1)**2*(a + 5)/5
Let y(k) be the second derivative of -5/4*k**4 + 1/6*k**6 - 14*k + 0 - 1/4*k**5 + 5/6*k**3 + 5*k**2. Factor y(g).
5*(g - 2)*(g - 1)*(g + 1)**2
Factor -2/11*p**3 + 0*p + 0 + 4/11*p**2 - 2/11*p**4.
-2*p**2*(p - 1)*(p + 2)/11
Let y = 4379 + -4376. Factor 2/5*j - 4/5 + 4/5*j**2 - 2/5*j**y.
-2*(j - 2)*(j - 1)*(j + 1)/5
Let y be 584 + -583 + (2 + -1 - 8/(-5)). Suppose 2/5*n**4 + 0 + 6/5*n**2 + y*n - 2*n**3 = 0. What is n?
-1, 0, 3
Let g = 205/119 + -1/119. Factor -22/7*p - 8/7*p**2 + 2/7*p**3 - g.
2*(p - 6)*(p + 1)**2/7
Let w(m) be the first derivative of 2*m**5/25 - 23*m**4/10 - 2*m**3/15 + 23*m**2/5 - 34. Let w(j) = 0. Calculate j.
-1, 0, 1, 23
Solve 27/7*j**2 + j**3 + 10/7 - 1/7*j**4 + 29/7*j = 0 for j.
-1, 10
Let t(x) = 7*x + 9. Let d(s) = -s. Let c(l) = 6*d(l) + t(l). Let p be c(-3). Determine u, given that 68*u + 160*u**2 + 7 + p + 5*u**3 - 5 + 59*u**3 = 0.
-2, -1/4
Let g(x) = 12*x**4 - 3*x**3 + 11*x**2 + 5*x + 5. Let p(h) = -2*h**4 - h**3 - h**2 - h - 1. Let c(o) = -g(o) - 5*p(o). Suppose c(z) = 0. What is z?
0, 1, 3
Let x(a) be the second derivative of -a**7/112 - 7*a**6/80 - 3*a**5/10 - a**4/4 + a**3 + 3*a**2 + 6*a. Factor x(j).
-3*(j - 1)*(j + 2)**4/8
Let r(a) be the first derivative of -a**6/24 + a**5/4 - a**4/4 - 4*a**3/3 + 4*a**2 - 4*a - 75. Factor r(f).
-(f - 2)**3*(f - 1)*(f + 2)/4
Let p(z) be the third derivative of -23*z**2 + 0 + 7/2*z**4 + 0*z + 81/20*z**5 + 3/2*z**3 + 8/35*z**7 + 9/5*z**6. Determine d so that p(d) = 0.
-3, -1, -1/4
Suppose -2*l + 38 + 0 = 0. Factor 17*n - 4*n**2 + 28 + l*n - 60.
-4*(n - 8)*(n - 1)
Suppose -38*p + 96 = -35*p. Let h = -1 + 4. Let -3*z**2 - 21*z**2 + p*z - 11 - 5 + 2*z**3 - z**4 + 6*z**h = 0. Calculate z.
2
Suppose 4 + 11 = 3*y. Suppose t = 3*p - 5, -y*p + 27 = 2*t + t. Factor p + 14*m + 12*m**2 + 3*m**3 + 2*m**2 + 1 + m**3.
2*(m + 1)*(m + 2)*(2*m + 1)
Let y(k) be the second derivative of -k**4/4 - k**3 - 3*k**2/2 - 77*k. Find p, given that y(p) = 0.
-1
Let w(n) be the first derivative of 4/3*n**3 + 0*n + 1/72*n**4 - 11/2160*n**6 + 0*n**2 - 1/80*n**5 + 4. Let d(q) be the third derivative of w(q). Factor d(v).
-(v + 1)*(11*v - 2)/6
Let w be 1 + -2*((-2)/(-4) - 1). Determine n, given that 156*n**2 + 3*n**4 - 25*n**5 - 126*n**w + 20*n**3 + 5*n - 33*n**4 = 0.
-1, -1/5, 0, 1
Let y(i) be the second derivative of 0 + 1/35*i**5 + 1/21*i**4 - 10/21*i**3 + 20*i + 6/7*i**2. Solve y(t) = 0 for t.
-3, 1
Let h(t) = -4*t**5 - 6*t**4 + 10*t**3 + 2*t**2 + 4. Let r(a) = -15*a**5 - 23*a**4 + 41*a**3 + 9*a**2 + 18. Let x(c) = -18*h(c) + 4*r(c). Factor x(l).
4*l**3*(l + 2)*(3*l - 2)
Let z(b) be the third derivative of 7*b**5/240 + 187*b**4/96 - 9*b**3/4 - 524*b**2. Factor z(i).
(i + 27)*(7*i - 2)/4
Determine n so that 0*n + 3*n**2 + 0 + 1/6*n**4 + 11/6*n**3 = 0.
