23. Let d be 11/k - (-8)/24. Factor -9*q**2 + q**2 + 3 + 4*q**d + 1 + 0*q**4.
4*(q - 1)**2*(q + 1)**2
Let s(j) be the second derivative of -j**7/12600 + j**5/600 - 3*j**4/2 - 8*j. Let p(g) be the third derivative of s(g). Let p(z) = 0. What is z?
-1, 1
Suppose 1/7*b**4 - 6/7*b**3 - b**2 + 2/7*b**5 - 2/7*b + 0 = 0. What is b?
-1, -1/2, 0, 2
Let v(t) be the second derivative of -t**7/70 - 8*t**6/25 - 72*t**5/25 - 64*t**4/5 - 128*t**3/5 + 147*t. Factor v(o).
-3*o*(o + 4)**4/5
Solve -30/7*y**2 - 11/7*y**3 + 9/7*y + 0 = 0 for y.
-3, 0, 3/11
Let k(v) be the second derivative of -v**4/36 - v**3/6 - v**2/3 + 12*v - 2. Factor k(a).
-(a + 1)*(a + 2)/3
Let k(q) = -2*q**2 + 9*q - 8. Let j be k(7). Let t = 130/3 + j. Factor 8/3 + 2*l**2 - 4*l - t*l**3.
-(l - 2)**3/3
Let c(u) be the first derivative of -4/7*u**5 + 1/7*u**6 + 6/7*u**4 + 1/7*u**2 - 1 + 0*u - 4/7*u**3. Solve c(k) = 0.
0, 1/3, 1
Let a(o) = 2*o + 10. Let h be a(-3). Factor -13*q + 11*q**4 + 25*q - 14*q**h - 9*q**3.
-3*q*(q - 1)*(q + 2)**2
Let i(x) = x**2 + 2*x + 32. Let y be i(-14). Factor -16*r + 0*r - 103*r**3 - 80*r**2 + y*r**3 - 165*r**3 - 16*r**4.
-4*r*(r + 2)**2*(4*r + 1)
Let k(m) be the second derivative of -m**6/10 - 33*m**5/10 - 97*m**4/4 + 132*m**3 - 216*m**2 + 172*m. Factor k(d).
-3*(d - 1)**2*(d + 12)**2
Let j(g) = -6*g**4 + 20*g**3 + g**2 - 63*g + 53. Let c(z) = -10*z**4 + 30*z**3 + 2*z**2 - 94*z + 80. Let h(i) = -5*c(i) + 8*j(i). Factor h(n).
2*(n - 1)**2*(n + 3)*(n + 4)
Let l(x) be the third derivative of 0*x + 0 + 33*x**2 + 1/420*x**7 + 1/72*x**4 + 0*x**3 + 1/72*x**6 + 1/40*x**5. Determine p so that l(p) = 0.
-2, -1, -1/3, 0
Factor -72 + 21*r + 5*r + 2*r**3 - 15*r + 17*r + 22*r**2 + 20*r.
2*(r - 1)*(r + 6)**2
Let j(i) = 11*i - 218. Let m be j(20). Let 2/3*v**m - 2/3*v + 0 = 0. Calculate v.
0, 1
Let o = -3208/15 + 214. Let j(x) be the first derivative of 0*x + o*x**3 + 5 + 0*x**2. Solve j(s) = 0.
0
Determine j so that -30*j**2 + 6*j**2 + 115*j**3 + 23*j**4 - 20*j**5 - 6*j**2 - 13*j**4 + 15*j**4 = 0.
-2, 0, 1/4, 3
Let g(f) be the first derivative of -49*f**5/5 + 3297*f**4/2 - 223717*f**3/3 + 63114*f**2 - 17956*f - 466. Factor g(b).
-(b - 67)**2*(7*b - 2)**2
Let d(s) = 5*s**2 + 50*s + 47. Let r(y) = 21*y**2 + 201*y + 189. Let i(v) = 9*d(v) - 2*r(v). Factor i(t).
3*(t + 1)*(t + 15)
Let h(p) be the third derivative of p**5/30 + 4*p**4 + 192*p**3 - 101*p**2. Factor h(i).
2*(i + 24)**2
Let p be 145 + (2 + -3)*3. Let i(x) = 32 - 111*x + 32 + 29*x**2 + p - 17. Let t(s) = 7*s**2 - 28*s + 47. Let c(b) = -2*i(b) + 9*t(b). Factor c(z).
5*(z - 3)**2
Suppose -28*t - 1039 = -1095. Let b(w) be the first derivative of -4/3*w**3 + 0*w**t + 4*w - 7. Factor b(g).
-4*(g - 1)*(g + 1)
Factor -1/4*f**3 + 0 + 0*f**2 + 1/2*f**4 + 0*f - 1/4*f**5.
