0*f**4 + 0*f - 1/5*f**2 + 7/15*f**3 - 1/30*f**6. Factor z(g).
-g*(g - 2)*(g - 1)**3/5
Let y(a) be the second derivative of 2*a + 2*a**2 - 1/3*a**3 - 51 + 1/40*a**5 - 1/12*a**4. Suppose y(o) = 0. Calculate o.
-2, 2
Suppose 33*c = -2*d - 16, 13*c - 8 = 12*c + d. Solve c - 22/15*n - 2/15*n**2 = 0 for n.
-11, 0
Let r(c) be the third derivative of -1/24*c**5 + 1/6*c**4 + 1/240*c**6 - 1/3*c**3 + 25*c**2 + 2*c + 0. What is b in r(b) = 0?
1, 2
Factor 85/8*u - 275/8 - 1/8*u**3 - 1/8*u**2.
-(u - 5)**2*(u + 11)/8
Let n(q) = 51*q**3 + 228*q**2 - 60*q - 6. Let t(s) = 151*s**3 + 683*s**2 - 182*s - 17. Let c(d) = -17*n(d) + 6*t(d). Factor c(v).
3*v*(v + 6)*(13*v - 4)
Let n(l) be the first derivative of 0*l**3 + 3 + 3/5*l**5 + 1/2*l**6 - 3/2*l**4 + 0*l + 0*l**2. Find k such that n(k) = 0.
-2, 0, 1
Let -35344/9 - 2/9*i**3 - 380/9*i**2 - 18424/9*i = 0. Calculate i.
-94, -2
Let j be (7935/(-253))/23*55/(-20). Let c be 1/4 - (-30)/8. What is x in 3/2 - 3/4*x**c + 3/4*x**3 + 9/4*x**2 - j*x = 0?
-2, 1
Suppose -17018*f + 17001*f = -34. Find w such that w + 3/4 + 1/4*w**f = 0.
-3, -1
Let z(q) = 42*q**3 - 8*q**2 + 6*q - 4. Let j be z(2). Let k be (-4)/11*j/(-78). What is b in 12/11*b**2 - 2/11*b + k*b**4 + 0 + 30/11*b**3 = 0?
-1, 0, 1/8
Let l(y) be the third derivative of -y**7/840 + y**6/180 - 25*y**3/3 - 72*y**2. Let k(r) be the first derivative of l(r). Factor k(a).
-a**2*(a - 2)
Let l = 5966/4569 + 42/1523. What is m in 0 + l*m**3 + 1/9*m**4 + 4*m**2 + 32/9*m = 0?
-8, -2, 0
Let a(r) be the second derivative of -197192*r**4/3 + 1256*r**3 - 9*r**2 - 8*r + 107. Factor a(l).
-2*(628*l - 3)**2
Let g(q) = -16867*q**4 - 830250*q**3 - 165604*q**2 - 11034*q - 241. Let x(n) = 2*n**4 - n**2 - n + 1. Let l(f) = -g(f) + 4*x(f). Determine h so that l(h) = 0.
-49, -1/15
Suppose -23*p + 21*p = -13*p - 36*p - 3*p. Suppose -4*y = -7 - 1. Factor 0 + p*f + 4/5*f**y - 2/5*f**4 - 2/5*f**3.
-2*f**2*(f - 1)*(f + 2)/5
Let w(c) be the third derivative of -c**6/8 - 175*c**5/12 + 295*c**4/12 + 385*c**2. Determine d so that w(d) = 0.
-59, 0, 2/3
Let a(r) be the second derivative of 3*r**5/140 - 5*r**4/14 - 27*r**3/14 + 54*r**2/7 + 22*r - 14. Factor a(d).
3*(d - 12)*(d - 1)*(d + 3)/7
Let s be (-5 - (-885)/105)*25/125 + 6/10. Suppose -12/7 + s*l + 3/7*l**2 = 0. Calculate l.
-4, 1
Let u(j) be the first derivative of -2*j**3/33 + 345*j**2/11 - 1372*j/11 - 174. Factor u(s).
-2*(s - 343)*(s - 2)/11
Suppose 18*b = 3*b - 60. Let p(c) = -18*c**2 - 12*c - 3. Let v(m) = -m**3 + 18*m**2 + 11*m + 4. Let u(q) = b*p(q) - 3*v(q). Solve u(g) = 0 for g.
-5, -1, 0
Factor 585827*z + 3423*z**2 - 1350244 + 759769*z + 4*z**3 + 1221*z**2.
4*(z - 1)*(z + 581)**2
Let v(j) = j**2 + 2*j - 9*j**3 - 8*j - 9 - 3 + 15 + 5*j**4. Let q(o) = 16*o**4 - 28*o**3 + 2*o**2 - 20*o + 10. Let a(x) = -3*q(x) + 10*v(x). Factor a(c).
