- 2)*(c + 2)/3
Let v(y) be the first derivative of 276 - 9/2*y**2 + 1/4*y**4 + 14*y - 2*y**3. Find k such that v(k) = 0.
-2, 1, 7
Let l = -4512 - -4518. Let n(m) be the third derivative of 4/3*m**3 - 2/15*m**5 + 1/6*m**4 + 0 + 12*m**2 - 1/30*m**l + 0*m. Find c, given that n(c) = 0.
-2, -1, 1
Let u(b) = -19*b**4 - 16*b**3 + 86*b**2 + 507*b + 72. Let g(j) = -5*j**4 - 4*j**3 + 22*j**2 + 135*j + 18. Let z(w) = -22*g(w) + 6*u(w). Factor z(m).
-4*(m - 3)*(m + 1)**2*(m + 3)
Let k(y) be the third derivative of -1/135*y**5 - 1 - 12*y**2 + 0*y**3 + 0*y + 1/54*y**4. Determine r, given that k(r) = 0.
0, 1
Let f(p) = p**3 - 12*p**2 - 7*p + 87. Let z be f(12). Let k = 4 + -1. Factor x**z + 2 - 3*x**2 + 1 - x**3 - 3*x**k + 3*x.
-3*(x - 1)*(x + 1)**2
Factor 0 + 50/9*s**3 + 190/3*s - 619/9*s**2 - 1/9*s**4.
-s*(s - 30)*(s - 19)*(s - 1)/9
Let p(m) be the third derivative of -m**3 - 3/20*m**5 + m**2 + 1/2*m**4 + 1/40*m**6 - 1/560*m**7 - 11 + 0*m. Factor p(i).
-3*(i - 2)**4/8
Let p be 1*(81/243 - (-16)/6). Determine r so that -5/4*r**p + 10 - 15*r + 15/2*r**2 = 0.
2
Suppose -54/5*j**3 - 243/5*j**2 - 336/5*j - 144/5 - 3/5*j**4 = 0. Calculate j.
-12, -4, -1
Let s(f) be the first derivative of f**8/840 - 11*f**7/840 + 17*f**6/360 - f**5/20 + 2*f**3/3 - 4*f - 29. Let x(m) be the third derivative of s(m). Factor x(j).
j*(j - 3)*(j - 2)*(2*j - 1)
Let c be (65/(-4))/(83/(-4980)). Let d be c/390*((-228)/130 + 2). Factor -2/13*p**3 - 10/13*p**2 - 16/13*p - d.
-2*(p + 1)*(p + 2)**2/13
Let c(z) be the second derivative of z**6/45 - 14*z**5/3 - 71*z**4/9 + 140*z**3/9 + 47*z**2 - 2347*z. Suppose c(h) = 0. Calculate h.
-1, 1, 141
Let i be (-4 - ((-3059)/230)/19)*(-6)/11. Solve 54/5 - 1/5*y**4 - i*y - 33/5*y**2 - 11/5*y**3 = 0 for y.
-6, -3, 1
Suppose 17*f + 26*f - 108 = 64. Let i(s) be the third derivative of 0 + 7*s**2 - 1/30*s**6 + 8/3*s**3 + 2/15*s**5 + 7/6*s**f + 0*s. Factor i(j).
-4*(j - 4)*(j + 1)**2
Factor 315/4 - 3/4*q**2 - 6*q.
-3*(q - 7)*(q + 15)/4
Let p be (-225)/((-5625)/(-10))*(255/(-8))/1. Factor -p - 15/8*c**2 + 261/8*c.
-3*(c - 17)*(5*c - 2)/8
Suppose 330*u - 317*u - 2*p = -14, 0 = 3*u + p - 7. Factor -4/11*o + 2/11*o**4 - 8/11*o**3 + u + 10/11*o**2.
2*o*(o - 2)*(o - 1)**2/11
Let n(o) be the third derivative of 59*o**5/60 + 39*o**4/16 - o**3/12 + 1177*o**2. Solve n(d) = 0 for d.
-1, 1/118
Let k = 2554 + -2551. Let l(b) be the third derivative of 16*b**2 - 1/12*b**4 - 1/90*b**5 + 0*b**k + 0*b + 0. Factor l(j).
-2*j*(j + 3)/3
Let t(k) be the third derivative of 7*k**5/20 + 31*k**4/18 - 2*k**3/9 + 2*k**2 - 509*k. Solve t(g) = 0 for g.
-2, 2/63
Suppose -10 = 52*h - 54*h. Factor 0*m - 100*m**h + 0*m + 3456*m**4 - 3336*m**4 - 36*m**3.
