h). Factor q(r).
-r*(r - 2)*(r + 1)**2/4
Let v(m) be the second derivative of -2*m + 0*m**5 + 1/9*m**2 - 1/27*m**4 + 0*m**3 + 0 + 1/135*m**6. Let v(r) = 0. What is r?
-1, 1
Let i(q) be the second derivative of -q**4/36 - 8*q**3/9 + 2*q