5
Suppose 5*k = 4*h - 202, -3*h - 7 = -k - 43. Let p be (2/3*-3)/(k/63). Factor 0*w + 4/15*w**p + 0 - 2/15*w**2 - 2/15*w**4.
-2*w**2*(w - 1)**2/15
Let p be 32/18 + (6 - 110/15). Let v(t) be the first derivative of p*t + 2/27*t**3 - 1/3*t**2 + 4. What is c in v(c) = 0?
1, 2
Let l(b) be the first derivative of b**3 - 3*b**2 + 4*b - 1/8*b**4 - 5. Factor l(x).
-(x - 2)**3/2
Let k = -130858/15 + 8724. Factor -k + 4/15*r - 2/15*r**2.
-2*(r - 1)**2/15
Suppose 0 = 2*s + 555 - 559. Let d(c) be the second derivative of 0*c**3 + 7*c + 0*c**s - 1/4*c**4 + 1/20*c**5 + 0. Factor d(y).
y**2*(y - 3)
Let u(a) be the third derivative of a**6/840 + 11*a**5/420 - a**4/12 - 4*a**3/7 + 2*a**2 + 113. Let u(i) = 0. Calculate i.
-12, -1, 2
Let m(n) be the second derivative of -2*n**2 - 4/3*n**3 + 0 - 15*n - 1/3*n**4. Factor m(p).
-4*(p + 1)**2
Let w(m) be the third derivative of -m**8/1176 - 11*m**7/735 - 2*m**6/35 + 6*m**5/35 - 503*m**2. Suppose w(v) = 0. Calculate v.
-6, 0, 1
Let n(p) = 2*p**2 + 2*p + 1. Let a(k) = -8*k**2 - 28*k - 474. Let w(g) = a(g) + 6*n(g). Solve w(d) = 0.
-9, 13
Let r(i) be the third derivative of -i**5/60 + 5*i**4/24 + 4*i**3/3 - 3*i**2. Let m be r(6). Factor -3*b**2 + b + 4 + 2 + m*b.
-3*(b - 2)*(b + 1)
Let h(t) = -t**3 + t**2. Let q(w) be the first derivative of 0*w - 1/3*w**3 + 4/5*w**5 + 4 - 1/4*w**4 - w**2. Let a(z) = -3*h(z) + q(z). Factor a(u).
2*u*(u - 1)*(u + 1)*(2*u + 1)
Factor -93/2*r**2 - 15*r - 99/2*r**3 - 3/2*r**5 + 0 - 39/2*r**4.
-3*r*(r + 1)**3*(r + 10)/2
Let g(a) be the third derivative of 0*a + 2/35*a**5 + 0 + 1/392*a**8 + 0*a**3 + 2/35*a**6 + 1/49*a**7 + 0*a**4 + 6*a**2. Factor g(s).
6*s**2*(s + 1)*(s + 2)**2/7
Let a(k) be the first derivative of 5/4*k**4 - k**5 - 5/6*k**6 + 5/3*k**3 + 20 + 0*k**2 + 0*k. Determine c, given that a(c) = 0.
-1, 0, 1
Let f(v) be the second derivative of v**7/189 - 2*v**6/135 - v**5/45 + 2*v**4/27 + v**3/27 - 2*v**2/9 - 67*v. Let f(l) = 0. Calculate l.
-1, 1, 2
Let k(v) = v**2 + v + 1. Let z(n) = 3*n**2 - 10*n + 19. Let y(g) = -4*k(g) + z(g). Let l be y(-15). Factor 1/4*f**5 + 1/4*f + 3/2*f**3 + f**2 + l + f**4.
f*(f + 1)**4/4
Let v be (-6 - 6/(-3)) + 7. Let t = -512 - -2051/4. Factor -v + 0*b + t*b**2.
3*(b - 2)*(b + 2)/4
Solve 70*x**3 + 120*x**2 - x**4 + 17*x**4 + 50*x - 12 - 4*x**4 = 0 for x.
-3, -2, -1, 1/6
Let n be ((-12)/(-70))/(7 + -96*(-8)/(-112)). Factor 18/5*i**4 + 0 - 2*i**2 + 2/5*i + n*i**3.
2*i*(i + 1)*(3*i - 1)**2/5
Let q = 114 - 70. Factor 4*r**4 + 5*r + q*r**2 + 24*r + 28*r**3 - 9*r.
4*r*(r + 1)**2*(r + 5)
Suppose -4*c - 23 = c - h, -3*c - 3*h = 3. Let x = 9/2 + c. Let 0 + 0*k - x*k**2 = 0. Calculate k.
0
Let c = -2119/2 + 1060. Determine d, given that -9/2*d**4 - 6*d**3 + 0 - c*d**2 + d = 0.