-9, -2, 0
Let k = -843 - -20233/24. Let s(g) be the third derivative of -13*g**2 + k*g**4 + 0*g + 0*g**3 - 1/120*g**5 + 0. Suppose s(h) = 0. Calculate h.
0, 2
Let w(y) = 2*y**3 - y**4 - 2*y**3. Suppose 0 = 4*f - t - 0 + 13, f - t = -7. Let x(a) = a**4 + 3*a**3 - 3*a**2 - 3*a. Let u(q) = f*w(q) + x(q). Factor u(r).
3*r*(r - 1)*(r + 1)**2
Let d(g) = -g**2 - g. Let w(z) = 5*z**3 + z**2 - 4*z. Let r = 13 - 14. Let o(j) = r*w(j) - 6*d(j). What is h in o(h) = 0?
-1, 0, 2
Let -12/5*l + 3*l**2 - 3/5*l**3 + 0 = 0. Calculate l.
0, 1, 4
Let x(y) be the third derivative of 5*y**8/112 - 19*y**7/70 + 21*y**6/40 - y**5/4 - y**4/4 + 193*y**2. Let x(q) = 0. What is q?
-1/5, 0, 1, 2
Let m be 19/(-7) - ((-30)/(-7) - 4). Let l be (27/(-9))/(-9 - 0/m). Factor -1/3*r**2 + 0 + l*r.
-r*(r - 1)/3
Let i(x) = x**2 + 14*x + 2. Let q be i(-14). Let g(s) = s**3 - 2*s**2 + 3*s - 3. Let d be g(q). Let 0*f**3 - 3*f - d*f**2 + 5*f + f**3 = 0. Calculate f.
0, 1, 2
Suppose -4*o = 2*d - 6, 2 = 3*o + 4*d - 5*d. Let w be (7 - o) + (-11 - -7). Factor 0*t + 3*t + 3 - t**2 - w*t + t.
-(t - 3)*(t + 1)
Let p(h) be the second derivative of h**5/30 + 19*h**4/18 - 20*h**3/9 + h + 20. Factor p(w).
2*w*(w - 1)*(w + 20)/3
Factor -4*c**3 + 48 + 103*c - 28*c - 43*c - 20*c**2.
-4*(c - 2)*(c + 1)*(c + 6)
Let o = -101877 - -101879. Let t = -1 - -1. Factor t*u**3 - 1/3*u**4 - 2/3*u + u**o + 0.
-u*(u - 1)**2*(u + 2)/3
Let g be (1/4)/((45/340)/9). Suppose 2*h**2 + 28*h**5 - g*h**2 - 10*h**3 + 16*h**4 - 30*h**3 - h**2 + 12*h = 0. Calculate h.
-1, 0, 3/7, 1
Let o(s) be the first derivative of -7*s**6/10 - 57*s**5/25 - 3*s**4/20 + 23*s**3/5 + 12*s**2/5 - 12*s/5 - 800. Suppose o(n) = 0. Calculate n.
-2, -1, 2/7, 1
Let x(p) be the first derivative of 5*p**4/4 - 345*p**3 + 71415*p**2/2 - 1642545*p - 105. Suppose x(j) = 0. Calculate j.
69
Let s(l) = 11*l**2 + 35*l - 150. Let h(d) = d**2. Let p(w) = 6*h(w) - s(w). Factor p(x).
-5*(x - 3)*(x + 10)
Let u(n) be the first derivative of n**4/4 - 38*n**3/3 - n**2/2 + 38*n + 90. Solve u(a) = 0 for a.
-1, 1, 38
Suppose -1/4*o**2 - 5/2*o - 21/4 = 0. What is o?
-7, -3
Factor 0*u + 1/3*u**5 + 0*u**2 + u**3 + 0 + 4/3*u**4.
u**3*(u + 1)*(u + 3)/3
Let d(z) be the third derivative of -z**5/30 + 2*z**4/3 - 2*z**2 - 25. Solve d(l) = 0 for l.
0, 8
Let c = -93/7 + 307/21. Factor -c + 2/3*m**2 - 2/3*m.
2*(m - 2)*(m + 1)/3
Let q(m) be the second derivative of -m**7/7140 + 2*m**6/765 - 4*m**5/255 + 13*m**3/3 - m**2/2 + m + 1. Let g(r) be the second derivative of q(r). Factor g(x).
-2*x*(x - 4)**2/17
Factor 75*q + 21*q**2 + 32*q**2 + 16*q**2 - 12*q**3 - 6*q**2.
-3*q*(q + 1)*(4*q - 25)
Let o(c) be the first derivative of c**2/2 + c + 12. Let h(d) = d**2 - 3*d - 6. Let s(z) = h(z) + 6*o(z). Factor s(k).
k*(k + 3)
Let x(l) be the first derivative of -l**4 - 32*l**3/3 + 22*l**2 + 72*l + 37. Factor x(b).