-4*m**3*(5*m - 3)**2
Let c(d) be the first derivative of d**6/7 - 16*d**5/7 - 8*d**4/7 + 2500*d**3/21 - 387*d**2/7 - 1620*d/7 + 7657. Find f such that c(f) = 0.
-5, -2/3, 1, 9
Let r(o) be the second derivative of 5*o**4/12 + 315*o**3/2 + 470*o**2 - 415*o - 1. Find j such that r(j) = 0.
-188, -1
Let d(r) be the second derivative of -r**4/78 + 1172*r**3/39 - 343396*r**2/13 + 1585*r. Determine p, given that d(p) = 0.
586
What is d in -86/5*d**2 - 64/5 + 156/5*d - 6/5*d**3 = 0?
-16, 2/3, 1
Let m(d) = -2 + 15*d**2 - 10*d**2 - 3*d - 6*d**2 - 5*d**3. Let j be m(-1). Factor -4*y**2 + j*y**5 - 19*y**3 + 64*y**3 - 25*y**4 - 31*y**2 + 10*y.
5*y*(y - 2)*(y - 1)**3
Let o(y) = -5*y**4 + 14*y**3 - 25*y**2 + 16*y + 9. Let n(w) = 4*w**4 - 11*w**3 + 19*w**2 - 12*w - 7. Let f(x) = 9*n(x) + 7*o(x). Determine m so that f(m) = 0.
-2, 0, 1, 2
Suppose 3*c + 2*o = -8 + 1235, 3 = -o. Suppose -c*y = -417*y + 48. Factor y + 33/2*i**2 + 1/2*i**4 - 20*i - 5*i**3.
(i - 4)**2*(i - 1)**2/2
Let a(h) = -7822*h - 179903. Let g be a(-23). Determine z so that 48/7*z - 2/7*z**g + 6*z**2 - 88/7 = 0.
-2, 1, 22
Let z(s) be the first derivative of 3/2*s**2 + 1/18*s**3 - 169 + 17/6*s. Factor z(c).
(c + 1)*(c + 17)/6
Factor -2/11*p + 18/11*p**2 - 210/11 + 2/11*p**3.
2*(p - 3)*(p + 5)*(p + 7)/11
Let n be (-527)/(-85) - (-2)/(-10). Solve 16*c**3 + 0*c**3 + 6*c**3 + 33*c - 51*c**2 - n - 4*c**3 = 0.
1/3, 1/2, 2
Let h(b) = -7*b**4 + 6*b**3 - 6*b - 1. Let i(n) = -27*n**4 + 24*n**3 - 24*n - 3. Suppose -90 = 11*d - 5*d. Let a(z) = d*h(z) + 4*i(z). Factor a(w).
-3*(w - 1)**3*(w + 1)
Let x(c) be the third derivative of c**6/320 - 3*c**5/16 + 225*c**4/64 - 125*c**3/4 + 3935*c**2. What is t in x(t) = 0?
5, 20
Let l(q) be the second derivative of -q**4/3 + 242*q**3/3 + 492*q**2 - 469*q. Factor l(t).
-4*(t - 123)*(t + 2)
Suppose -318*i = -338*i + 60. Let l be i + 0 + (-29 - -9) + 19. Suppose y**2 - 4 - l*y + 1/2*y**3 = 0. What is y?
-2, 2
Let -8895*u - 3*u**2 + 625883 - 3970199 + 122277 - 3985461 - 405*u = 0. Calculate u.
-1550
Let t(s) = -2*s**3 + 10*s**2 - 30*s - 2. Let p(o) = -6*o**3 + 20*o**2 - 61*o - 5. Let r(x) = 2*p(x) - 5*t(x). Factor r(y).
-2*y*(y - 2)*(y + 7)
Suppose 1080845*b**2 - 47961*b**3 - 29984*b**2 + 657*b**4 - 3*b**5 + 116190*b**2 = 0. Calculate b.
0, 73
Let s(g) be the first derivative of -g**6/10 + 3*g**5/2 - 17*g**4/4 + 4*g**3 + 19*g - 220. Let j(f) be the first derivative of s(f). Let j(x) = 0. What is x?
0, 1, 8
Let z(l) be the second derivative of -2*l**6/15 - 2*l**5/5 + 3*l**4 + 12*l**3 - 898*l. Solve z(k) = 0.
-3, -2, 0, 3
Let i(a) be the first derivative of -10/3*a**2 + 0*a + 212 + 16/9*a**3 - 1/15*a**5 - 1/12*a**4. Factor i(o).
-o*(o - 2)**2*(o + 5)/3
Let a = -1130 + 7946/7. Let d = -1/94446 - -566683/661122. Let d + a*m**2 + 27/7*m + 15/7*m**3 = 0. Calculate m.
