4 - 3*q**3/2 - 3*q**2 + 2*q - 8. Factor c(x).
-3*(x + 1)*(x + 2)
Let q = -159 - -319/2. Factor q*s**3 + 1/2*s**2 + 0*s + 0 - 1/2*s**5 - 1/2*s**4.
-s**2*(s - 1)*(s + 1)**2/2
Let f(y) = y**3 - y**2 - 3*y + 2. Let u be f(2). Suppose -2*a = -u*a - 4. Factor -6*k**2 + 2*k - 1 + 7*k**a + 2.
(k + 1)**2
Let q = 1621/4 - 405. Factor 0 - 1/4*k**2 - q*k.
-k*(k + 1)/4
Let m = 42 - 37. Suppose -3*a = -4*t - 1 - 2, 25 = m*a. What is z in 0 + 4/9*z**2 + 2/9*z**t + 2/9*z = 0?
-1, 0
Suppose -23*q = -22*q. Let x = -2 + 4. Find m, given that 0*m**x + 2/3*m**3 + 0*m + q + 2/3*m**5 - 4/3*m**4 = 0.
0, 1
Let v be 0 - (-7 + 1 - -1). Suppose -2*s + v = -1. Factor -s*n**2 + 2*n - 3 + 2 - n**2 + 3*n**2.
-(n - 1)**2
Solve 0*g**3 + 0*g**2 + 0*g**4 + 0*g + 1/2*g**5 + 0 = 0.
0
Let v(q) be the first derivative of q**3/3 - 4*q**2 + 12*q - 22. Determine z, given that v(z) = 0.
2, 6
Let r(x) = 2*x**2 - 8*x + 6. Let g be r(3). Solve 1/4*f**2 + g*f - 1/4 = 0.
-1, 1
Let a(s) be the first derivative of -s**4/7 + 6*s**2/7 - 8*s/7 + 2. Factor a(j).
-4*(j - 1)**2*(j + 2)/7
Let k(f) = f - 9. Let d be k(7). Let g be d/(-20)*(-2 - -4). What is b in g*b**2 + 0*b + 0 - 1/5*b**3 = 0?
0, 1
Let c be -3 - (-7 + 4) - (-2)/5. Factor 2/5 - 2/5*g**2 - c*g**3 + 2/5*g.
-2*(g - 1)*(g + 1)**2/5
Let q = -48 + 51. Let q - 3/2*o**2 + 3/2*o = 0. What is o?
-1, 2
Suppose -2*i + 12 = 2*i. Let m(z) = z**2 + 9*z + 8. Let a be m(-8). Factor 2/7*r**4 + a*r + 0 - 2/7*r**i + 0*r**2.
2*r**3*(r - 1)/7
Let j(v) be the second derivative of v**7/840 - v**6/120 + v**5/40 + 5*v**4/12 - 6*v. Let r(u) be the third derivative of j(u). Solve r(i) = 0.
1
Suppose -2 = -3*q + 5*k, -2*q - 10 = -4*q - k. Suppose -2*j**4 + q*j + j - 2*j**3 + 2*j**2 - 3*j = 0. What is j?
-1, 0, 1
Let q(a) be the first derivative of 2*a**5/15 + a**4/6 - 2*a**3/3 - 5*a**2/3 - 4*a/3 + 22. Factor q(v).
2*(v - 2)*(v + 1)**3/3
Let d(v) = -3*v**4 - 19*v**3 - 18*v**2 - 19*v - 3. Let j(x) = 2*x**4 + 13*x**3 + 12*x**2 + 13*x + 2. Let u(g) = -5*d(g) - 7*j(g). Factor u(p).
(p + 1)**4
Let z(r) be the third derivative of -3*r**7/280 + r**6/40 - r**5/40 - r**4/4 + 3*r**2. Let u(x) be the second derivative of z(x). Factor u(f).
-3*(3*f - 1)**2
Suppose 0 = h - 2. Let k be (1 + -3 - -2) + h. Factor 0*t**5 + t**k + t**2 + 2*t**5 + 6*t**4 + 6*t**3.
2*t**2*(t + 1)**3
Suppose 4 = 2*g - 0. Factor -g*t**3 - t**2 + 3*t**4 - 4*t**4 + 2*t**4 + 2*t.
t*(t - 2)*(t - 1)*(t + 1)
Determine b, given that 0 - 2/9*b - 4/9*b**3 + 8/9*b**4 + 2/3*b**5 - 8/9*b**2 = 0.
-1, -1/3, 0, 1
Let n be 1 + (-3)/((-309)/(-101)). Let z = 212/309 - n. Factor -2*h + 2*h**2 - z*h**3 + 2/3.
-2*(h - 1)**3/3
Let q(r) = -3*r**2 - 4*r - 2. Let z(d) = -d**2 + 1. Let t(j) = q(j) - 2*z(j). Solve t(s) = 0.
