 5. Let r(j) = -2 - 2 + 0 + j**2 + j + 3 + j**3. Let p(o) = 4*g(o) + 12*r(o). Factor p(q).
-4*(q - 2)*(q - 1)**2
Let o(z) be the second derivative of -3*z**5/20 - 6*z**4 + 25*z**3/2 - 33*z. Determine k so that o(k) = 0.
-25, 0, 1
Solve 7/2*y**5 - 7*y**2 + 0 + 33/2*y**3 + 27*y**4 + 0*y = 0.
-7, -1, 0, 2/7
Let b(a) be the second derivative of 0*a**4 + 0*a**2 - 50*a - 2/15*a**6 + 0 + 0*a**3 + 2/5*a**5. Factor b(f).
-4*f**3*(f - 2)
Let i(c) be the second derivative of -c**4/4 + 2*c**3 + 6*c**2 + 31*c. Let y(f) = -3*f**2 + 12*f + 11. Let v(g) = -4*i(g) + 3*y(g). Factor v(b).
3*(b - 5)*(b + 1)
Let p(g) be the third derivative of -g**8/2184 - 2*g**7/455 - 2*g**6/195 + 83*g**2 - g. Suppose p(m) = 0. Calculate m.
-4, -2, 0
Let n(f) = 5*f**3 + 10*f**2 - 37*f + 22. Let v(o) = 9*o**3 + 100*o**2 + 155 - 260*o - 30*o**2 + 26*o**3. Let r(m) = -15*n(m) + 2*v(m). Factor r(l).
-5*(l - 1)**2*(l + 4)
Let k(p) be the first derivative of p**7/490 - p**6/280 - p**5/140 + p**4/56 + p**2 + 7. Let m(i) be the second derivative of k(i). Factor m(a).
3*a*(a - 1)**2*(a + 1)/7
Let -6*p - 6 + 20/3*p**2 + 20/3*p**3 - 2/3*p**5 - 2/3*p**4 = 0. What is p?
-3, -1, 1, 3
Let q(b) be the third derivative of -b**6/240 - 7*b**5/120 + 41*b**4/48 - 11*b**3/4 + 16*b**2. Factor q(r).
-(r - 3)*(r - 1)*(r + 11)/2
Let p(t) be the first derivative of t**6/2 - 6*t**5/5 - 3*t**4/2 + 8*t**3 - 21*t**2/2 + 6*t - 75. Factor p(n).
3*(n - 1)**4*(n + 2)
Let f(q) be the second derivative of 289*q**4/12 + 34*q**3/3 + 2*q**2 + 92*q. Find h such that f(h) = 0.
-2/17
Suppose u - 10 + 8 = 0. Factor 27*r**4 + 805*r - 5*r**u + 26*r**2 + 45*r**3 - 802*r.
3*r*(r + 1)*(3*r + 1)**2
Let z = -2774 - -99865/36. Let p(x) be the third derivative of -z*x**4 + 0 + 14*x**2 + 0*x - 1/45*x**5 - 1/180*x**6 + 0*x**3. Determine j, given that p(j) = 0.
-1, 0
Let i(c) = -c - 22. Let l be i(-25). Determine p, given that 8*p + 3*p**3 + 20*p**2 - 4 + 14*p**2 - 2*p**l - 39*p**2 = 0.
1, 2
Let y(q) be the first derivative of 9*q**5/40 + q**4/4 - 7*q**3/4 + 3*q**2/2 + 45*q + 11. Let g(m) be the first derivative of y(m). Factor g(d).
3*(d - 1)*(d + 2)*(3*d - 1)/2
Let q(n) be the second derivative of n**4/3 - 52*n**3/3 - 174*n**2 - 73*n. Factor q(s).
4*(s - 29)*(s + 3)
Let q = 336 + -333. Let k(a) be the second derivative of -1/2*a**3 + 0 - 9/80*a**5 + 5/8*a**4 - q*a**2 + 3*a. Suppose k(f) = 0. Calculate f.
-2/3, 2
Suppose -4*n - 12 = 0, 2*m - n + 2*n = 1. Let -8 + 5*x**2 + 11*x - x**m + 9*x + 8*x**2 = 0. What is x?
-2, 1/3
Let w = 115 - 112. What is l in w*l - l**3 + 9*l**2 - 3*l - 2*l**3 = 0?
0, 3
Let 32/7*h**3 + 400/7*h + 180/7*h**2 + 250/7 + 2/7*h**4 = 0. Calculate h.
-5, -1
Let v(y) = 4*y**2 - 4*y + 4. Let f be v(-3). Factor -f + 105 - 4*g - 59 + 2*g**2.
2*(g - 3)*(g + 1)
Find w such that -15*w**4 + 75*w**4 - 8*w**5 + 13*w - 53*w + 114*w**3 - 136*w**2 + 10*w**4 = 0.