-4*(b - 2)*(b + 1)*(b + 9)
Find h, given that 3/2*h**2 + 0*h - 3/8*h**4 + 0*h**3 + 0 = 0.
-2, 0, 2
Let v be ((-7)/((-21)/(-36)))/(164 - 210). What is w in 2/23*w + 2/23*w**5 - 4/23*w**3 - 12/23*w**2 + v*w**4 + 6/23 = 0?
-3, -1, 1
Let q(p) be the first derivative of -p**9/9072 + p**8/1260 - p**7/504 + p**6/540 - p**3 - 24. Let d(v) be the third derivative of q(v). Factor d(s).
-s**2*(s - 2)*(s - 1)**2/3
Let b(q) = q**2 - 17*q + 12. Let z be b(17). Suppose -2*h + 14 = 3*g, -5*g + 15 = 2*h - 7. Let -z*w**2 + 21 + 0*w - 9 - g*w + 4*w**3 = 0. What is w?
-1, 1, 3
Let s(x) be the first derivative of 6 + 0*x**2 + 0*x + 8/9*x**3 + 1/3*x**4. Suppose s(d) = 0. Calculate d.
-2, 0
Suppose 5*g = -5*s - 65, 4*s = -g + 9*s - 19. Let i be -15*((g - 0) + 3). Factor -i*l**2 + 3*l**4 + 165*l**2 + 6*l**3 - 9*l**5.
-3*l**3*(l - 1)*(3*l + 2)
Let z(w) = w**3 - 26*w**2 + 26*w - 23. Let t be z(25). Factor -9/2*f**t + 9/2*f - 3/2 + 3/2*f**3.
3*(f - 1)**3/2
Let z(w) = -w**3 + 250*w**2 + 255*w - 12. Let b(t) = -10*t**3 + 2250*t**2 + 2295*t - 105. Let y(d) = -4*b(d) + 35*z(d). Factor y(n).
5*n*(n - 51)*(n + 1)
Let d(i) be the third derivative of 35*i**8/144 + 2*i**7/9 - 143*i**6/72 + 7*i**5/18 + 55*i**4/18 + 20*i**3/9 + 45*i**2 - i. Determine l so that d(l) = 0.
-2, -2/7, 1
Let v(d) = 104*d - 310. Let n be v(3). Let x(y) be the second derivative of -4/3*y**3 - 1/5*y**5 + 0 - y**4 + 0*y**n - 3*y. Factor x(z).
-4*z*(z + 1)*(z + 2)
Let d(a) be the second derivative of 0*a**2 - 1/45*a**5 - 2*a + 0 - 2/135*a**6 - 2/9*a**3 + 5/27*a**4. Factor d(x).
-4*x*(x - 1)**2*(x + 3)/9
Suppose -p - 2*v = 2*p - 313, 1 = -v. Suppose 0 = -104*o + p*o - 4. Suppose 11/4*y**2 - 7/4*y**o - 1 + 5/4*y**5 + 2*y - 13/4*y**3 = 0. What is y?
-1, 2/5, 1, 2
Factor 0 - 2*r + 2/11*r**2.
2*r*(r - 11)/11
Let x = -125420/3 + 41809. Solve 4 + x*q**3 + 37/3*q**2 + 52/3*q = 0 for q.
-3, -2, -2/7
Factor 4*b**3 - 8572*b**4 + 11*b**3 + 8577*b**4 - 20*b**2.
5*b**2*(b - 1)*(b + 4)
Let m(s) be the second derivative of s**5/4 - 5*s**3/2 + 5*s**2 - 4*s - 2. Solve m(k) = 0 for k.
-2, 1
Let q be (4/(-2))/((-2)/5). Suppose -15 = -q*x + 3*n, -x + 2*x + 4*n = 3. Suppose 3*m**2 + 3*m**3 + 0*m**5 - 6*m**3 - 12*m**5 - 21*m**4 - 3*m**x = 0. What is m?
-1, 0, 1/4
Factor 2/9*r**2 + 2/9 - 4/9*r.
2*(r - 1)**2/9
Factor 0*q + 17/4*q**2 + 0 - 1/4*q**4 + 4*q**3.
-q**2*(q - 17)*(q + 1)/4
Let c = 4030 + -4028. Factor -1/8*p**c + 1/2 + 0*p.
-(p - 2)*(p + 2)/8
Let r(c) be the second derivative of 0*c**3 - 1/10*c**5 + 1/30*c**6 - 1 + 0*c**4 + c + 0*c**2. Factor r(f).
f**3*(f - 2)
Let o be 3 + -8 + 9 + 0. Let k be (0 - -3)*(o + (-328)/84). Find f, given that -2/7 - k*f**2 - 4/7*f = 0.