-f**3*(f - 1)**2/4
Let n(w) = w**3 + 7*w**2 + 8*w - 4. Let r be n(-5). Let i be r/10*3*4/36. Factor -2/5*t + i + 1/5*t**2.
(t - 1)**2/5
Let k(r) be the first derivative of 2535*r**6/2 + 1599*r**5 - 3605*r**4/2 - 7990*r**3/3 - 395*r**2/2 - 5*r - 212. Suppose k(a) = 0. Calculate a.
-1, -1/39, 1
Suppose 0 = n + 3*o - 2*o - 2, 0 = 3*n + o - 6. Let s(k) be the first derivative of -2*k**3 - k**n + k**3 - 2*k + 1 - 2*k**2 - k. Find y, given that s(y) = 0.
-1
Let i = 24880 + -24878. Factor -2/9*b**3 - 16/9*b**i + 0 + 0*b.
-2*b**2*(b + 8)/9
Let o(c) = c**3. Let b(j) be the third derivative of j**6/120 + j**5/4 + j**4 + 2*j**3 + 9*j**2. Let u(v) = b(v) + 2*o(v). Solve u(z) = 0 for z.
-2, -1
Let q be (2670/444 - 6)*1/(-2). Let w = 293/444 - q. Suppose 0*o**2 - 2/3*o**4 + w*o**3 + 0 + 0*o = 0. What is o?
0, 1
Let p = -2574 + 2576. Factor 0 - 1/3*x - 2*x**3 + 4/3*x**p - 1/3*x**5 + 4/3*x**4.
-x*(x - 1)**4/3
Let d(u) be the second derivative of -3*u**5/20 + 11*u**4/4 - 13*u**3 + 24*u**2 - 4*u + 43. Factor d(j).
-3*(j - 8)*(j - 2)*(j - 1)
Suppose -5*c + 32 = 4*f - 40, 3*c = 5*f - 90. Determine t, given that -80*t**3 - 55 + 21 - 24*t**2 + f + 64*t - 25*t**4 = 0.
-2, 2/5
Let f(n) be the third derivative of -n**6/120 - n**5/10 - n**4/24 - n**3/2 - 14*n**2. Let d be f(-6). Factor 6/5 + 14/5*y + 2/5*y**d + 2*y**2.
2*(y + 1)**2*(y + 3)/5
Suppose 0 = 3*t - 10*t - 28. Let h be ((-1)/t)/((-27)/(-36)). Factor 4/3*g**2 + 0*g + 4/3*g**3 + h*g**4 + 0.
g**2*(g + 2)**2/3
Let j(o) = -41 - o + 55 - o. Let n be j(6). Determine u, given that -2*u**5 - 3*u**4 - 2*u**3 + n*u**4 - 3*u**4 = 0.
-1, 0
Let b = 823 + -817. Let o(l) be the third derivative of -2*l**2 + 0 + 0*l + 0*l**4 - 1/60*l**b + 0*l**3 + 1/15*l**5. Factor o(c).
-2*c**2*(c - 2)
Let -34 - y + 8*y**2 + 31*y**3 + 34 + 16*y**4 - 5*y**5 - 49*y**3 = 0. What is y?
0, 1/5, 1
Let d be (0 + 0)*(-320)/320. Find u, given that d*u**2 + 0*u - 14/3*u**4 + 0 + 10/3*u**5 + 4/3*u**3 = 0.
0, 2/5, 1
Let v be 7*((-435)/910 - 4/(-8)). Suppose 2/13*s + 0 - v*s**2 = 0. What is s?
0, 1
Let x = -109 - -118. Suppose x*c - 55 = -2*c. Suppose 2/3*a**c + 0*a**2 + 2/3*a**3 + 4/3*a**4 + 0 + 0*a = 0. What is a?
-1, 0
Let p(j) be the first derivative of j**5/10 + j**4/6 - 2*j**3/3 + 5*j + 14. Let t(i) be the first derivative of p(i). Factor t(z).
2*z*(z - 1)*(z + 2)
Let x be 4/20 + 2 + 44/(-20). Let 0 + 6/5*s**4 + 2/5*s**5 - 8/5*s**2 + x*s + 0*s**3 = 0. What is s?
-2, 0, 1
Let u = -50507/4 + 12628. Factor -1/4*v**3 + u*v + 1/4*v**2 + 3/4.
-(v - 3)*(v + 1)**2/4
Let b(x) be the first derivative of 4*x**5/5 + 10*x**4 + 32*x**3 - 20*x**2 - 100*x + 27. Factor b(d).
4*(d - 1)*(d + 1)*(d + 5)**2
Let x(u) be the third derivative of -1/70*u**7 + 0*u + u**3 - 3/8*u**4 - 33*u**2 + 3/40*u**6 + 0 - 1/20*u**5. Suppose x(g) = 0. What is g?