-2
Let -6/11 - 18/11*t - 6/11*t**2 + 18/11*t**3 + 12/11*t**4 = 0. What is t?
-1, -1/2, 1
Find l, given that 2/3*l**5 + 0 - 8/9*l + 2/9*l**3 + 26/9*l**2 - 26/9*l**4 = 0.
-1, 0, 1/3, 1, 4
Solve 2/9*g + 4/9*g**2 - 2/9*g**4 - 2/9 - 4/9*g**3 + 2/9*g**5 = 0 for g.
-1, 1
Factor 3*q**2 - 4*q**3 - 23*q + 6*q**2 + 3*q**2 - 8 + 27*q - 4*q**4.
-4*(q - 1)**2*(q + 1)*(q + 2)
Factor 0*q**2 + 0 + 0*q + 2/17*q**4 + 2/17*q**3.
2*q**3*(q + 1)/17
Let a(t) be the first derivative of -4*t**5/5 + t**3 - t**2/2 - 3*t + 1. Let l(k) = -15*k**4 + 12*k**2 - 3*k - 11. Let g(v) = -22*a(v) + 6*l(v). Solve g(s) = 0.
-1, 0, 2
Let s = -103371467240/1253 - -82499182. Let x = s - -10/179. Find y such that 2*y + 36/7*y**2 + 26/7*y**4 + x*y**3 + 6/7*y**5 + 2/7 = 0.
-1, -1/3
Let d = 71 - 67. Let t(s) be the second derivative of -2*s + 1/3*s**3 + 3/10*s**5 + 0 + 0*s**2 + 1/15*s**6 + 1/2*s**d. Factor t(w).
2*w*(w + 1)**3
Let y(i) be the third derivative of 0*i**4 + 0*i - 4/105*i**7 + i**2 - 1/15*i**5 + 0*i**3 + 1/12*i**6 + 0 + 1/168*i**8. Factor y(w).
2*w**2*(w - 2)*(w - 1)**2
Suppose 0 = -q - 4*h + 15, -21 = -3*q + q - 5*h. Suppose -2*p - 2*p**2 - 3*p**2 + 3*p**q + 4*p = 0. What is p?
0, 2/3, 1
Let y(h) be the third derivative of h**7/420 + h**6/240 - h**5/40 - 5*h**4/48 - h**3/6 + 5*h**2. Factor y(w).
(w - 2)*(w + 1)**3/2
Let p(g) = 7*g**5 + 7*g**4 - 6*g**2 + 6. Let q(j) = j**5 + j**4 - j**2 + 1. Let t(f) = p(f) - 6*q(f). Suppose t(x) = 0. What is x?
-1, 0
Let z be (1 + 4 + -4)*2. Let v(b) be the second derivative of -4*b - 3/100*b**5 + 1/60*b**4 + 0*b**z + 0 + 0*b**3 - 2/75*b**6. Factor v(f).
-f**2*(f + 1)*(4*f - 1)/5
Let i(u) = -8*u**5 - 8*u**4 - 4*u**3 + 8*u**2 + 4*u - 4. Let x(p) = -p**5 - p**3 - 1. Let v(d) = i(d) - 4*x(d). Suppose v(n) = 0. Calculate n.
-1, 0, 1
Suppose -30/7*o + 4*o**3 + 2/7*o**5 + 18/7 - 2*o**4 - 4/7*o**2 = 0. Calculate o.
-1, 1, 3
Let m be -2*30/(-12) - 5. Let k(y) be the first derivative of 4 + m*y**2 + 0*y - 1/8*y**4 + 1/3*y**3. Let k(v) = 0. What is v?
0, 2
Suppose 2*i + 2*s - 8 = -2, -4*s + 3 = i. Factor -i*x**3 - 6*x**2 + 0*x - 6*x + 3*x.
-3*x*(x + 1)**2
Let b(j) = j + 4. Let t be b(0). Suppose -n + 3*n = t. Solve -24/5*o**4 + 4/5*o**n + 6/5*o**3 + 14/5*o**5 + 0*o + 0 = 0.
-2/7, 0, 1
Let v(d) be the third derivative of -4*d**7/35 - d**6/10 + 39*d**5/40 - 17*d**4/16 + d**3/2 - 15*d**2 + 3. Suppose v(h) = 0. Calculate h.
-2, 1/4, 1
Let g(k) be the second derivative of k**6/150 - k**5/20 + 3*k**4/20 - 7*k**3/30 + k**2/5 + 4*k. Determine t, given that g(t) = 0.
1, 2
Let v(f) = -4*f**4 + 19*f**3 + 19*f**2 - 7*f - 7. Let p(d) = -3*d**4 + 18*d**3 + 18*d**2 - 6*d - 6. Let y(j) = 7*p(j) - 6*v(j). What is a in y(a) = 0?
-2, 0
Let q = -1379/10 + 138. Let o(i) be the second derivative of i**2 - i + 1/3*i**3 - 1/6*i**4 - q*i**5 + 0. Solve o(g) = 0.
