*h**3 + 0*h**4 + 0*h**2 - 1/20*h**5. Factor q(f).
-f**2*(f - 1)*(f + 1)/4
Suppose r = -5, -2*u - 3*r = u + 6. Factor -4*c**3 - 20*c**2 + 26*c - 4*c**u + 3*c**3 - 46*c.
-5*c*(c + 2)**2
Let f be (7/(-14))/((-3)/518). Let v = 87 - f. Factor -v*x**3 - 2/3*x + 0 - 4/3*x**2.
-2*x*(x + 1)**2/3
Factor -273/4*s + 3/4*s**2 - 69.
3*(s - 92)*(s + 1)/4
Let z(y) be the first derivative of y**6/90 + y**5/30 + 17*y**3/3 - 15. Let a(j) be the third derivative of z(j). Factor a(s).
4*s*(s + 1)
Let n(z) = 2*z**2 - 16*z + 20. Let q(b) = 2*b**2 - 15*b + 19. Let l(j) = 3*n(j) - 4*q(j). Let l(g) = 0. Calculate g.
2, 4
Suppose 2*u = -o + 6*o + 203, -270 = -3*u - 4*o. Let k = 106 - u. Factor -9*w**3 - k*w + 0 + 3/2*w**4 + 18*w**2.
3*w*(w - 2)**3/2
Let p(a) be the third derivative of -a**8/216 - a**7/105 + 19*a**6/540 + 13*a**5/270 - a**4/9 - 4*a**3/27 - 154*a**2. Solve p(c) = 0.
-2, -1, -2/7, 1
Let q = -66967/2 + 33488. Factor -1/2 + 11/2*s - 19/2*s**2 + q*s**3.
(s - 1)**2*(9*s - 1)/2
Suppose 8*j - 6*j = 3*x - 12, -5*x + 25 = -5*j. Suppose 39/4*l - 3/2 - 33/4*l**x = 0. What is l?
2/11, 1
Let l(s) be the first derivative of 1 - 1/7*s**3 - 6/7*s**2 - 12/7*s. Factor l(h).
-3*(h + 2)**2/7
Let g be (-1 - 45/(-39)) + (-32870)/(-130). Let d = g - 238. Solve 0 - 12/5*r + 12*r**2 - d*r**3 = 0.
0, 2/5
Let m be 0 - ((-11)/33 - (1150/105 + -1)). Determine t, given that -m*t**3 + 0 - 24/7*t**2 + 0*t - 54/7*t**4 = 0.
-2/3, 0
Suppose 0 = -30*r - 5*r + 140. Let q(v) be the second derivative of 1/20*v**r + 1/10*v**3 + 0 + 1/10*v**2 - 2*v + 1/100*v**5. What is p in q(p) = 0?
-1
Let w(f) be the second derivative of f**7/63 + 7*f**6/135 - f**5/10 - 7*f**4/54 + 2*f**3/9 - 66*f. Let w(i) = 0. What is i?
-3, -1, 0, 2/3, 1
Let s(w) = 656*w + 3. Let z be s(0). What is m in -3/5*m**2 - 4/5*m + 0 + 1/5*m**z = 0?
-1, 0, 4
Let n(y) = -y + 0*y + 1 + 0*y. Let j(r) be the second derivative of -r**5/10 + r**4/2 - 2*r**3 + 4*r**2 - 6*r + 2. Let l(k) = -j(k) + 6*n(k). Factor l(o).
2*(o - 1)**3
Let o(f) be the third derivative of -f**7/245 - f**6/420 + f**5/15 + f**4/21 - 8*f**3/21 + 5*f**2 - 2. Suppose o(h) = 0. What is h?
-2, -1, 2/3, 2
Let f = -14 + 49. Let c be ((-2)/f)/(242/(-40) + 6). Factor 8/7*m**3 + 0*m + 0*m**2 - c*m**4 + 2/7*m**5 + 0.
2*m**3*(m - 2)**2/7
Factor -1/3*x**2 + 70/3*x - 1225/3.
-(x - 35)**2/3
Let t be (-4)/60*3*6/(-4). Let j(v) be the second derivative of 0 + 1/14*v**7 + 0*v**4 + 3/10*v**6 + 0*v**3 + v + 0*v**2 + t*v**5. Factor j(p).
3*p**3*(p + 1)*(p + 2)
Suppose 64 - 22 = -14*r. Let b be ((-3)/5)/(r/3). Factor 0*g**3 - b*g**4 + 9/5*g**2 + 6/5*g + 0.
-3*g*(g - 2)*(g + 1)**2/5
Factor 65*l - 1813*l**3 - 48*l**2 - 3*l**5 + 31*l - 48 - 1833*l**3 + 15*l**4 + 3634*l**3.