-1, -2/5
Let s be 1 + 1480/(-192) - -6. Let w = 25/24 + s. Let -8/3 - 2/3*m + w*m**2 = 0. What is m?
-2, 4
Let f(k) = 5*k**2 + 2*k - 700. Let t(u) = -10*u**2 - u + 1400. Let q(h) = 13*f(h) + 6*t(h). Factor q(w).
5*(w - 10)*(w + 14)
Let -498*k + 250 + 2*k**3 - 100*k**2 + 182*k**2 + 164*k**2 = 0. Calculate k.
-125, 1
Let d(k) be the third derivative of 1/5*k**5 - 9/4*k**3 - 275*k**2 - 5/8*k**4 + 1/8*k**6 + 1/140*k**7 + 0*k + 0. Determine x, given that d(x) = 0.
-9, -1, 1
Let v(g) be the first derivative of -256*g**5/5 + 13968*g**4 - 3055492*g**3/3 + 380628*g**2 - 47524*g - 197. Factor v(f).
-4*(f - 109)**2*(8*f - 1)**2
Let z(n) = -3*n**3 - 147*n**2 - 174*n - 6. Let o(q) = -9*q**3 - 440*q**2 - 526*q - 19. Let u(x) = -6*o(x) + 19*z(x). Let u(a) = 0. Calculate a.
-50, -1, 0
Let r be ((-2)/8)/(20/(-400)). Factor 4*z + 2*z**2 - 309*z**4 + 307*z**4 - 6*z**3 + z**r + z**5.
2*z*(z - 2)*(z - 1)*(z + 1)**2
Let r(v) = 5*v**2 - v + 28. Let q be r(25). Solve 6*t - q + 3128 + 3*t**2 = 0.
-2, 0
Let h be (-10)/90 + 2/18. Let m be (h/(-1))/(48 + -47). Factor 0*q + 0*q**2 - 2/5*q**3 + m.
-2*q**3/5
Let u(r) be the second derivative of r**5/40 - r**4/8 + r**3/4 + 13*r**2 - 2*r - 7. Let p(z) be the first derivative of u(z). Solve p(m) = 0 for m.
1
Suppose -5*y = -4*y + 3*c - 22, 103 = 4*y - 3*c. Find r such that -25*r**2 - 26*r - y*r + 57*r - 21*r = 0.
-3/5, 0
Suppose 268*k + 195 = 333*k. Let v(x) be the first derivative of 72/5*x - 1/5*x**4 + 6/5*x**2 + 1 - 16/15*x**k. Factor v(t).
-4*(t - 2)*(t + 3)**2/5
Let c(h) be the first derivative of -h**3/2 + 2*h**2/3 + h/6 - 1053. Suppose c(f) = 0. Calculate f.
-1/9, 1
Let h(p) be the first derivative of 15*p**4/4 - 125*p**3/6 - 15*p**2 + 10*p + 35. Let t(a) be the first derivative of h(a). Let t(s) = 0. Calculate s.
-2/9, 3
Factor 23450 + 1492*n**3 - 1490*n**3 + 3910*n**2 + 16344*n + 182*n**2 - 7114.
2*(n + 2)**2*(n + 2042)
Let o be (24/105)/(121/3388). Solve -4*m - o - 2/5*m**2 = 0 for m.
-8, -2
Factor -2/3*m**2 + 1040/3*m - 135200/3.
-2*(m - 260)**2/3
Let i = -118 - -20. Let n = 110 + i. What is r in -13*r - 3*r**3 - n - 8*r**2 - 14*r - 17*r**2 + 7*r**2 = 0?
-4, -1
Let l(g) be the third derivative of -g**6/12 - 11*g**5/12 - 85*g**4/24 - 5*g**3 + 170*g**2 + 2. Factor l(q).
-5*(q + 2)*(q + 3)*(2*q + 1)
Factor -34*m + 4/3*m**2 - 52/3.
2*(m - 26)*(2*m + 1)/3
What is i in 88788/5*i - 172872/5 + 4/5*i**3 - 1184/5*i**2 = 0?
2, 147
Let r(g) be the first derivative of -5/2*g**4 + 8*g**2 + 2/5*g**5 + 0*g + 4/3*g**3 - 240. Suppose r(c) = 0. Calculate c.
-1, 0, 2, 4
Let r(h) be the first derivative of -h**4/6 - 5*h**3/3 - 4*h**2 - 63*h + 79. Let m(p) be the first derivative of r(p). Factor m(i).
-2*(i + 1)*(i + 4)
Let r(l) be the third derivative of l**6/60 - 11*l**5/30 - 101*l**4/3 - 252*l**3