-2, -1/4, 0, 1, 10
Let d(z) = -z**3 + 8*z**2 + 11*z - 16. Let g be d(9). Find v such that -2*v + 1 + 17*v**g - 10*v**2 - 6*v**2 = 0.
1
Let t = 38 + -66. Let m = t - -41. Factor m*j + 5*j - 2*j**2 + 8*j - 30*j.
-2*j*(j + 2)
Let b = 31 - 27. Suppose -3*z + z = -b*o + 4, 2*z + 2 = 3*o. What is f in -1/3*f**3 + 1/3*f - 1/3*f**4 + 1/3*f**o + 0 = 0?
-1, 0, 1
Let g(k) be the second derivative of 5*k**7/42 + 3*k**6/2 + 13*k**5/2 + 85*k**4/6 + 35*k**3/2 + 25*k**2/2 + 114*k. Factor g(a).
5*(a + 1)**4*(a + 5)
Let k(g) be the first derivative of g**3/3 - 45*g**2/2 - 144*g - 91. Factor k(s).
(s - 48)*(s + 3)
Factor 1/3*n - 17/3 + 17/3*n**2 - 1/3*n**3.
-(n - 17)*(n - 1)*(n + 1)/3
Let l be (-60)/160*(-3)/(5 + -2). Factor -3/4 - 3/8*n + 3/4*n**2 + l*n**3.
3*(n - 1)*(n + 1)*(n + 2)/8
Let w = -65 + 67. Determine h so that 9 + 15*h + 42*h**3 + 7*h**w - 22*h**3 - 19*h**3 = 0.
-3, -1
Suppose -54*a**5 + 6*a**3 - 21*a**3 + 49*a**5 - 5*a**2 - 15*a**4 = 0. What is a?
-1, 0
Let p(t) be the first derivative of t**7/210 - t**5/50 + t**3/30 + 31*t - 9. Let f(s) be the first derivative of p(s). What is x in f(x) = 0?
-1, 0, 1
Factor -48 - 21/2*w**2 + 93/2*w - 3/8*w**3.
-3*(w - 2)**2*(w + 32)/8
Let d(x) = 12*x**2 - 6*x + 3. Suppose 4*z - 8 = k, 19 = 3*k + 5*z - 8. Let v(o) = o**3 + 13*o**2 - 5*o + 3. Let p(h) = k*d(h) - 3*v(h). Factor p(j).
-3*(j - 1)**3
Let t(f) = -2*f - 14. Let i be t(-10). Let q = i - 3. Factor 3*j**2 + 4*j**2 - 3 - 3*j**q - 4*j**2 - j + 4*j.
-3*(j - 1)**2*(j + 1)
Let w(i) be the first derivative of -2*i**6/15 + 16*i**5/5 - 78*i**4/5 - 176*i**3/3 - 242*i**2/5 + 191. Solve w(k) = 0 for k.
-1, 0, 11
Let r(p) be the second derivative of -31*p + 1/3*p**2 + 1/9*p**4 + 0 + 1/60*p**5 + 5/18*p**3. Suppose r(t) = 0. What is t?
-2, -1
Suppose -180 + 145 = 5*x, -5*x = 3*i + 23. Solve 64/3*k - 32/3*k**2 + 64/3 - 32/3*k**3 + 4/3*k**i + 4/3*k**5 = 0.
-2, -1, 2
Let t = -929 + 7435/8. What is b in 3/8 + 0*b - t*b**2 = 0?
-1, 1
Suppose 5/3*p**5 - 46475/3*p + 710/3*p**3 - 9490/3*p**2 + 274625/3 + 145/3*p**4 = 0. Calculate p.
-13, 5
Let r(c) be the second derivative of 2*c**6/45 - 6*c**5/5 + 97*c**4/9 - 32*c**3 + 128*c**2/3 - 47*c. Suppose r(t) = 0. Calculate t.
1, 8
Let n be (2492/(-16) - 0) + 1 + 0. Let k = 156 + n. Factor k*z**3 + 1 + z - 13/4*z**2.
(z - 2)*(z - 1)*(5*z + 2)/4
Let g be -2 + (-120)/210 + (-4867)/(-1890). Let b(n) be the third derivative of -1/27*n**4 - g*n**5 + 0*n**3 + 0 + 9*n**2 + 0*n. Factor b(z).
-2*z*(z + 4)/9
Let n(c) be the third derivative of -c**7/21420 - c**6/1224 - 13*c**4/24 - 16*c**2. Let u(k) be the second derivative of n(k). Solve u(i) = 0 for i.
-5, 0
Let n(w) be the first derivative of 15 + 1/5*w**5 - 30*w**2 + 37/3*w**3 - 5/2*w**4 + 36*w. What is u in n(u) = 0?
