1/18*u**4 - 1/120*u**6 - 2/9*u**3. Let p(m) be the first derivative of x(m). Factor p(k).
-(k - 2)*(k + 1)*(3*k - 2)/3
Factor 149*u - 332*u - 100*u**2 + 48*u - 15*u**3 - 50.
-5*(u + 1)*(u + 5)*(3*u + 2)
Let i be (-32885)/(-28140) + 6/(-8). Let g = i + 2/201. Factor 3/7*c + g*c**3 + 6/7*c**2 + 0.
3*c*(c + 1)**2/7
Let z(h) be the second derivative of -h**6/30 - 26*h**5/5 + 53*h**4/2 - 160*h**3/3 + 107*h**2/2 + 64*h + 3. Determine k so that z(k) = 0.
-107, 1
Let k(h) = -5*h**3 - h + 2. Let j(m) = 27*m**3 + 1161*m**2 - 149763*m + 6440055. Let f(o) = -j(o) - 6*k(o). Determine y so that f(y) = 0.
129
Suppose -22*x + 9*x = -14*x. Determine f so that 1/3*f**3 - 1/3*f**5 + 1/3*f**2 + 0*f - 1/3*f**4 + x = 0.
-1, 0, 1
Let w(f) be the third derivative of 0*f + 57*f**2 + 0 + 0*f**5 + 0*f**6 + 0*f**4 + 0*f**3 + 1/378*f**7 - 1/3024*f**8. Factor w(n).
-n**4*(n - 5)/9
Let z = 8 - 23/3. Let j be 4/3 - (-60)/(-90). Factor 1/3 + j*h**2 - h**4 + h - z*h**5 - 2/3*h**3.
-(h - 1)*(h + 1)**4/3
Suppose -4*s + 51 = 39. Suppose -z + 4 = 0, s*z = 3*b - 0*z + 6. Let -b + 2/3*n**2 + 4/3*n = 0. What is n?
-3, 1
Factor -1/10*t**2 - 19/10*t + 0.
-t*(t + 19)/10
Let t(r) be the third derivative of -r**8/3360 + r**7/1260 - 7*r**5/20 + 13*r**2. Let z(x) be the third derivative of t(x). Suppose z(o) = 0. Calculate o.
0, 2/3
Let t be 154/(-8) + (-1)/(-4). Let m = t + 19. Solve 2 + 4*l**2 + m*l + 2 + 0 + 8*l = 0.
-1
Factor 6*p + 30 + 49 + 29*p - 5*p**3 - 49.
-5*(p - 3)*(p + 1)*(p + 2)
Let b(s) be the second derivative of s**4/36 + 7*s**3/18 + 20*s. Suppose b(w) = 0. Calculate w.
-7, 0
Solve 381*y + 4*y**2 + 3 - 186*y + 0 + 9 - 211*y = 0 for y.
1, 3
Let z be 6*1 + (-184)/(-23). Suppose -14*d + 0*d + z = 0. Suppose w - d - 1/4*w**2 = 0. What is w?
2
Let w(u) be the second derivative of 3*u**5/80 + 29*u**4/48 - 5*u**3/12 - 32*u + 2. Factor w(f).
f*(f + 10)*(3*f - 1)/4
Let y(a) be the second derivative of -a**4/30 - 58*a**3/45 - 19*a**2/15 + 2*a - 52. Factor y(j).
-2*(j + 19)*(3*j + 1)/15
Suppose -4*d + 31 = -5*s, 0 = 5*d - 5*s - 15 - 20. Suppose -d*b + 5*b = -0*b. Solve 0*q + 2/13*q**2 + b - 2/13*q**3 = 0 for q.
0, 1
Let r(o) = -o**4 - o**3 - o - 1. Let t = -40 - -41. Let b(a) = -6*a**4 + 6*a**3 - 6*a**2 - 14*a + 4. Let n(p) = t*b(p) - 4*r(p). Factor n(h).
-2*(h - 4)*(h - 1)**2*(h + 1)
Suppose -8*w - 588 - 76 = 0. Let y = w + 86. Factor -24/5*c + 2/5*c**4 - 16/5 + 6/5*c**y - 4/5*c**2.
2*(c - 2)*(c + 1)*(c + 2)**2/5
Let k(z) be the first derivative of -z**4 + 4*z**3/3 + 4*z**2 - 83. Solve k(h) = 0 for h.
-1, 0, 2
Suppose -m = -0*m. Let h = -450 - -1352/3. Determine n so that 2/3*n**2 + h*n + m = 0.
-1, 0
Let i(q) be the third derivative of q**6/840 - q**5/105 - q**4/6 - 16*q**3/21 - 126*q**2. Find z, given that i(z) = 0.
