- 1. Let t(v) = 9*v - 2*v - 6*v**3 - 4*v**2 + 2*v**2 + 1 + v. Let f(y) = -3*j(y) + 3*t(y). Factor f(c).
-3*(c - 1)*(c + 1)*(7*c + 2)
Let h be (1 - (-5)/(-25))/(2/15). Suppose -20*n**2 + 5*n**2 + 15*n - h*n + 3 + 4*n**3 - n = 0. Calculate n.
-1/4, 1, 3
Let a(q) be the first derivative of q**3/3 + 23*q**2 + 529*q - 75. Find s such that a(s) = 0.
-23
Suppose -295*q - 750 = -545*q. Find h, given that 0*h + 0*h**q + 0 + 2/7*h**4 + 2/7*h**5 + 0*h**2 = 0.
-1, 0
Let y = -62 - -66. Let t(n) be the second derivative of 0*n**2 - 1/42*n**7 + 0*n**4 + 0*n**3 + 0 - 1/10*n**5 - 1/10*n**6 - y*n. Let t(i) = 0. Calculate i.
-2, -1, 0
Let t be ((-20)/35)/(4/14*-5). Let g(x) be the first derivative of -1/10*x**2 + 7 - t*x + 1/15*x**3. Factor g(c).
(c - 2)*(c + 1)/5
Let a(s) be the second derivative of s**7/14 - s**6/2 + 6*s**5/5 - s**4 + 59*s. Suppose a(o) = 0. What is o?
0, 1, 2
Let c(o) = -48*o**2 + 100*o + 148. Let j(f) = -7*f**2 + 14*f + 21. Let s(d) = 3*c(d) - 20*j(d). Factor s(g).
-4*(g - 6)*(g + 1)
Let k(q) be the second derivative of q**5/6 + 11*q**4/18 + 7*q**3/9 + q**2/3 + 109*q. Suppose k(r) = 0. Calculate r.
-1, -1/5
Let b(g) be the first derivative of -2*g**7/63 - 4*g**6/45 + 2*g**4/9 + 2*g**3/9 + 12*g - 6. Let y(x) be the first derivative of b(x). Factor y(a).
-4*a*(a - 1)*(a + 1)**3/3
Let w(a) = 3*a**3 + 5*a**2 - 5*a - 1. Let x(b) be the second derivative of b**5/20 + b**4/12 + b**3/6 - b**2/2 - 25*b. Let h(u) = w(u) - x(u). Factor h(s).
2*s*(s - 1)*(s + 3)
Suppose 1674 = -31*n + 37*n. Factor 20*h + 28*h + n + 11*h**2 - 87 - 8*h**2.
3*(h + 8)**2
Let k(n) be the first derivative of -n**3/9 - 17*n**2/3 - 289*n/3 + 439. Determine b so that k(b) = 0.
-17
Let x = -25374 - -25376. Factor 2/11*n**x - 4/11*n**4 + 1/11*n**5 + 4/11*n**3 + 2/11 - 5/11*n.
(n - 2)*(n - 1)**3*(n + 1)/11
Let f(p) be the third derivative of 0 - 1/12*p**4 + 0*p - 1/30*p**5 + 2*p**2 + 2/3*p**3. Factor f(u).
-2*(u - 1)*(u + 2)
Let d(a) = -10*a + 80. Let j be d(8). Let k(f) be the third derivative of -1/24*f**4 + 0*f - 7/180*f**5 + j + 2/9*f**3 - f**2. Solve k(n) = 0.
-1, 4/7
Let x(p) be the first derivative of -2*p**5/9 - 4*p**4 - 182*p**3/9 - 98*p**2/9 + 8. Find s such that x(s) = 0.
-7, -2/5, 0
Let 0 + 8/9*j - 2/3*j**3 + 0*j**2 + 2/9*j**4 = 0. Calculate j.
-1, 0, 2
Let b(n) be the second derivative of 2/63*n**7 + 1/36*n**4 + 11/90*n**6 - 12*n + 3/20*n**5 + 0*n**2 - 1/18*n**3 + 0. Factor b(k).
k*(k + 1)**3*(4*k - 1)/3
Let i(y) be the first derivative of y**6/30 - 21*y**2/2 + 8. Let v(x) be the second derivative of i(x). Factor v(a).
4*a**3
Let k(m) = 985*m + 3943. Let i be k(-4). Factor 0 + 1/3*l**4 + 0*l**i - l**2 - 2/3*l.
l*(l - 2)*(l + 1)**2/3
Let i(a) be the second derivative of -a**6/75 - 3*a**5/50 + 4*a**4/5 + 16*a**3/3 - 850*a. Factor i(h).
