- 1)*(5*m + 2)
Let d be 49/392 - 18/(-112). Let -d*w**2 + 0 + 4/7*w = 0. Calculate w.
0, 2
Let s(y) be the first derivative of y**4/2 - 4*y**3/9 - 9*y**2 + 12*y + 114. Factor s(v).
2*(v - 3)*(v + 3)*(3*v - 2)/3
Let s = -6 + 14. Factor -r**3 + 5*r**2 + 6 - s*r - 3 + 1.
-(r - 2)**2*(r - 1)
Let s be (-12)/(-21) + 23288/(-84). Let k = s + 279. Suppose 0 + 0*o + 7/3*o**5 + 2/3*o**4 - 2/3*o**2 - k*o**3 = 0. Calculate o.
-1, -2/7, 0, 1
Suppose 2*i = -2*i + 32. Let o be 36/24*i/3. Factor -4*r**o - 2 + 4*r**2 + 0*r**5 + 2*r**5 + 2 - 2*r.
2*r*(r - 1)**3*(r + 1)
Let w(g) be the first derivative of 3*g**5/20 + 17*g**4/16 - 9*g**3/2 + 2*g**2 - 560. Factor w(n).
n*(n - 2)*(n + 8)*(3*n - 1)/4
Factor 0*w**2 + 0*w**3 + 0*w + 1/2*w**4 + 0.
w**4/2
Let f(y) be the first derivative of 9*y**5/2 + 93*y**4/8 - 65*y**3/3 - y**2 + 12*y + 197. Suppose f(m) = 0. What is m?
-3, -2/5, 2/3
Suppose -2*c + 14 = 3*m, 5*c - c + 4*m = 24. Let w(h) = h**3 + 12. Let n be w(0). Find p such that -3*p**2 + 4*p + 0*p - c*p + n = 0.
-2, 2
Suppose -3*n - 81*o = -79*o + 7, 55 = 5*n - 5*o. Factor 189/2*j**2 + 3/4*j**4 + 147*j + 15*j**n - 1029/4.
3*(j - 1)*(j + 7)**3/4
Let z(q) be the first derivative of -q**5/5 + 9*q**4/4 - 371. Factor z(n).
-n**3*(n - 9)
Suppose -2*u - 2 = -10. Suppose -5*x = b - 2 - 15, -15 = -5*x. Factor -6/5*o**b + 4/5*o - 14/5*o**u - 24/5*o**3 + 0.
-2*o*(o + 1)**2*(7*o - 2)/5
Let j = -28 + 32. Let 1 - 33*d + 3 - j*d**2 + 33*d = 0. Calculate d.
-1, 1
Let q(d) be the second derivative of -d**6/6 + 5*d**4/4 - 5*d**3/3 + 44*d. Factor q(w).
-5*w*(w - 1)**2*(w + 2)
Factor -24/7*u + 2/7*u**2 + 72/7.
2*(u - 6)**2/7
Suppose -66*r + 76*r = 50. Factor 0*i + 0*i**2 - 1/3*i**r + 0 + 0*i**4 + 1/3*i**3.
-i**3*(i - 1)*(i + 1)/3
Suppose 701 - 668 = 11*h. Suppose 2/7 - 16/7*d**4 + 39/7*d**2 + 17/7*d + 8/7*d**h = 0. What is d?
-1, -1/4, 2
Let k(f) be the second derivative of f**6/150 + 7*f**5/50 + 23*f**4/20 + 14*f**3/3 + 10*f**2 + 150*f. Factor k(a).
(a + 2)**2*(a + 5)**2/5
Let h = -160 + 95. Let u = 67 + h. Factor 2/9*z**3 + 0 + 4/9*z + 2/3*z**u.
2*z*(z + 1)*(z + 2)/9
Let m(z) be the third derivative of z**5/75 + 89*z**4/15 + 15842*z**3/15 - 2*z**2 + 184. Let m(p) = 0. What is p?
-89
Suppose 12 = d - 4*d. Let b be 4/(-8) + 2 + 6/d. Let b + 0*z**2 + 1/2*z**5 + 0*z**4 - z**3 + 1/2*z = 0. What is z?
-1, 0, 1
Suppose -5*g**4 - 77828*g**2 + 137 + 30788*g**2 + 1208256*g - 137 + 840*g**3 - 330176*g = 0. What is g?
0, 56
Suppose 0 = 2*l - 7*l + 100. Let j be l/(-80)*(0 - 14 - -2). Factor 1/4*z**2 + 0*z + 0 - 1/4*z**j.
-z**2*(z - 1)/4
Suppose -35 + 32 = -3*f. Let g be f/(-5) - 57/(-135). Solve g - 4/9*p + 2/9*p**2 = 0 for p.
