*2 + 2*o**4 + 2*o**2 = 0.
-2, -1, 0, 1
Let m(z) be the second derivative of z**9/45360 - z**7/7560 - z**4/4 + 2*z. Let r(b) be the third derivative of m(b). Determine a, given that r(a) = 0.
-1, 0, 1
Let v(u) be the third derivative of 1/56*u**7 + 7/80*u**5 + 0*u - 9/160*u**6 - 1/448*u**8 + 0*u**3 + 0 + 3*u**2 - 1/16*u**4. Suppose v(g) = 0. Calculate g.
0, 1, 2
Suppose -436 = 15*q - 466. Suppose 0*z + 0 + 2/5*z**q = 0. What is z?
0
Let u = -3 + 5. Suppose -u*x + x = -9. Solve -8*a + x*a**2 + 3 + 3*a**3 - 7*a - 3*a**4 + 3 = 0 for a.
-2, 1
Let y be 2/(-4) + 3/(-6). Let p(k) = 2*k + 1 - 3*k + k**2 + 0*k**2 - 3. Let j(x) = 1. Let s(h) = y*p(h) - 2*j(h). Factor s(q).
-q*(q - 1)
Let 18/11*c + 2/11*c**2 + 0 = 0. Calculate c.
-9, 0
Let w = 20 + -10. Suppose 4*f + f - w = 0. Factor 1/3 + 0*q - 2/3*q**f + 1/3*q**4 + 0*q**3.
(q - 1)**2*(q + 1)**2/3
Let v(t) be the second derivative of -t**6/6 + 5*t**4/6 - 5*t**2/2 - 22*t. Factor v(w).
-5*(w - 1)**2*(w + 1)**2
Factor -1/2*h**3 + 0*h + h**4 + 0 + 1/2*h**5 - h**2.
h**2*(h - 1)*(h + 1)*(h + 2)/2
Suppose 24/5*x + 48/5 + 3/5*x**2 = 0. Calculate x.
-4
Let f(k) be the first derivative of k**3/9 + 20*k**2/3 + 400*k/3 - 68. Factor f(b).
(b + 20)**2/3
Let h(z) be the third derivative of -z**7/2310 + z**5/220 - z**4/132 + 6*z**2. Factor h(j).
-j*(j - 1)**2*(j + 2)/11
Let m(x) be the third derivative of x**6/150 - 3*x**5/100 + x**4/20 - x**3/30 - 15*x**2. What is q in m(q) = 0?
1/4, 1
Let i(a) be the first derivative of 7*a**5/5 + 5*a**4/4 - 2*a**3/3 - 7. Factor i(x).
x**2*(x + 1)*(7*x - 2)
Let r be (-4)/4*5/(-1). Determine q so that -4 + 0 + r + q**2 - 2*q = 0.
1
Let u(k) = 8*k**3 - k**2 + 8*k - 5. Let z(i) = 39*i**3 - 6*i**2 + 39*i - 24. Let a(t) = -24*u(t) + 5*z(t). Determine r so that a(r) = 0.
0, 1
Find x such that -4/7*x**2 + 0*x + 0 - 2/7*x**3 = 0.
-2, 0
Determine m, given that -2/11*m**2 + 2/11*m + 4/11 = 0.
-1, 2
Suppose -3*c - 3/8*c**2 - 6 = 0. What is c?
-4
Let n = 3/5 + -1/10. Solve -n*g**3 + g**2 - 1/2*g + 0 = 0.
0, 1
Suppose 5 = p, 0 = -5*l - p + 5*p. Let b**3 - 3*b**l + 2*b**4 + 0*b**3 = 0. What is b?
0, 1
Suppose 6*t = 5*t + 2. Suppose 4*a = 5*u + 36, 4*a = a - t*u + 4. Let -62/9*n**2 + 58/9*n**3 + 58/9*n**a + 4/9 - 56/9*n**5 - 2/9*n = 0. Calculate n.
-1, -1/4, 2/7, 1
Let t(u) = -8*u**2 - 37*u - 152. Let g(d) = -33*d**2 - 147*d - 609. Let w(n) = 5*g(n) - 21*t(n). Factor w(c).
3*(c + 7)**2
Let g(p) = 13*p + 42. Let r be g(-3). Suppose 3/5*h + 0 + 0*h**r - 3/5*h**5 + 6/5*h**4 - 6/5*h**2 = 0. Calculate h.