-2, 8
Let k(f) be the first derivative of -f**6/21 - 6*f**5/35 + f**4/14 + 22*f**3/21 + 12*f**2/7 + 8*f/7 - 83. Suppose k(h) = 0. Calculate h.
-2, -1, 2
Factor -797 + 797 + 3*a**5 + 4*a**4 + 2*a**5 - a**5.
4*a**4*(a + 1)
Let f(t) be the first derivative of 2*t**3/9 + 57*t**2/2 - 86*t/3 + 41. Factor f(o).
(o + 86)*(2*o - 1)/3
Let w(i) be the third derivative of 0*i**7 + 0*i**5 + 0*i**3 + 1/784*i**8 + 0 - 9*i**2 - 1/140*i**6 + 0*i + 1/56*i**4. Suppose w(a) = 0. What is a?
-1, 0, 1
Let m(b) = b**3 - 12*b**2 + 16*b + 1. Let g be m(4). Let y be (g/(-42) - (-6)/(-4)) + 0. Factor -x**4 + y*x**3 - 1/2*x + 0 + x**2 + 1/2*x**5.
x*(x - 1)**3*(x + 1)/2
Let t(w) be the second derivative of w**6/6 - 9*w**5/4 + 25*w**4/3 + 225*w. Suppose t(n) = 0. What is n?
0, 4, 5
Let g(v) = 3*v**4 - 104*v**3 + 350*v**2 + 195*v - 2000. Let p(a) = -4*a**4 + 156*a**3 - 524*a**2 - 292*a + 3000. Let z(u) = 8*g(u) + 5*p(u). Factor z(l).
4*(l - 5)**3*(l + 2)
Let q(c) be the first derivative of -2*c**6/15 + 8*c**5/25 + c**4/5 - 8*c**3/15 - 146. Solve q(h) = 0.
-1, 0, 1, 2
Let b(q) be the third derivative of -3*q**8/560 - q**7/70 - q**6/120 + 2*q**3/3 - 8*q**2. Let c(r) be the first derivative of b(r). Factor c(d).
-3*d**2*(d + 1)*(3*d + 1)
Let s(o) be the second derivative of -o**3 - 9*o**2/2 + 3*o - 1. Let y be s(-2). Factor -1/2 + 1/2*k**4 - k**y + k + 0*k**2.
(k - 1)**3*(k + 1)/2
Let n be (3 + -1577)/((-22)/4*1). Let h = -286 + n. Solve -2/11*r + 2/11*r**3 - h*r**2 + 2/11 = 0.
-1, 1
Suppose -21*w + 132 = w. Let f(x) be the second derivative of -2/105*x**7 - 2/25*x**w - 1/15*x**4 + 0*x**3 + 0 - 3*x + 0*x**2 - 3/25*x**5. Factor f(j).
-4*j**2*(j + 1)**3/5
Let n be 4/1 - (-1 + 0). Let v be 130/(-60)*96/(-78). Factor -v*a**2 + 2/3*a**n + 0 + 4*a**3 + 2/3*a - 8/3*a**4.
2*a*(a - 1)**4/3
Let l(a) = -6*a**3 + 135*a**2 - 729*a + 573. Let h(j) = 3*j**3 - 68*j**2 + 365*j - 285. Let m(b) = 9*h(b) + 5*l(b). Suppose m(i) = 0. Calculate i.
1, 10
Let g(w) be the first derivative of w**5/40 - w**4/24 - w**3/12 + w**2/4 - 13*w + 2. Let x(y) be the first derivative of g(y). Let x(h) = 0. Calculate h.
-1, 1
Let n be 2/11 - 78/(-55). Let y = -102 - -104. What is o in 0*o + 2/5*o**5 + 0*o**y + n*o**4 + 0 + 8/5*o**3 = 0?
-2, 0
Let f(p) be the third derivative of -p**10/352800 + p**8/6720 + p**7/1960 - 5*p**5/12 - 27*p**2. Let j(h) be the third derivative of f(h). Factor j(c).
-3*c*(c - 3)*(c + 1)*(c + 2)/7
Let x(p) be the third derivative of p**6/24 + 5*p**5/12 - 5*p**4 + 22*p**2 - 3*p. Factor x(k).
5*k*(k - 3)*(k + 8)
Let z(j) = -31*j**2 - 52*j + 43. Let f(i) = -50*i**2 - 78*i + 64. Let d(s) = 5*f(s) - 8*z(s). Factor d(l).
-2*(l - 12)*(l - 1)
Let n = -176/17 - -18662/85. Let i = n - 208. Find b such that i*b**2 - 2/5*b - 4/5 = 0.
-2/3, 1
Let y = 473 + -822. Let z = -347 - y. Determine x so that 0*x + 3/7*x**z + 9/7*x**4 + 0 + 3/7*x**5 + 9/7*x**3 = 0.