-1, -2/3, 0, 1/3
Let r(s) be the first derivative of -2*s**3 + 6*s + 2. Let h(a) = 5*a**2 - a - 6. Let k(p) = -3*h(p) - 2*r(p). Determine v, given that k(v) = 0.
-1, 2
Determine m so that -3*m**4 + 109*m**2 - 18*m - 65*m**2 - 83*m**2 - 24*m**3 = 0.
-6, -1, 0
Let j(r) = -r**2 + 15*r - 56. Let g be j(7). Let b(d) be the second derivative of -1/3*d**3 + 1/10*d**5 + 8*d + 0*d**4 + 0*d**2 + g. Factor b(x).
2*x*(x - 1)*(x + 1)
Let m = 9/2 - 59/14. Suppose -5*b = -5*x - 10*b + 25, -4*x - 5 = -b. Factor 6/7*h**2 - m*h + x - 4/7*h**3.
-2*h*(h - 1)*(2*h - 1)/7
Let l(c) be the first derivative of c**4/60 + c**3/15 - 16*c + 18. Let u(v) be the first derivative of l(v). Find r such that u(r) = 0.
-2, 0
Let u(x) = 2*x**3 + 16*x**2 + 23*x + 3. Let v be u(-6). Suppose -v*q = 22*q. What is h in -8/15*h**3 + 8/15*h**2 + q + 0*h - 2/5*h**4 = 0?
-2, 0, 2/3
Let p(a) be the second derivative of -a**7/189 + a**5/45 - a**3/27 - 187*a. Solve p(h) = 0 for h.
-1, 0, 1
Let m be (12/144)/(-3 - -6). Let g(q) be the first derivative of 7 - 2/9*q + m*q**4 - 1/18*q**2 + 2/27*q**3. Factor g(c).
(c - 1)*(c + 1)*(c + 2)/9
Let a(z) = 3*z**2 - 556*z + 15680. Let q(m) = 5*m**2 - 1110*m + 31360. Let p(l) = 5*a(l) - 2*q(l). What is k in p(k) = 0?
56
Determine l, given that 3*l**3 + 3*l**2 - 15*l + 10 + 5 + 9 - 15 = 0.
-3, 1
Let x(h) = h**3 + 21*h**2 + 4*h + 86. Let s be x(-21). Let n = -515 + 2583/5. Let -n - 2/5*q**s + 8/5*q = 0. What is q?
2
Let j(i) be the third derivative of 0*i + 0 - 1/1365*i**7 - 1/195*i**6 - 3/13*i**3 + 1/13*i**4 - 6*i**2 + 1/195*i**5. Find k such that j(k) = 0.
-3, 1
Let z(w) be the second derivative of 3*w**5/140 - 6*w**3/7 + 24*w**2/7 - 103*w. Factor z(d).
3*(d - 2)**2*(d + 4)/7
What is k in -170/3*k**3 + 80/3*k - 8/3 - 82/3*k**2 = 0?
-1, 2/17, 2/5
Factor 0 - 2/7*z**2 + 2/7*z**4 - 2/7*z + 2/7*z**3.
2*z*(z - 1)*(z + 1)**2/7
Let z(g) = -15*g**2 + 150*g + 345. Let p(o) = -23*o**2 + 225*o + 518. Let k(v) = 5*p(v) - 8*z(v). Factor k(w).
5*(w - 17)*(w + 2)
Find o such that -14/19*o**4 - 44/19 - 374/19*o**2 + 186/19*o**3 + 246/19*o = 0.
2/7, 1, 11
Let l = -5692 + 17077/3. Factor 0 + l*k**3 + 4/3*k - 4/3*k**2.
k*(k - 2)**2/3
Let a(g) = 5*g**4 - 9*g**3 - 31*g**2 + 7*g - 7. Let k(x) = -2*x**4 + 5*x**3 + 15*x**2 - 3*x + 3. Let y(j) = 6*a(j) + 14*k(j). Factor y(w).
2*w**2*(w + 2)*(w + 6)
Let t(w) = w**3 - 4*w**2 - 7*w. Let b be t(6). Factor -16*y**3 - 9*y**3 + b*y**3.
5*y**3
Let c be 46/16 - (-1)/8. Let h be (c + 0 + 3)/2. Factor j**4 - 15*j**h + 6*j**3 + 8*j**3 - j**2 + j**5.
j**2*(j - 1)*(j + 1)**2
Let g be 71/23 - (550/(-253))/(-25). Factor 0 - 1/2*d**g - 5*d**2 - 25/2*d.
-d*(d + 5)**2/2
Let j(o) be the first derivative of o**4 - 8*o**3/3 + 46. Factor j(l).
4*l**2*(l - 2)
Suppose d - 3*w + 41 = 0, -3*d = -4*w + 6*w + 90. Let o = d + 228/7. Find r such that 0*r**3 + 0*r + 5/7*r**2 - o - 1/7*r**4 = 0.