-2*h*(h - 5)*(h + 4)**2/5
Solve -4/7 - 26/7*q**2 - 30/7*q = 0.
-1, -2/13
Let h(m) be the first derivative of 12 - 4/55*m**5 + 0*m**2 - 1/22*m**4 + 0*m + 1/11*m**6 + 0*m**3. Let h(y) = 0. Calculate y.
-1/3, 0, 1
Let b(v) be the third derivative of v**5/45 + 11*v**4/180 + v**3/45 + 28*v**2. Factor b(x).
2*(x + 1)*(10*x + 1)/15
Let 2/7*r**5 + 54/7*r + 0*r**4 + 4/7*r**2 - 36/7 - 24/7*r**3 = 0. Calculate r.
-3, -2, 1, 3
Let m(g) be the second derivative of 0*g**2 + 4/3*g**3 + 0 - 1/3*g**4 - 2/5*g**5 - 48*g + 2/15*g**6. Factor m(b).
4*b*(b - 2)*(b - 1)*(b + 1)
Let t(m) = 7*m**2 - 7*m + 7. Let s be t(1). Let y(u) be the first derivative of 8/17*u**2 + 10/17*u**3 + 2/17*u**4 - 6/17*u - s. Factor y(c).
2*(c + 1)*(c + 3)*(4*c - 1)/17
Let y(k) be the first derivative of -2/15*k**3 + 0*k - 8/5*k**2 + 2. Determine h, given that y(h) = 0.
-8, 0
Let g = -25 + 17. Let i be (g + 6)/(3*-1). Factor -4*x**2 + i*x**3 + 8*x - 16/3.
2*(x - 2)**3/3
Let d(z) be the third derivative of -z**6/1200 - z**5/200 + 46*z**2. Factor d(u).
-u**2*(u + 3)/10
Factor -19/3*f**2 + 0 + 0*f + 1/3*f**3.
f**2*(f - 19)/3
Let n = 25811 + -25808. Find s, given that 8/3*s + 10/3*s**4 - 14/3*s**n - 16/3*s**2 + 0 = 0.
-1, 0, 2/5, 2
Let v(w) be the third derivative of w**7/945 - w**6/270 - 14*w**5/135 - 23*w**4/54 - 7*w**3/9 + 485*w**2. Factor v(z).
2*(z - 7)*(z + 1)**2*(z + 3)/9
Let v(o) be the second derivative of -8*o**4/3 - 14*o**3 + 18*o**2 + 2*o - 86. Find k, given that v(k) = 0.
-3, 3/8
Let l(o) = 13*o + 69. Let i be l(-5). Let h be -2*(7/(-2) - -1). Let m(d) = -9*d**2 + 4. Let g(c) = 8*c**2 - 4. Let x(n) = h*g(n) + i*m(n). Factor x(f).
4*(f - 1)*(f + 1)
Suppose 0 = -3*o + o + 4*u + 8, 4*o = -3*u - 17. Let g = o + 4. Let -3*x**3 - 2*x**g - 3*x**3 + 8*x**3 = 0. What is x?
0, 1
Let d be (4 - (4 + -11)) + -1. Let h be d/(-40)*(-1 + -11). What is f in -4 + f**2 - 5*f**3 - 22*f - 9*f**h - 33*f**2 + 0 = 0?
-1, -2/7
Factor -22/7*f**2 + 2/7*f**4 + 20/7*f**3 + 0 + 0*f.
2*f**2*(f - 1)*(f + 11)/7
Let s(g) be the third derivative of -3*g**6/40 + g**5/4 + 3*g**4/4 - 4*g**3 + 5*g**2 - 8. Factor s(f).
-3*(f - 2)*(f - 1)*(3*f + 4)
Let g(p) be the first derivative of 2*p**3/9 + 394*p**2/3 + 77618*p/3 + 408. Factor g(h).
2*(h + 197)**2/3
Let f(n) be the second derivative of -n**5/10 - 2*n**4/3 - n**3/3 + 6*n**2 + 3*n - 12. Factor f(g).
-2*(g - 1)*(g + 2)*(g + 3)
Let b(i) be the first derivative of 0*i + 5*i**6 - 5 - 65/8*i**4 + 5/4*i**2 + 5/6*i**3 - 1/2*i**5. What is r in b(r) = 0?
-1, -1/4, 0, 1/3, 1
Let w(k) be the first derivative of 3*k**4/4 + 4*k**3 + 9*k**2/2 - 76. Find s such that w(s) = 0.
-3, -1, 0
Factor -427*c - 4*c**2 + 2 + 2*c**5 - 8*c**3 + 2 + 433*c.