-3*(l - 2)**3*(l - 1)*(l + 2)
Let h be ((-6)/4)/(7/(-14)). Suppose 5*c = h*i - 288, -4*c - 103 = -2*i + i. Factor -6*u - 3*u**2 - i + 91.
-3*u*(u + 2)
Let m = 26 - 6. Let k(i) be the first derivative of -m*i**2 + 3 + 2 - 4 + 17*i**2 - i**3 - 3*i. Find x, given that k(x) = 0.
-1
Let w(i) be the third derivative of -i**7/455 - 17*i**6/780 - 7*i**5/130 + 3*i**4/52 - 7*i**2 + 4. Find k, given that w(k) = 0.
-3, 0, 1/3
Let n be (-3)/(-1 + 20/16). Let a be (-14)/(-4) + (-6)/n. Let -12*c**a + 13*c + 0 + 5*c + 28*c**3 - 4 + 2*c**5 + 4*c**2 - 36*c**2 = 0. Calculate c.
1, 2
Solve 0 + 1832*y**2 - 145*y + 0 - 1837*y**2 = 0.
-29, 0
Suppose -3*f = -6, r - 2*r + 2*f = 0. Let p(n) = 9*n**3 - 8*n**2 - n. Let g(i) = -4*i**3 + 4*i**2. Let w(u) = r*p(u) + 10*g(u). Factor w(l).
-4*l*(l - 1)**2
Let f be 978/198 - 6/(-99). Let g(w) be the first derivative of 2*w**4 + 2/5*w**f + 4*w**3 + 4*w**2 + 10 + 2*w. Factor g(m).
2*(m + 1)**4
Let i = 50486/252455 + 1/50491. Determine a, given that -14/5*a + i*a**2 + 49/5 = 0.
7
What is x in 0 + 125/3*x**3 + 0*x - 5/3*x**2 = 0?
0, 1/25
Let c(o) be the second derivative of o**7/5880 + o**6/560 + o**5/140 + 23*o**4/12 + 30*o. Let d(b) be the third derivative of c(b). Suppose d(n) = 0. What is n?
-2, -1
Let t(w) be the third derivative of -1/270*w**6 + 0*w - 15*w**2 - 1/135*w**5 + 1/54*w**4 + 2/27*w**3 + 0. Factor t(j).
-4*(j - 1)*(j + 1)**2/9
Let u(f) = -f**3 + 14*f**2 - 13*f + 30. Let w be u(13). Let g be w/8 + (-4 + 13)/(-3). Factor -1/2*c - 1/4*c**4 + 5/4*c**2 + 1/4*c**5 + 0 - g*c**3.
c*(c - 1)**3*(c + 2)/4
Let t(j) = -j**5 - 6*j**4 + 10*j**3 + 4*j**2 - 11*j - 2. Let v(x) = 2*x**5 + 6*x**4 - 11*x**3 - 3*x**2 + 12*x + 3. Let n(b) = -6*t(b) - 4*v(b). Solve n(g) = 0.
-1, 0, 1, 3
Suppose 7*g = -13*g + 40. Let y(m) be the second derivative of 1/20*m**6 + 1/12*m**4 + 7/40*m**5 + 0*m**3 + 0 + m + 0*m**g. Factor y(q).
q**2*(q + 2)*(3*q + 1)/2
Factor 10549*c**3 - 10516*c**3 + 12*c - 3*c**4 - 51*c**2 - 6*c**2 + 15*c.
-3*c*(c - 9)*(c - 1)**2
Let b(f) = 13*f + 44. Let x be b(-3). Suppose 125 - 140 = -x*k. Find t such that 8/17*t**2 + 2/17*t - 4/17*t**k + 2/17*t**5 - 4/17 - 4/17*t**4 = 0.
-1, 1, 2
Let o = 34 + -33. Let r(a) = 4*a - 2. Let g be r(1). Find x such that 1 + o + 3*x + 7*x**g - 6*x**2 = 0.
-2, -1
Let h be 4 + ((-3750)/40)/25. Factor -h*k**3 - 1/2*k**2 + 0 + 3/4*k.
-k*(k - 1)*(k + 3)/4
Suppose 0 - 16/17*w**2 - 18/17*w + 2/17*w**3 = 0. Calculate w.
-1, 0, 9
Let c(x) be the third derivative of -x**6/96 - 9*x**5/16 - 15*x**4/4 - 68*x**2. Factor c(b).
-5*b*(b + 3)*(b + 24)/4
Factor -7/2*b**3 - 73/10*b + 53/5*b**2 + 1/5.
-(b - 2)*(b - 1)*(35*b - 1)/10
Let j(g) = g**3 + 6*g**2 - 7*g. Suppose 4*m + 96 = -0*m. Let z(w) = w**2 - w. Let i(t) = m*z(t) + 3*j(t). Factor i(n).