-1, 1, 2
Solve 232/3*x**2 + 0 + 36*x**3 + 0*x - 4/3*x**4 = 0.
-2, 0, 29
Suppose -34 - 9 = -3*q - 4*c, -c = -2*q + 14. Suppose 4*i = 2*i + 6. Solve -14*s**3 - q*s**2 + 2*s + s + 2*s**i = 0 for s.
-1, 0, 1/4
Let i(d) be the first derivative of d**7/420 - d**6/180 - d**5/30 - 5*d**3/3 - 4*d + 24. Let h(w) be the third derivative of i(w). Factor h(b).
2*b*(b - 2)*(b + 1)
Let f(p) = 3*p**4 - 13*p**3 - 5*p**2 + 11*p + 3. Let n(v) = -5*v**4 + 27*v**3 + 9*v**2 - 23*v - 7. Suppose -2 = y + 1. Let m(z) = y*n(z) - 7*f(z). Factor m(q).
-2*q*(q - 2)*(q + 1)*(3*q - 2)
Let o(n) be the second derivative of n**5/20 - 7*n**4/12 + n**3 + 4*n**2 + n. Let h be o(6). Factor 4 + 2*r - r**2 + r**2 - h*r + 2*r**3.
2*(r - 1)**2*(r + 2)
Let i be (178/44 - 4)*5/15. Let d(r) be the second derivative of 0*r**2 + 8*r - 2/55*r**5 + 0*r**3 + i*r**4 + 0. Factor d(n).
-2*n**2*(4*n - 1)/11
Let h(t) be the first derivative of t**4/26 - 140*t**3/39 + 1152*t**2/13 + 5184*t/13 - 58. Find n such that h(n) = 0.
-2, 36
Let c be 8/2 - (-1 + 1). Factor 16*t**3 + 36*t**2 - 10 - 40 - 4 + 2*t**c.
2*(t - 1)*(t + 3)**3
Let k = -41183/7 + 5887. Determine r so that k*r + 40/7*r**2 + 4/7 + 18/7*r**3 = 0.
-1, -2/9
Let h(p) be the third derivative of p**7/4200 + p**6/900 - p**5/120 - p**4/20 + 10*p**3/3 + 8*p**2. Let c(r) be the first derivative of h(r). Factor c(u).
(u - 2)*(u + 1)*(u + 3)/5
Let v(p) = 4*p**3 - 64*p**2 + 120*p - 60. Let r = -69 + 58. Let t(w) = -w**3 + 13*w**2 - 24*w + 12. Let b(m) = r*t(m) - 2*v(m). Suppose b(c) = 0. Calculate c.
1, 2
What is b in b**2 + 27*b**3 + 31*b**2 + 6*b**2 + 13*b**3 - 4*b**5 + 4*b**4 - 6*b**2 = 0?
-2, -1, 0, 4
Let q(z) = 5*z**2 - 14*z - 3. Let v be q(5). Let p = 209/4 - v. Let 1/4*s**3 - p - 3/4*s**2 + 3/4*s = 0. Calculate s.
1
Let i(u) be the third derivative of 21*u**2 + 1/120*u**7 + 5/48*u**5 + 1/1344*u**8 + 0 + 0*u + 19/480*u**6 + 1/6*u**3 + 1/6*u**4. Find j, given that i(j) = 0.
-2, -1
Let o(j) be the first derivative of -2/75*j**5 + 4/45*j**3 + 0*j**2 - 6 + 0*j**4 - 2/15*j. Factor o(b).
-2*(b - 1)**2*(b + 1)**2/15
Let i = 1 + 1. Suppose -4*m = 4*h - i*h, 2*m = -2. Factor 2*l**2 + 2*l**h + 2*l - 5*l**2.
-l*(l - 2)
Determine g, given that -42*g**2 + 2*g**4 - 841*g - 21*g**3 + 1753*g - 836*g - 15*g**3 = 0.
-2, 0, 1, 19
Let o = 23789/78177 - 3/2369. Let f(j) be the second derivative of o*j**4 + 5/22*j**5 - 6*j + 0*j**2 + 0 + 4/33*j**3. Factor f(h).
2*h*(5*h + 2)**2/11
Let t = 10 - 6. Let q = -285 + 288. Factor -t*f**2 + 1/2*f**5 - 7/2*f - f**q + f**4 - 1.
(f - 2)*(f + 1)**4/2
Let i be (-1638)/(-378) + 4/(-3). Determine c, given that 0 + 0*c + 2/3*c**2 + c**i = 0.
-2/3, 0
Let y(k) be the second derivative of 0*k**4 + 1/105*k**7 - 18*k - 4/25*k**6 + 0 + 0*k