2*c**2*(c - 2)*(c - 1)
Suppose 76*k + 58*k + 8*k - 20*k = 0. Let f(t) be the second derivative of k - 2/21*t**4 + 1/35*t**5 + 25*t + 0*t**2 - 16/21*t**3. Suppose f(b) = 0. What is b?
-2, 0, 4
Let u = 301715 - 301715. Factor u + 0*t + 1/9*t**3 + 0*t**2.
t**3/9
Let s(q) = -q**2 + 92*q - 1585. Let x be s(23). Let g(n) be the third derivative of -11*n**x + 0 + 0*n - 1/22*n**3 - 1/660*n**5 - 1/66*n**4. Factor g(b).
-(b + 1)*(b + 3)/11
Factor -138*n - 4660*n**2 + 56 + 2405*n**2 + 3*n**4 + 2387*n**2 - 191 + 138*n**3.
3*(n - 1)*(n + 1)**2*(n + 45)
Factor 2688/11 + 1992/11*a**2 + 4016/11*a + 324/11*a**3 - 2/11*a**4.
-2*(a - 168)*(a + 2)**3/11
Let m(j) = -21*j**2 - 768*j - 765. Let l(c) = 3*c**2 - c - 1. Let q(y) = 6*l(y) + m(y). Determine v so that q(v) = 0.
-257, -1
Let w(q) be the second derivative of -q**5/5 + 2*q**3/3 - 1238*q. Factor w(t).
-4*t*(t - 1)*(t + 1)
Let x(k) = 5*k**2 + 15 + 3*k**3 + 2*k + 19 + 6 - 36. Let b(a) = a**3 - 3*a. Let j(h) = 6*b(h) - 3*x(h). Let j(y) = 0. What is y?
-2, -1
Let z be (62/(-2480))/((-6)/3 - 2). Let x(l) be the third derivative of -5/64*l**4 + 0*l + 0 + z*l**5 - 3/8*l**3 - 11*l**2. Suppose x(y) = 0. Calculate y.
-1, 6
Factor o - 54*o + 12 + 23 + 17*o + 15*o**2 - 14*o.
5*(o - 1)*(3*o - 7)
Let k be -30 + (9 - (-803)/33). What is a in -4/9*a**2 + k + 26/9*a = 0?
-1, 15/2
Suppose 0 + h**4 - 1/4*h**5 + 11/4*h**3 + 18*h - 33/2*h**2 = 0. What is h?
-4, 0, 2, 3
Let c(q) be the second derivative of 77*q - 49/60*q**4 - 90*q**2 + 0 + 14*q**3. Suppose c(v) = 0. Calculate v.
30/7
Let b(d) be the third derivative of 2*d**7/525 + 91*d**6/75 - 2971*d**2. Factor b(a).
4*a**3*(a + 182)/5
Suppose -2*o + 7 = -5*u + 24, 4*u - 3*o - 15 = 0. Factor -5*i**u - i**3 + 8 - 4 + 2*i - 8*i**2.
-2*(i + 1)**2*(3*i - 2)
Let c(w) = -58*w**3 + 2*w**2 + w - 8. Let p be c(-2). Let y be 1/(-2)*(p/98 - 5). Find f, given that -1/7*f + y*f**2 + 1/7*f**3 - 1/7 = 0.
-1, 1
Let l = 12963/4 - 3240. Let i(z) be the first derivative of 3/2*z**2 - l*z**4 + 6*z + 14 - 2*z**3. Solve i(k) = 0.
-2, -1, 1
Factor 4 - 4/3*i**4 - 2*i**3 + 29/3*i + 1/3*i**5 + 16/3*i**2.
(i - 4)*(i - 3)*(i + 1)**3/3
Let t(p) = 14*p**4 + 26*p**3 + 224*p**2 - 243*p. Let u(m) = -36*m**4 - 76*m**3 - 672*m**2 + 728*m. Let c(v) = -8*t(v) - 3*u(v). Factor c(z).
-4*z*(z - 10)*(z - 1)*(z + 6)
Let q(k) be the first derivative of -k**5 - 25*k**4/2 - 185*k**3/3 - 150*k**2 - 180*k + 465. Solve q(v) = 0.
-3, -2
Suppose 10184*l = 10088*l. Factor 0 + l*g - 1/2*g**3 + 3/4*g**2 - 1/4*g**4.
-g**2*(g - 1)*(g + 3)/4
Let v(n) be the first derivative of n**4 + 104*n**3 - 318*n**2 + 320*n - 1336. Solve v(f) = 0 for f.
-80, 1
Let w(r) = r**5 + 55*r**4 + 54*r**3 - 18*r. Let z(t) = t**5 - t**3 - 3*t. Let l(d) = -w(d) + 6*z(d). Factor l(s).