2*(c - 2)*(c - 1)*(c + 1)**3
Let n(d) be the second derivative of -1/20*d**2 - 4*d + 1/120*d**4 + 0*d**3 + 0. Factor n(q).
(q - 1)*(q + 1)/10
Factor -47*x**4 + 16*x**4 - 65*x**4 + 20*x**4 - 3*x**5 - x**5.
-4*x**4*(x + 19)
Let f(z) be the third derivative of 9/8*z**4 + 0*z**3 + 0*z - 3/40*z**5 + 0 + 1/140*z**7 - 1/20*z**6 + z**2. Let f(k) = 0. What is k?
-2, 0, 3
Suppose 5*g - 469 = 4*k - 162, 5*g - 151 = 2*k. Let y = 236/3 + k. Suppose -32/3*z**2 - y*z**5 - 4*z**4 - 6*z - 28/3*z**3 - 4/3 = 0. Calculate z.
-2, -1
Let g(i) be the first derivative of i**6/2 - 2*i**5 + 3*i**4 - 2*i**3 + i**2/2 - 304. Factor g(j).
j*(j - 1)**3*(3*j - 1)
Let p(y) = 102*y - 201. Let t be p(2). Let b = 75/2 + -36. Factor 0 + 0*s - 3/2*s**5 - b*s**4 + 3/2*s**2 + 3/2*s**t.
-3*s**2*(s - 1)*(s + 1)**2/2
Let o(v) be the third derivative of 5*v**8/84 - 46*v**7/105 - 4*v**6 - 124*v**5/15 - 16*v**4/3 - 206*v**2. Determine q, given that o(q) = 0.
-2, -1, -2/5, 0, 8
Let -432*p**2 + 440*p**3 + 2916/5 - 1944/5*p - 100*p**4 = 0. What is p?
-1, 9/5
Let k(a) be the first derivative of -a**6/120 - a**5/60 + a**4/24 + a**3/6 + 4*a**2 - 1. Let l(n) be the second derivative of k(n). Factor l(o).
-(o - 1)*(o + 1)**2
Let h(f) = 10*f**2. Let q be h(-1). Let -34*n**2 + q*n**3 - 45 + 80 - 43 + 32*n = 0. Calculate n.
2/5, 1, 2
Let o(v) be the second derivative of -v**5/80 - 11*v**4/48 + 7*v**3/12 + 3*v**2 + 633*v. Suppose o(h) = 0. Calculate h.
-12, -1, 2
Let i(c) be the first derivative of 1/240*c**6 + 0*c**4 + 0*c**3 - 9/2*c**2 - 12 + 1/120*c**5 + 0*c. Let d(n) be the second derivative of i(n). Factor d(j).
j**2*(j + 1)/2
Let q(c) be the first derivative of c**4/4 - 11*c**3/3 + 35*c**2/2 - 25*c - 4. Suppose q(j) = 0. Calculate j.
1, 5
Let n(b) = 135*b - 850. Let v(f) = f**2 + 136*f - 851. Suppose 2*z = 20 - 32. Let u(x) = z*n(x) + 5*v(x). Factor u(g).
5*(g - 13)**2
Let k(j) = -8*j**3 + 14*j**2 + 11. Suppose 11 - 44 = -3*p. Let y(r) = -3*r**3 + 5*r**2 + 4. Let d(s) = p*y(s) - 4*k(s). Factor d(z).
-z**2*(z + 1)
Let i(c) be the first derivative of -2*c**3/9 - 7*c**2/3 + 16*c/3 + 183. Factor i(g).
-2*(g - 1)*(g + 8)/3
Let v be 24/(-3 + 20/8). Let k be v/(-18)*2/6. Factor -8/3*d + k - 14/9*d**2.
-2*(d + 2)*(7*d - 2)/9
Let x(t) be the first derivative of -t**8/112 + t**7/70 + 3*t**2/2 - 4. Let c(m) be the second derivative of x(m). Let c(g) = 0. Calculate g.
0, 1
Let n(q) be the first derivative of 2*q**5/5 + 3*q**4 + 2*q**3 - 10*q**2 - 56. Suppose n(g) = 0. What is g?
-5, -2, 0, 1
Let p(c) be the second derivative of 0*c**3 + 1/9*c**2 + 3*c - 1/54*c**4 + 0. Factor p(j).
-2*(j - 1)*(j + 1)/9
Suppose 13 - 17 = -h. Find n, given that -10*n**2 - n**3 + 4*n + 60 - n**5 + 60 + h*n**4 - 112 = 0.
-1, 2
Let k(j) be the third derivative of j**8/1008 - j**7/420 + 17*j**2 - 2*j. Let k(g) = 0. What i