1
Let l(b) = -b**2 - 6*b - 5. Let t be -3 + (2 - 3 - 0). Let d be l(t). Factor -x**2 + 0*x**2 + 0*x**d + 2*x**3 - 3*x**3.
-x**2*(x + 1)
Suppose -t = -9 - 2. Suppose -5 + 27 = t*q. Find x such that -1/2*x**4 - 1/2*x**3 + 1/2*x + 1/2*x**q + 0 = 0.
-1, 0, 1
Let x = 5/648 + 623/3240. Let -x*t**4 - 4/5*t + 0 - 8/5*t**2 - t**3 = 0. What is t?
-2, -1, 0
Factor -6*a**2 - 9*a + 42*a - 12*a**3 + 36 + 9*a**3.
-3*(a - 3)*(a + 1)*(a + 4)
Let u(g) be the first derivative of g**7/70 + g**6/20 + g**5/20 - 5*g**2/2 + 17. Let r(w) be the second derivative of u(w). Let r(o) = 0. What is o?
-1, 0
Let k(d) be the first derivative of d**7/315 + d**6/60 + d**5/30 + d**4/36 + 11*d**2 - 22. Let u(r) be the second derivative of k(r). Solve u(n) = 0 for n.
-1, 0
Suppose -9*s + 11*s - 4 = 0. Let o(f) be the second derivative of 10*f - 1/2*f**4 + 3/4*f**5 + 0*f**3 + 0*f**s + 1/14*f**7 + 0 - 2/5*f**6. Factor o(l).
3*l**2*(l - 2)*(l - 1)**2
Factor -9/5*n**2 + 9/5 + 3/5*n - 3/5*n**3.
-3*(n - 1)*(n + 1)*(n + 3)/5
Let q(n) = -6 + n + 0*n - 7*n**3 - 13*n**2 + 8*n**3. Let g be q(13). Factor -g*r + 0 + r - r**3 + 5*r**2 + 3 - r.
-(r - 3)*(r - 1)**2
Let i(n) be the third derivative of 6*n**7/35 - 13*n**6/15 + 8*n**5/5 - n**4 - 2*n**3/3 + 3*n**2 - 12*n. Suppose i(h) = 0. Calculate h.
-1/9, 1
Let b(r) be the second derivative of -r**4/132 - 9*r**3/11 - 53*r**2/22 + 44*r. Suppose b(q) = 0. Calculate q.
-53, -1
Let j(b) be the first derivative of b**3 + 15*b**2/2 - 72*b - 212. Factor j(c).
3*(c - 3)*(c + 8)
Suppose 11*h = 4*h + 14. Factor -7*t**2 + 5*t**2 + 0*t**4 - 6*t**4 + h*t**5 + 6*t**3.
2*t**2*(t - 1)**3
Factor 2/9*p - 2/9*p**3 - 8/9 + 8/9*p**2.
-2*(p - 4)*(p - 1)*(p + 1)/9
Suppose -2*l + n = -2*n - 20, -l + 5*n = -24. Let w(a) be the second derivative of -1/2*a**3 + 0 + 3*a + 3/4*a**l - 3*a**2. Factor w(z).
3*(z - 1)*(3*z + 2)
Let h be -1 - (610/8)/5. Let k = -16 - h. Find m, given that 0 + 3/4*m - k*m**2 = 0.
0, 3
Factor -37*y**2 + 33*y**2 - 14*y**2 - 118*y**2 - 128*y - 36*y**3.
-4*y*(y + 2)*(9*y + 16)
Determine t so that 0*t**3 - 1675*t**2 - 4*t**3 + 68*t - 36 + 1647*t**2 = 0.
-9, 1
Let s(v) be the third derivative of v**8/1680 - v**7/1050 - v**6/150 + v**5/75 + v**2 - 84. Factor s(h).
h**2*(h - 2)*(h - 1)*(h + 2)/5
Let f be 8/1 + -1 - (-754)/(-116). Factor -4*u**3 + 2*u**2 + 5/2*u**4 + 0*u + 0 - f*u**5.
-u**2*(u - 2)**2*(u - 1)/2
Let v = -3343 - -10285/3. Factor 64*i + 4/3*i**3 + v + 16*i**2.
4*(i + 4)**3/3
Let i(x) be the third derivative of x**5/30 + x**4/3 - 4*x**3/3 - 6*x**2. Let y be i(-5). Suppose 1/7*v**3 - 1/7*v**y + 0 + 0*v = 0. What is v?
0, 1
Let l be (12 + -13)/((-1)/3). Suppose -12*f + 10*f**2 - 7*f**l + 4*f**3 - f**3 + 6*f**2 = 0. Calculate f.