2, 3
Let k = -102 - -116. Let b be ((-4)/k - (-66)/(-63))/(-1). Factor 0*w + 0 + 0*w**3 - 1/3*w**5 - b*w**2 + w**4.
-w**2*(w - 2)**2*(w + 1)/3
Factor 1/5*t**2 - t + t**3 + 0 - 1/5*t**4.
-t*(t - 5)*(t - 1)*(t + 1)/5
Let g be 649 + -642 + (-39)/17*3. Factor -2/17 - 4/17*m - g*m**2.
-2*(m + 1)**2/17
Factor -21/2*b**2 - 15*b + 0 - 3/2*b**3.
-3*b*(b + 2)*(b + 5)/2
Let q(c) = -14*c**3 - 3*c**2 - 12*c - 5. Let j(x) = -5*x**3 - x**2 - 4*x - 2. Let a(n) = -17*j(n) + 6*q(n). What is y in a(y) = 0?
-2, 1, 2
Suppose 0 = -13*p + 36 + 29. Let f(g) be the third derivative of -1/5*g**4 - 1/75*g**6 + 0 - 11/150*g**p + 0*g - 1/1050*g**7 - 3/10*g**3 + 3*g**2. Factor f(l).
-(l + 1)**2*(l + 3)**2/5
Suppose 4 = 2*t - 2*v, 0 = 3*t + t - v - 23. Let g be t + (-4 - 2 - -3). Solve r**3 + 2*r**2 - 5*r**3 + 2*r**2 - 5*r**4 + 2*r**g = 0.
-2, 0, 2/3
Let w(n) be the first derivative of -5*n**6/2 - 7*n**5 + 95*n**4/4 + 335*n**3/3 + 140*n**2 + 60*n + 19. Let w(p) = 0. What is p?
-2, -1, -1/3, 3
Let r = 23 - 32. Let i = r - -13. Factor -6*x**4 + 0*x**4 + 2*x**3 + 4*x**4 + 4*x**i.
2*x**3*(x + 1)
Let b(z) be the first derivative of z**6/60 + z**5/10 + z**4/6 - 9*z**2 + 21. Let t(w) be the second derivative of b(w). Factor t(k).
2*k*(k + 1)*(k + 2)
Suppose -4*s - 18 = -4*v - 14, -4*v + 1 = -5*s. Solve 1/5 - 3/5*q + 3/5*q**2 - 1/5*q**s = 0.
1
Solve -11*f**3 - 2*f**5 + 7*f**2 + 4*f**4 + f**2 + 6*f**5 - 2*f**2 - 3*f**5 = 0.
-6, 0, 1
Let t(f) be the first derivative of 1/12*f**4 + 2*f**2 - 2 + 0*f**3 - 1/120*f**6 - 1/60*f**5 + 0*f. Let l(a) be the second derivative of t(a). Factor l(v).
-v*(v - 1)*(v + 2)
Let f(b) = b**2 + 39*b + 350. Let u be f(-14). Find h such that -1/2*h**4 + 0*h + 5/8*h**3 + u - 1/4*h**2 + 1/8*h**5 = 0.
0, 1, 2
Let b(f) be the first derivative of -f**5/35 - 17*f**4/28 - 5*f**3/7 + 17*f**2/14 + 16*f/7 - 119. Solve b(r) = 0.
-16, -1, 1
Let i(d) = d**2 - 7*d + 12. Let y be i(3). Let t(s) be the first derivative of -8 + y*s + 1/10*s**2 + 1/20*s**4 - 2/15*s**3. Factor t(g).
g*(g - 1)**2/5
Let r(t) be the first derivative of t**6/24 + t**5/10 - t**4/8 - t**3/3 + t**2/8 + t/2 + 8. What is y in r(y) = 0?
-2, -1, 1
Let s(w) be the third derivative of 39*w**6/40 - 77*w**5/20 + 37*w**4/8 + w**3/2 - 2*w**2 - 235. Factor s(y).
3*(y - 1)**2*(39*y + 1)
Suppose p = -p + 2*j + 6, 5 = -p + 3*j. Let x be 4 + -1 + p/7. What is v in 69*v**3 + 25*v**4 - x - 19*v**3 - 8*v + 5*v**2 + 16*v**2 = 0?
-1, -2/5, 2/5
Let b = 19 + -16. Factor -4 - 4*v - b*v**3 + 2*v + 5*v**3 + 4*v**2.
2*(v - 1)*(v + 1)*(v + 2)
Let m(y) be the first derivative of -1/42*y**4 + 0*y**2 + y + 1/105*y**6 + 2/21*y**3 + 1 - 1/35*y**5. Let r(f) be the first derivative of m(f)