3*n*(n - 1)**2
Suppose 41*k = -37*k + 29*k. Suppose k + 1/6*d**4 - 1/6*d - 1/2*d**3 + 1/2*d**2 = 0. What is d?
0, 1
Let n(x) be the first derivative of 0*x + 15 + 3/2*x**4 + 2/3*x**2 + 1/9*x**6 + 2/3*x**5 + 14/9*x**3. Suppose n(d) = 0. What is d?
-2, -1, 0
Let x(o) = -5*o**3 + 276*o**2 - 4083*o - 1688. Let k(d) = -2*d**2 + d - 1. Let r(c) = -6*k(c) + x(c). Find y, given that r(y) = 0.
-2/5, 29
Let m(l) be the second derivative of -l**4/3 + 2*l**3/3 + 217*l. Factor m(b).
-4*b*(b - 1)
Let x(k) be the first derivative of -3*k**5/10 - 273*k**4/8 - 2113*k**3/2 - 5535*k**2/4 + 6075*k + 188. Determine n, given that x(n) = 0.
-45, -2, 1
Factor 2/3*u**3 + 0 + 1/3*u + 0*u**4 - 1/9*u**5 - 8/9*u**2.
-u*(u - 1)**3*(u + 3)/9
Factor 2567*o**2 - 25*o + 25*o**3 - 4*o**4 - 2562*o**2 - o**4.
-5*o*(o - 5)*(o - 1)*(o + 1)
Let b(f) be the third derivative of f**5/80 + 31*f**4/32 - 4*f**3 + f**2 + 5*f. Suppose b(s) = 0. Calculate s.
-32, 1
Suppose -4*j + 15 = -5*z, 4*z + 12 = 3*j - 0*z. Let r(u) be the third derivative of -1/20*u**4 - u**2 + 1/300*u**5 + 3/10*u**3 + 0*u + j. Factor r(x).
(x - 3)**2/5
Let o be -1 + (5 - 0) + ((-1400)/91)/4. Factor o*f**3 + 70/13*f + 50/13 + 22/13*f**2.
2*(f + 1)*(f + 5)**2/13
Let u(z) = z + 14. Let n = 2 - 13. Let g be u(n). Determine q, given that q**2 - 30*q**3 + 16*q**3 - q**4 + 14*q**g = 0.
-1, 0, 1
Let y = -47 + 35. Let c(w) = -w**3 - 11*w**2 + 11*w - 9. Let t be c(y). Factor 3*z**2 + 23*z**t + z**2 - 22*z**3 + 3*z.
z*(z + 1)*(z + 3)
Let p be (-30)/(-225) + (-562)/165. Let n = p + 202/55. Factor 0 - n*t**2 + 6/5*t.
-2*t*(t - 3)/5
Let k(v) be the second derivative of -3/4*v**4 - 13*v - 1/10*v**6 + 9/20*v**5 + 1/2*v**3 + 0 + 0*v**2. Determine h so that k(h) = 0.
0, 1
Factor 7*y - 1/3*y**4 - 3*y**3 - 11/3*y**2 + 0.
-y*(y - 1)*(y + 3)*(y + 7)/3
Let h(j) be the first derivative of j**6/30 - 17*j**4/20 + 8*j**2/5 + 525. What is a in h(a) = 0?
-4, -1, 0, 1, 4
Let x(l) be the first derivative of 11*l + 5/48*l**3 + 1/24*l**4 - 1 + 1/16*l**2. Let j(c) be the first derivative of x(c). Let j(h) = 0. Calculate h.
-1, -1/4
Suppose a = 4*a - 27. Let v be 57/a + -5 - (-1 + -3). Factor -8*x**2 - 4/3 + 16/3*x**3 + v*x - 4/3*x**4.
-4*(x - 1)**4/3
Let m(g) be the first derivative of -17*g**3/6 + 37*g**2/8 - 3*g/4 - 78. Factor m(f).
-(f - 1)*(34*f - 3)/4
Let x = 116 - 115. Let g(c) = 3 + 3*c**3 - c**2 - 4 - 2*c**3 + c**4. Let i(f) = 9*f**4 + 3*f**3 - 6*f**2 - 6. Let a(y) = x*i(y) - 6*g(y). Factor a(u).
3*u**3*(u - 1)
Let g = 75147/7 - 10735. Suppose -2/7*v**5 + 4/7*v**4 + 4/7*v**3 - 8/7*v**2 - g*v + 4/7 = 0. Calculate v.
-1, 1, 2
Let h be (16/10)/2 - (-634 + 634). Factor -h*g + 8/5 - 4/5*g**2.
-4*(g - 1)*(g + 2)/5
Let g(m) = -2*m + 3. Let y(x) = 2*x - 2. Let j(t) = -5*g(t) - 4*y(t). Let k be j(6). Suppose -3*i**3 + k - 6*i**2 - 5 = 0. What is i?
-2,