-1, 0
Factor -1/4*m**2 + 1/4*m + 5.
-(m - 5)*(m + 4)/4
Suppose 6*y + 7*y = -8*y. Factor -36/11*v**2 + 162/11*v + y + 2/11*v**3.
2*v*(v - 9)**2/11
Let t(n) = -n**4 + 8*n**3 + n**2 - 10*n + 4. Let m(s) = 3*s**4 - 16*s**3 - 3*s**2 + 21*s - 10. Let q(p) = -6*m(p) - 15*t(p). Find f, given that q(f) = 0.
-8, -1, 0, 1
Suppose l = -d + 3*d - 12, 20 = 3*d - 2*l. Let g = d - 19/5. Suppose 3/5*t**3 + g*t**4 + 1/5*t + 3/5*t**2 + 0 = 0. What is t?
-1, 0
Let u(i) be the first derivative of -2*i**5/15 + 2*i**4/3 + 32*i**3/3 + 112*i**2/3 + 160*i/3 - 155. Factor u(z).
-2*(z - 10)*(z + 2)**3/3
Suppose -6*n + 10 = -5*n. Suppose 14*h**2 - n*h**2 + 2 + 12*h + 6 = 0. Calculate h.
-2, -1
Find m such that 0*m + 0 - 18*m**4 - 34*m**3 - 50/3*m**2 - 2/3*m**5 = 0.
-25, -1, 0
Let n(k) = k**3 + 3*k**2 - k - 3. Let v be (-5 - (-12 - -6))*2. Let w be n(v). What is a in -10*a**2 - w*a**3 + 0 - 15/2*a**4 - 5/4*a**5 + 0*a = 0?
-2, 0
Determine d so that 0 + 555/2*d + 5/2*d**3 - 100*d**2 = 0.
0, 3, 37
Factor z**4 - 9*z**4 + 10*z**3 - 10*z**4 + 8*z**2.
-2*z**2*(z - 1)*(9*z + 4)
Let z(x) be the first derivative of x**4/24 + 43*x**3/18 + 83*x**2/12 + 41*x/6 + 207. Let z(s) = 0. What is s?
-41, -1
Let f(a) be the first derivative of -486*a**4/7 - 144*a**3/7 + 33*a**2/7 - 2*a/7 - 628. Factor f(d).
-2*(3*d + 1)*(18*d - 1)**2/7
Let -2 - 22/9*t**2 - 2/9*t**3 - 38/9*t = 0. Calculate t.
-9, -1
Let g(o) be the second derivative of -o**9/7560 + o**7/2100 + 3*o**3/2 + 7*o. Let f(l) be the second derivative of g(l). Suppose f(d) = 0. Calculate d.
-1, 0, 1
Solve -49 - 64*r + 14 - 4*r**2 + 39*r**2 - 5*r**3 + 69*r = 0.
-1, 1, 7
Let l(s) = 104*s**3 - 52*s**2 + 76*s + 40. Let m(v) = -21*v**3 + 9*v**2 - 15*v - 8. Let b(c) = -5*l(c) - 24*m(c). Let b(x) = 0. Calculate x.
-1/4, 1, 2
Let a = 19576/7 + -2796. Determine k so that a*k + 0 - 2/7*k**2 = 0.
0, 2
Let o(g) be the second derivative of g**4/120 + g**3/10 - 4*g**2/5 + 62*g + 1. Factor o(t).
(t - 2)*(t + 8)/10
Let y(m) = -m**3 - 4*m**2 - 3*m + 3. Let q be y(-3). Let w be 3/(-12) + 21/(-12) + 6. Factor 7*s**3 + 1 - w*s + 2*s**4 - 3*s**q - 3.
2*(s - 1)*(s + 1)**3
Solve -237276 - 235/2*n**3 - 9243*n**2 - 1/2*n**4 - 246402*n = 0 for n.
-78, -1
Let c(d) = 3*d**3 - d**2 + 10*d. Let p(i) = -8*i**3 + 3*i**2 - 28*i. Let y(u) = -11*c(u) - 4*p(u). Let y(t) = 0. Calculate t.
-2, 0, 1
Let u = -55084 + 55087. Solve 9 + 1/4*a**2 - u*a = 0 for a.
6
Let n(z) be the third derivative of z**7/315 - 7*z**6/20 + 147*z**5/10 - 1029*z**4/4 + 2*z**2 + z. Let n(c) = 0. What is c?
0, 21
Factor -32*d**4 - 12*d**3 + 4*d**5 - 11*d**5 - 16*d**5 + 3*d**5.
-4*d**3*(d + 1)*(5*d + 3)
Let l(k) be the first derivativ