0, 1, 3
Suppose 0*r = 4*r - 8. Let u be (-4)/(-14 + 10 + -8). Factor 0 + u*c**r - 2/3*c + 1/3*c**3.
c*(c - 1)*(c + 2)/3
Let w = -1153/36 + 292/9. Let q(x) be the second derivative of w*x**4 + 6*x + 0 - 5/3*x**3 + 5/2*x**2. Suppose q(r) = 0. What is r?
1
Let p be (-10 - 4) + 222/15. Suppose 20 - 8*f + p*f**2 = 0. What is f?
5
Let l(a) be the second derivative of a**8/336 + a**7/84 - a**6/24 + 7*a**3/2 - 5*a. Let u(d) be the second derivative of l(d). Factor u(z).
5*z**2*(z - 1)*(z + 3)
Factor -3 + 18/7*n + 3/7*n**2.
3*(n - 1)*(n + 7)/7
Factor -8/7 + 2/7*g**4 + 8/7*g**3 + 6/7*g**2 - 8/7*g.
2*(g - 1)*(g + 1)*(g + 2)**2/7
Let s(x) be the third derivative of x**6/80 - 27*x**5/40 + 37*x**4/8 - 12*x**3 + 455*x**2. Determine u so that s(u) = 0.
1, 2, 24
Suppose -2*v = 8 + 8. Let l = v - -26/3. Find o, given that 2/3*o + l - 2/3*o**2 - 2/3*o**3 = 0.
-1, 1
Let d = -181/15 + 38/3. Factor d*y**4 - 3/5*y**3 + 0*y + 0 + 0*y**2.
3*y**3*(y - 1)/5
Let o(m) = 4*m**3 - 44*m**2 - 100*m - 57. Let q(w) = -1. Let h(n) = o(n) - 5*q(n). Suppose h(r) = 0. What is r?
-1, 13
Let a(k) be the first derivative of 0*k + 23 - 1/5*k**3 - 9/10*k**2. Find y such that a(y) = 0.
-3, 0
Let z(l) = 2*l**5 + l**3 + 2*l**2 - l. Let w(h) = -12*h**5 - 48*h**4 + 168*h**3 - 296*h**2 + 212*h - 56. Let f(r) = -w(r) - 8*z(r). Factor f(p).
-4*(p - 7)*(p - 2)*(p - 1)**3
Suppose 4*v - 5*x - 24 = 6, -v - 5*x - 5 = 0. Suppose 68 = v*d + 8. Find g such that 6*g**3 + 4*g**3 + 0 + 4 + 2*g**3 - 4*g**2 - d*g = 0.
-1, 1/3, 1
Let i(v) be the second derivative of v**7/7560 - v**6/360 + v**5/40 - v**4 - 9*v. Let q(c) be the third derivative of i(c). Determine h, given that q(h) = 0.
3
Suppose 0 = -3*x + 7*x + 8. Let y(w) = 8*w**5 + 7*w**4 + 11*w**2 - 8*w + 9. Let s(g) = g**5 + g**4 + g**2 - g + 1. Let a(p) = x*y(p) + 18*s(p). Factor a(b).
2*b*(b - 1)*(b + 1)**3
Let b(z) be the third derivative of 0 + 0*z**4 + 0*z**3 + 0*z + 14*z**2 + 1/960*z**6 + 1/80*z**5. Factor b(j).
j**2*(j + 6)/8
Let v = 134 - 132. Determine d so that 0*d + 52*d + 108 + 3*d**v - 16*d = 0.
-6
Factor -194/7 - 390/7*p - 2/7*p**3 - 198/7*p**2.
-2*(p + 1)**2*(p + 97)/7
Let w(x) be the third derivative of 4*x**7/315 - 3*x**6/20 - 13*x**5/30 - 2*x**4/9 + 281*x**2. Find i such that w(i) = 0.
-1, -1/4, 0, 8
Let v(q) = -26*q**2 - 34*q + 44. Let k(t) = 20*t**2 + 35*t - 43. Let f(w) = 4*k(w) + 3*v(w). Find x, given that f(x) = 0.
-20, 1
Let t = 8836 + -8833. Find n such that 6/7*n + 10/7*n**t + 16/7*n**2 + 0 = 0.
-1, -3/5, 0
Let a(u) be the second derivative of -u**5/18 - 17*u**4/54 - 16*u**3/27 - 4*u**2/9 - 126*u + 2. Factor a(g).
-2*(g + 1)*(g + 2)*(5*g + 2)/9
Let m(j) be the first derivative of 4/3*j**3 + 9 + 16*j - 10*j**2. Suppose m(a) = 0. Calculate a.
1, 4
Let f(t) be the first derivative of -t**8/840 - t**7/210 + t**5/30 + t**4/12 - t**3/3 - 4. Let r(k) be the third derivative of f(k). Find w such that r(w) = 0.
-1, 1
Find y such that 5*y**4