-2, -1, 1, 2
Let s = -10465 - -10465. Let -32/3*u**5 + 14/3*u**3 + 0 + s*u - 16/3*u**4 - 2/3*u**2 = 0. What is u?
-1, 0, 1/4
Suppose -5*d - 1 = 3*x + 9, -10 = -5*x + 5*d. Suppose x = 2*h + 7*h. Factor 0*u - 1/3*u**4 + h + 0*u**2 + 1/3*u**3.
-u**3*(u - 1)/3
Let v(w) be the third derivative of w**5/12 - 5*w**4/8 + 5*w**3/3 - w**2 - 2. Factor v(s).
5*(s - 2)*(s - 1)
Let c(r) be the first derivative of r**4/7 - 4*r**3/3 - 16*r**2/7 + 136. Suppose c(h) = 0. Calculate h.
-1, 0, 8
Let c(i) be the first derivative of -2/3*i**3 - 13 + 1/2*i**4 - i**2 + 2*i. Factor c(j).
2*(j - 1)**2*(j + 1)
Suppose n - 390 = k + 4*k, 0 = -4*n. Let d = k - -81. Factor -588*q**2 - 8 - 2401/2*q**4 + 112*q + 1372*q**d.
-(7*q - 2)**4/2
Suppose 2*v = 6, -8*b + 5*v - 50 = -13*b. Determine k so that -k**2 + 2*k**4 + b*k**2 - 9*k**2 - 3*k**2 + 9*k**3 - 5*k = 0.
-5, -1/2, 0, 1
Determine v so that -82*v**2 + 273*v**2 + 28*v**2 - 11*v**2 - 64*v**3 + 26*v - 28*v**4 + 38*v = 0.
-4, -2/7, 0, 2
Let y(g) be the third derivative of 0*g**3 + 18*g**2 + 0*g + 0*g**4 - 1/600*g**5 + 0 - 1/1200*g**6. What is v in y(v) = 0?
-1, 0
Let t(w) be the third derivative of w**8/6720 - w**7/560 - w**6/60 + 2*w**5/5 - 20*w**2. Let l(r) be the third derivative of t(r). What is m in l(m) = 0?
-1, 4
Suppose -2*w - 20 = -50. Factor -92*m**2 - 43*m**2 - 60*m**4 - 135*m**3 - 5*m**5 + w*m**4.
-5*m**2*(m + 3)**3
Let n(z) = -z**5 + 8*z**4 - 3*z**3 - 12. Let s(j) = -2*j**5 + 17*j**4 - 7*j**3 - 26. Let h(f) = -13*n(f) + 6*s(f). Factor h(t).
t**3*(t - 3)*(t + 1)
Factor 58/3*h**2 - 150 - 2/3*h**3 - 130*h.
-2*(h - 15)**2*(h + 1)/3
Let r(l) be the third derivative of -l**4/24 - 5*l**3/6 - 12*l**2. Let i be r(-9). Suppose 0 - 3*u**i - 6*u**2 + 3/2*u + 15/2*u**3 = 0. Calculate u.
0, 1/2, 1
Let r(b) be the second derivative of -1/2*b**2 - 23*b - 1/12*b**3 - 1/60*b**6 + 1/40*b**5 + 0 + 1/8*b**4. Factor r(j).
-(j - 2)*(j - 1)*(j + 1)**2/2
Factor -4*u**4 - u + 4*u**2 - 46*u**3 + 50*u**3 - 3*u.
-4*u*(u - 1)**2*(u + 1)
Let a = 94 - 83. Suppose 2*k = a*k - 162. Let 32/5*p + 0 + k*p**5 + 0*p**2 - 176/5*p**3 + 96/5*p**4 = 0. What is p?
-2, -2/5, 0, 2/3
Let i = 143207/5 + -28641. Let 6/5*b - i*b**2 - 4/5 = 0. What is b?
1, 2
Let n(t) be the first derivative of -10 + 1/28*t**4 + 9/7*t + 3/14*t**2 - 5/21*t**3. Factor n(m).
(m - 3)**2*(m + 1)/7
Let v = 47683/7 + -6811. Factor -v*h**2 - 2/7*h**3 + 0 - 4/7*h.
-2*h*(h + 1)*(h + 2)/7
Let z(h) = -4*h**2 + 4*h - 1. Let s(c) = -9*c**2 + 8*c - 1. Let b = 23 + -16. Let i be (7/b)/((-1)/(-7)). Let q(w) = i*z(w) - 3*s(w). Factor q(d).
-(d - 2)**2
Let q(n) = n**3 + 112*n**2 + 1912*n + 95. Let p be q(-91). Determine l so that 85/2*l**2 - 85/4*l**3 + 15/4*l**p - 35*l