 = -43 - -40. Let u(d) = 28*d - 4. Let g(j) = -j**2 + 27*j - 3. Let p(w) = k*u(w) + 4*g(w). Factor p(y).
-4*y*(y - 6)
Let o be 5 - (-9 + 8 + (21/3 - 1)). Factor 0*n - 4/5*n**2 + 2/5*n**3 + o.
2*n**2*(n - 2)/5
Suppose 0 + 8/7*c**3 + 2/7*c**4 - 10/7*c**2 + 0*c = 0. What is c?
-5, 0, 1
Let n(w) be the third derivative of 31*w**2 - 1/100*w**5 - 1/20*w**4 + 0 + 0*w + 3/10*w**3. Factor n(a).
-3*(a - 1)*(a + 3)/5
Let g = -21191 + 148369/7. What is f in g*f**2 - 48/7*f + 18/7 = 0?
3/4
Suppose -4*d + 16 = 0, 2*p - 3*d - d = -10. Solve -p*t**2 - 2*t**2 + 3*t**3 + 2*t**2 = 0.
0, 1
Let h = -555 - -555. Let i(k) be the first derivative of 1/15*k**5 + h*k + 1/12*k**4 + 0*k**2 - 2/9*k**3 + 3. Factor i(r).
r**2*(r - 1)*(r + 2)/3
Let -5/4*k**3 - 675/4*k - 1215/4 - 105/4*k**2 = 0. Calculate k.
-9, -3
Factor -5*a**3 - 19*a**3 + 73*a - 127*a - 75*a**2.
-3*a*(a + 2)*(8*a + 9)
Let i = -1791 + 19703/11. Factor -4/11*j**3 + 4/11*j + 0*j**2 - i + 2/11*j**4.
2*(j - 1)**3*(j + 1)/11
Let l(y) = -y**2 + 5*y - 3. Let d be ((-33)/44)/((-1)/4). Let v = 6 - 1. Let t(k) = k**2 - 9*k + 5. Let a(n) = d*t(n) + v*l(n). Let a(f) = 0. Calculate f.
-1, 0
Let v(d) = -d**3 + 4*d**2 - 4*d + 2. Let w be v(2). Suppose -s + 9 = w*s. Factor 3*x**3 + 5*x**s - 6*x**4 - 22*x**4 + 20*x**5.
4*x**3*(x - 1)*(5*x - 2)
Let b(o) be the first derivative of 10*o**3/3 + o**2 - 8*o - 120. Let b(n) = 0. Calculate n.
-1, 4/5
Let q(y) be the first derivative of y**4/2 + 34*y**3/3 + 52*y**2 - 684. Find h such that q(h) = 0.
-13, -4, 0
Suppose i**4 - 3*i**4 + 50*i**2 - 2*i**3 - 92*i**2 + 46*i**2 = 0. Calculate i.
-2, 0, 1
Let a(q) be the third derivative of 1/1680*q**8 + 1/350*q**7 + 2*q**2 - 1/150*q**5 + 1/300*q**6 + 0 - 1/30*q**3 - 1/40*q**4 + 0*q. Factor a(b).
(b - 1)*(b + 1)**4/5
Let i be (-1)/3*1776/(-370)*4/2. Find j, given that 2/5*j**4 - 12/5*j**2 - 8/5*j + i + 2/5*j**3 = 0.
-2, 1, 2
Let k = 1/378 - -1/14. Let r = 73/108 + k. Factor 0 - a**2 + 1/4*a**3 + r*a.
a*(a - 3)*(a - 1)/4
Let t(p) be the third derivative of p**5/240 + p**4/24 + p**3/6 + 28*p**2 + 2. What is k in t(k) = 0?
-2
Let t(x) = -14*x**2 - 38*x + 4. Let q(m) = 11*m**2 + 37*m - 3. Let z(v) = -4*q(v) - 3*t(v). Determine p so that z(p) = 0.
-17, 0
Factor -4/3 + 5/3*h - 1/3*h**2.
-(h - 4)*(h - 1)/3
Factor -4/5*j**5 - 12/5*j**3 + 16/5*j**4 + 0*j**2 + 0*j + 0.
-4*j**3*(j - 3)*(j - 1)/5
Let m(c) be the third derivative of -c**8/2016 - c**7/630 + c**6/144 + c**5/36 - c**4/36 - 2*c**3/9 - 5*c**2 + 7*c. Let m(b) = 0. What is b?
-2, -1, 1, 2
Suppose 0 = -5*w + 15*w - 50. Let v(g) be the second derivative of -2/15*g**6 + 0 + 1/3*g**4 - 2/5*g**w + 4/3*g**3 - 6*g + 0*g**2. Factor v(q).