-1, 1
Let t(q) be the first derivative of q**4/26 + 1. Factor t(i).
2*i**3/13
Suppose -2*d + 3 = 7. Let l be d/(-7) + (-24)/(-14). Let -y**4 + y**5 + 4 + 2*y**l + y**3 - 5 - 3*y**3 + y = 0. Calculate y.
-1, 1
Let u(s) be the first derivative of s**4/4 + s**3/3 + 27. Factor u(f).
f**2*(f + 1)
Suppose 9 - 3 = u. Let v(a) be the first derivative of 1 - 3/10*a**5 + 1/3*a**3 - 3/4*a**2 + 1/2*a + 1/4*a**4 + 1/12*a**u. Find d such that v(d) = 0.
-1, 1
Factor -17/4*c + 4*c**2 + 1 - 3/4*c**3.
-(c - 4)*(c - 1)*(3*c - 1)/4
Let d(m) = 4*m + 4. Let c be d(-1). Factor a + c + 9/4*a**3 + 5*a**2.
a*(a + 2)*(9*a + 2)/4
Let r(l) be the first derivative of -1/4*l**4 + 7 + l - 1/3*l**3 + 1/2*l**2. Solve r(o) = 0.
-1, 1
Let p(n) be the second derivative of 1/200*n**6 + 0 + 0*n**4 + 0*n**3 + 1/300*n**5 - n - 1/2*n**2. Let d(t) be the first derivative of p(t). Factor d(c).
c**2*(3*c + 1)/5
Let x(w) be the first derivative of 3 + 3/14*w**4 + 0*w - 2/7*w**3 + 1/7*w**2 - 2/35*w**5. Let x(d) = 0. What is d?
0, 1
Suppose d = 3*k + k - 64, k + 4*d = -1. Let m = -15 + k. Factor 0*x**2 + m*x + 0 + 1/2*x**4 + 1/2*x**3.
x**3*(x + 1)/2
Factor 0*a**2 + 4*a + 7*a**3 - 6*a**2 + 6*a**4 - 11*a**3.
2*a*(a - 1)*(a + 1)*(3*a - 2)
Let u(o) be the second derivative of -o**7/56 + o**6/15 + o**5/10 - o**3/6 + 5*o. Let k(g) be the second derivative of u(g). Factor k(a).
-3*a*(a - 2)*(5*a + 2)
Let 81/8*l**2 - 15/8*l**4 + 9/8*l**3 + 75/8*l + 9/4 = 0. What is l?
-1, -2/5, 3
Factor 2/13*r**2 + 2/13*r**4 + 0*r + 0 - 4/13*r**3.
2*r**2*(r - 1)**2/13
Let p = 11 - 7. Let z(v) = -v**5 + v**4 - 1. Let r(b) = -6*b**4 + 4*b**2 + 2*b + 2. Let m(k) = p*z(k) + 2*r(k). Solve m(d) = 0.
-1, 0, 1
Factor -19*m**2 + 47*m**2 + 10*m - 5*m**3 - 23*m**2.
-5*m*(m - 2)*(m + 1)
Solve 1575*v + 35*v**3 + 297 - 480*v**2 + 410 - 217 = 0.
-2/7, 7
Let k(m) be the third derivative of -m**8/420 + m**6/30 - m**5/15 - 5*m**3/6 - 5*m**2. Let h(n) be the first derivative of k(n). Factor h(s).
-4*s*(s - 1)**2*(s + 2)
Let g = 62 + -62. Let m(n) be the second derivative of 0*n**2 - 3*n - 1/6*n**3 - 1/15*n**6 + 0 + 1/6*n**4 + 1/42*n**7 + g*n**5. Factor m(f).
f*(f - 1)**3*(f + 1)
Let i(r) = -r**3 - 3*r**2 - r - 8. Let k be i(-4). Let n be 12/3 + (-45)/k. Factor 0 + 3/4*f**4 + 0*f + 1/4*f**5 + n*f**2 + 3/4*f**3.
f**2*(f + 1)**3/4
Let q = 118 + -116. Determine g, given that -4/3*g - 1/3 + 24*g**3 - 36*g**5 + 9*g**4 + 14/3*g**q = 0.
-1/3, 1/4, 1
Let h(a) = 3*a**2 - 4*a - 1. Let u be h(4). Suppose 35*n = u*n. Factor n - 2/7*b**3 + 4/7*b**2 + 0*b - 2/7*b**4.
-2*b**2*(b - 1)*(b + 2)/7
Solve -14*j - 30*j + 243 - 10*j + 3*j**2 = 0.
9
Let x(h) be the second derivative of -h**6/60 + h**4/12 - h**2/4 - 4*h. Factor x(y).
-(y - 1)**2*(y + 1)**2/2
Solve 240*u + 2*u**2 - 75*u**4 - 160*u