5*s**3*(s - 12)*(s + 1)
Let m = -223 - -225. Find p such that -296*p**2 + 301*p**m + 1847 - 2*p - 248*p + 1278 = 0.
25
Let u(p) be the second derivative of -p**5/5 - 138*p**4 - 28566*p**3 + 953*p. Factor u(m).
-4*m*(m + 207)**2
Let z = 163 + -149. Suppose 38 - z = 3*j - 2*t, 5*j = -t + 40. Factor 29/3*r**2 - j*r + 4/3 - 3*r**3.
-(r - 2)*(r - 1)*(9*r - 2)/3
Suppose 0 = -5*i + 3 + 7. Suppose -59*m + 4 = -58*m. Solve -6 - 5*n**i + 16*n - 10 - 3*n**2 + m*n**2 = 0 for n.
2
What is d in -1244*d**2 - 72 + 35*d**4 + 101*d**4 - 160*d**3 - 72*d**4 - 588*d = 0?
-3, -1/4, 6
Let d(c) = -4*c**2 + 142*c + 146. Let i(n) be the third derivative of -n**5/60 + 47*n**4/24 + 8*n**3 - 162*n**2 + n. Let s(v) = -3*d(v) + 10*i(v). Factor s(r).
2*(r + 1)*(r + 21)
Let q(c) = -1219*c + 7317. Let t be q(6). Factor -14/9*r**4 + 2/9*r**5 + 32/9*r**2 + 16/9*r**t + 0*r + 0.
2*r**2*(r - 4)**2*(r + 1)/9
Let h be (6 - 305/50)*-32. Let y = -99 - -103. Factor 8/5*u**2 + 12/5*u**5 + 0*u + 0 - h*u**y - 4/5*u**3.
4*u**2*(u - 1)**2*(3*u + 2)/5
Suppose 18*o = 12*o + 48. Suppose p + 22 = 3*g - 3*p, -2*g - o = 3*p. Factor 0*l + 1/5*l**5 + 4/5*l**g + 0 + l**4 + 8/5*l**3.
l**2*(l + 1)*(l + 2)**2/5
Let y(h) be the second derivative of 0*h**4 + 2/3*h**3 + 0 - 1/20*h**5 + 0*h**2 + 134*h. Factor y(s).
-s*(s - 2)*(s + 2)
Let l(f) be the first derivative of -5/4*f**4 - 255*f**2 + 83 - 15/2*f**6 - 75*f**5 + 80*f + 285*f**3. Solve l(v) = 0.
-8, -2, 1/3, 1
Let j = 245/3 + -481/6. Find m such that 9/2 + 3*m - j*m**2 = 0.
-1, 3
Suppose 3*j = 9*b - 11*b + 13, 3 = b + 5*j. Let s be (-10)/b + 5 + -3. Suppose -3/8*v**2 + s*v - 3/8 = 0. What is v?
1
Suppose -1/6*l**2 - 10/3*l - 33/2 = 0. What is l?
-11, -9
Let h(s) be the first derivative of s**5/300 + 13*s**4/120 + 6*s**2 - 2*s - 4. Let y(r) be the second derivative of h(r). What is i in y(i) = 0?
-13, 0
Let x(i) = -155*i**3 + 355*i**2 + 2985*i - 5. Let h(n) = 61*n**3 - 178*n**2 - 1493*n + 2. Let p(y) = 5*h(y) + 2*x(y). Determine d so that p(d) = 0.
-23, -13, 0
Let v(g) be the third derivative of g**5/140 - g**4/14 - 285*g**3/14 + 452*g**2. Determine u so that v(u) = 0.
-15, 19
Let d = 302/375 + 2771/750. Let -4*y - y**3 + d - 19/2*y**2 = 0. What is y?
-9, -1, 1/2
Let j = 59 + -53. Suppose -10 = r - j*r. Suppose -76*s + 81*s + 15*s**3 + 17*s**2 - r*s**2 + 5*s**4 = 0. Calculate s.
-1, 0
Let c(d) = 4*d - 2. Let b(k) = 4*k**3 - 2*k**2 + k - 1. Let y be b(1). Let w be c(y). Factor 7*g**4 + 5*g**4 - 3*g**4 - 6*g**4 + 3*g**2 + w*g**3.
3*g**2*(g + 1)**2
Let y(v) be the third derivative of -1/40*v**6 + 0*v + 0 + 1/8*v**4 - 3/2*v**3 - 83*v**2 + 3/20*v**5. Factor y(j).
-3*(j - 3)*(j - 1)*(j + 1)
Let q(x) = x + 13. Let u be q(-17). Let o be u/6*5/((-5)/18). Fin