-4*q*(q - 1)*(q + 1)*(q + 2)
Let l(b) be the third derivative of -b**8/84 - 22*b**7/105 - 11*b**6/10 - 37*b**5/15 - 7*b**4/3 + b**2 - 18*b. Determine f so that l(f) = 0.
-7, -2, -1, 0
Find p, given that 2/3*p**3 + 4*p**2 - 2/3*p - 4 = 0.
-6, -1, 1
Factor 2809/4 - 53/2*t + 1/4*t**2.
(t - 53)**2/4
Let i be ((-40)/(-25) - 2/(-5))*23. Suppose -47*b = -i*b - 2. Determine x, given that -b*x**2 + 0 + 4/5*x = 0.
0, 2/5
Suppose 12*l - 99 = -3. Let -h**2 + 4*h**2 + h**2 - l*h - 12 = 0. What is h?
-1, 3
Let x(m) be the second derivative of -m**6/180 - 2*m**5/5 - 12*m**4 + 3*m**3 - 8*m. Let w(b) be the second derivative of x(b). Find r such that w(r) = 0.
-12
Suppose -25*n - 6414 = -6464. Suppose 16/3*z + 7/3*z**n + 4 + 1/3*z**3 = 0. What is z?
-3, -2
Let l(h) = -16*h**2 - 18*h + 3. Let g be l(0). Factor 1/5*y**5 - 2/5*y**4 + 0*y + 0*y**2 + 0*y**g + 0.
y**4*(y - 2)/5
Let m(b) be the first derivative of b**3/3 + b**2 + b - 2. Let a be m(-3). Factor j**2 + 0*j**a - 2*j**4 + j**4.
-j**2*(j - 1)*(j + 1)
Let z(t) be the first derivative of -4/3*t**3 - 100*t - 20*t**2 + 11. Solve z(p) = 0.
-5
Suppose 60 = -4*n + 2*k, -k - 60 = 4*n - 6*k. Let r be ((-18)/(-140) + 3/n)*-8. Suppose -r - 10/7*l**2 - 2*l = 0. What is l?
-1, -2/5
Let k(j) = j**2 - 9*j - 9. Let a be k(10). Let h(u) = -u**2 - u. Let m(z) = -z**2 + 9*z - 8. Let p(o) = a*h(o) + m(o). Solve p(t) = 0 for t.
2
Let m(j) = 4*j - 15. Suppose 22 - 7 = 3*z. Let d be m(z). Find a such that -2*a**d - 15*a**4 + 10*a**5 - 20*a**3 - 21*a**4 + 20*a**5 - 8*a + 36*a**2 = 0.
-1, 0, 2/7, 1
Let o(k) = -5*k**2 - 35*k + 18. Let j(p) = 6*p**2 + 36*p - 19. Let b(v) = -4*j(v) - 5*o(v). Let f(t) = 30*t - 15. Let i(r) = 5*b(r) - 6*f(r). Factor i(q).
5*(q - 4)*(q - 1)
Let n(q) be the second derivative of -q**6/60 + 7*q**5/40 - 5*q**4/24 - 7*q**3/12 + 3*q**2/2 + 2*q - 4. Suppose n(x) = 0. Calculate x.
-1, 1, 6
Let c = 9519/11228 - -15/1604. Determine q, given that c*q**2 + 24/7*q + 18/7 = 0.
-3, -1
Let n be 4*(-1 - 28/(-16)). Suppose n*k - 6 = -0*k. Solve 6*x**2 - 5 - 10*x - 2*x**k - 9*x**2 = 0.
-1
Let d(u) be the third derivative of 1/390*u**6 + 1/78*u**4 + 7/390*u**5 + 0*u**3 + 11*u**2 + 0 - 1/455*u**7 + 0*u. What is z in d(z) = 0?
-1, -1/3, 0, 2
Let w = -7 + 12. Suppose -3*f - 9 = 0, 41 = p - 2*f + w. Determine o so that p*o + 9 + 9*o**3 + 11*o**3 - 2*o**3 + 3*o**4 + 36*o**2 = 0.
-3, -1
Factor 3/2*o**3 - 12*o + 18 - 3/2*o**2.
3*(o - 2)**2*(o + 3)/2
Let v(l) be the second derivative of 0 - 16/5*l**2 - 3*l + 7/25*l**5 + 24/5*l**3 - 2*l**4. Let v(b) = 0. What is b?
2/7, 2
Let u(h) be the first derivative of h**6/14 - 6*h**5/7 + 3*h**4 + 8*h**3/7 - 192*h**2/7 + 384*h/7 - 111. Determine x so that u(x) = 0.
-2, 2, 4
Let g(c) = -14*c**3 + 8*c**2 - 11*c. Let h be 13*(3 + 1 + -3). Suppose -2 = -b - h. Let t(j) = -5*j**3 + 3*j**2 - 4*j. Let l(p) = b*t(p) + 4*g(p). Factor l(k).
-k**2*(k + 1)
Let y(d) be the third derivative of -d**8/3192 - 11*d**7/1995 - d**6/60 - 3*d**5/190 - 96*d**2. Factor y(u).
-2*u**2*(u + 1)**2*(u + 9)/19
Let o(c) be the third derivative of -c**7/15120 - c**6/432 - 5*c**5/144 - c**4/2 + 23*c**2. Let w(b) be the second derivative of o(b). Factor w(x).
-(x + 5)**2/6
Let v be 3/(-36)*9/(108/(-16)). Let j(g) be the second derivative of 0 - 1/12*g**4 + v*g**3 + 0*g**2 + 5*g + 1/60*g**5. Factor j(q).
q*(q - 2)*(q - 1)/3
Factor 0 - 19/4*v**3 + 1/2*v - 17/4*v**2.
-v*(v + 1)*(19*v - 2)/4
Let i(t) = -t**2 + 6*t - 3. Let a(q) = -q - 1. Let k(z) = -5*a(z) + i(z). Let c be k(11). Factor 13*o + 12 + 3*o**c - 4*o + 3*o.
3*(o + 2)**2
Let z(j) = -13 + 5*j - 15 + 27 - 4*j + j**2. Let s(h) = 25*h**2 + 35*h - 20. Let y(p) = -s(p) + 30*z(p). Factor y(v).
5*(v - 2)*(v + 1)
Let q be (7 - 9) + 1*9. Factor -9*j - 13 + 3*j**4 + j**2 + 3*j**2 - j**2 + 9*j**3 + q.
3*(j - 1)*(j + 1)**2*(j + 2)
Let r be (-9)/(-6) - 6/4. Factor 4*n**4 - 6*n**2 - 4*n + 4*n**3 + 2*n**2 + r*n**3.
4*n*(n - 1)*(n + 1)**2
Let f = -156/25 + 2116/275. Solve 2/11*x**5 + 10/11*x**4 + f*x**3 + 0 + 0*x + 8/11*x**2 = 0.
-2, -1, 0
Suppose 5*h = 5*u - 4*u + 23, -u + 12 = 2*h. Find v, given that 6/11*v**h + 6/11*v**3 + 24/11*v**2 + 0 - 8/11*v - 20/11*v**4 = 0.
-1, 0, 1/3, 2
Let t = 1597/210 - 11/105. Find y, given that 12*y - t*y**2 + 3/2*y**3 - 6 = 0.
1, 2
Let r(d) = 8*d**4 - 212*d**3 + 202*d**2 + 218*d - 213. Let w(z) = 7*z**4 - 213*z**3 + 203*z**2 + 217*z - 212. Let t(m) = 2*r(m) - 3*w(m). Factor t(h).
-5*(h - 42)*(h - 1)**2*(h + 1)
Suppose 3*s - 2*s = 9. Let a = -4 + s. Factor -n**3 - 4*n**a - 23*n**3 - 4*n - 16*n**2 - 161*n**4 + 145*n**4.
-4*n*(n + 1)**4
Let o(k) be the second derivative of k**4/20 + 8*k**3/5 + 49*k. Factor o(r).
3*r*(r + 16)/5
Let s(h) be the first derivative of -2*h**3/27 - 74*h**2/9 - 2738*h/9 + 56. Determine j, given that s(j) = 0.
-37
Let g be (-6)/(-2) + 14 + 1. Suppose i + 2*i = 5*y - 25, 4*y - g = 2*i. Find r, given that 0 - 1/3*r**3 + 1/6*r + 1/6*r**y = 0.
-1/2, 0, 1
Let b be (-12)/(-25 - -13) - (-3 - 0). Find u such that 0 - 3/4*u**5 - u**b + 1/2*u**3 + 1/4*u + u**2 = 0.
-1, -1/3, 0, 1
Suppose -3 = 2*a + 3, 0 = f - 2*a - 11. What is k in 3*k**3 - 5*k**3 + 15*k**4 - 121*k**5 - 15*k**2 + 126*k**f - 3*k**3 = 0?
-3, -1, 0, 1
Let d(g) be the first derivative of g**4/48 + g**3/12 - 3*g**2/8 - 13*g + 12. Let l(u) be the first derivative of d(u). Factor l(m).
(m - 1)*(m + 3)/4
Let x(o) be the third derivative of -o**5/300 - 29*o**4/60 - 841*o**3/30 + o**2 - 1. Let x(l) = 0. Calculate l.
-29
Let b be 3 + (-15 - 0) - (-183)/15. Solve 1/5*y**4 + 1/5*y - b*y**3 - 1/5*y**2 + 0 = 0 for y.
-1, 0, 1
Let l(b) = b**4 + 2*b**3 - b**2. Let f(p) = -3*p**4 - 18*p**3 - 33*p**2 - 22*p. Let z(d