-1, 0, 1
Let f(p) be the second derivative of -p**6/10 - 3*p**5/20 + p**4/4 + p**3/2 + 6*p. Factor f(y).
-3*y*(y - 1)*(y + 1)**2
Suppose -5*y + 6 = -124. Factor 32*u**5 + u**2 + 4*u**3 + y*u**4 + u**2 + 14*u**3 + 22*u**4.
2*u**2*(u + 1)*(4*u + 1)**2
Suppose 3*s = 5*u + 38, -2*u + 6*u = -16. Let n be ((-3)/s)/(12/(-16)). Factor n*z**2 + 8/3*z**3 + 0 + 0*z.
2*z**2*(4*z + 1)/3
Suppose 6 = -3*o - 3. Let c be (3 + o)*2/2. What is y in -2/7*y**3 + c*y + 0 + 0*y**2 = 0?
0
Let q(j) be the third derivative of -j**2 + 0 - 1/15*j**3 + 1/20*j**4 + 0*j + 2/75*j**5. Factor q(h).
2*(h + 1)*(4*h - 1)/5
Factor -12/11*g - 2/11*g**2 + 0.
-2*g*(g + 6)/11
Let f(k) be the first derivative of 1/12*k**4 - 3 + 0*k - 1/9*k**3 + 0*k**2. Factor f(a).
a**2*(a - 1)/3
Let k = 2 - -1. Find i, given that 4*i**k - 2*i**2 - 2*i**4 + 7*i - 7*i = 0.
0, 1
Find q such that -2/3*q - 8/3*q**2 + 0 = 0.
-1/4, 0
Solve 4*b**2 + 5*b + 3*b - b**3 + 7*b - 19*b = 0.
0, 2
Suppose -4*p + 216 = -4*a, 2*p - 3*p + 39 = 2*a. Let u be (-14)/p - 64/(-126). Factor 2/3*z**5 - 8/9*z**4 - u*z**3 + 0 + 4/9*z**2 + 0*z.
2*z**2*(z - 1)**2*(3*z + 2)/9
Suppose 0*n + 5*n + 46 = -2*u, -8 = -4*u. Let z = 13 + n. Factor 1/2*p**2 + 1/4*p + 0 + 1/4*p**z.
p*(p + 1)**2/4
Let c(p) be the third derivative of p**7/42 + p**6/12 - 5*p**4/12 - 5*p**3/6 + 17*p**2. Determine s so that c(s) = 0.
-1, 1
Let a(u) = -u**3 + u**2 + 5*u + 2. Let d be a(-2). Factor 0 - 2/7*j**d + 0*j - 2/7*j**3 + 0*j**2.
-2*j**3*(j + 1)/7
Suppose 2*b = 4*b. Let l(t) be the first derivative of -2 - 3/16*t**4 - 1/12*t**3 + b*t**2 + 0*t. Determine m so that l(m) = 0.
-1/3, 0
Let b(p) be the second derivative of -p**6/10 + 9*p**5/5 - 27*p**4/2 + 54*p**3 - 243*p**2/2 - 8*p. Factor b(j).
-3*(j - 3)**4
Let p be -13*(-9)/(-6)*-2. Factor -6*o**3 - 33*o + 4*o**2 - 4 + 0*o**3 + p*o.
-2*(o - 1)*(o + 1)*(3*o - 2)
Let t = 18 - 18. Suppose t*k + k = 2. Factor -4/5 - 7/5*r**k + 16/5*r.
-(r - 2)*(7*r - 2)/5
Let l(p) be the first derivative of -2*p**3/15 - p**2/5 - 2. Factor l(y).
-2*y*(y + 1)/5
Factor -4/3*m - 6*m**3 + 0 - 2/3*m**5 + 14/3*m**2 + 10/3*m**4.
-2*m*(m - 2)*(m - 1)**3/3
Let y = -4 - -4. Factor -1/3*g + y + 1/3*g**4 + g**2 - g**3.
g*(g - 1)**3/3
Factor 15*l**2 + 1040*l - 1040*l - 18*l**3 + 3*l**4.
3*l**2*(l - 5)*(l - 1)
Let i be 0*((-12)/8 - -2). Let d(y) be the second derivative of i*y**3 - y + 0 + 0*y**2 + 1/30*y**5 + 1/18*y**4. Solve d(o) = 0.
-1, 0
Suppose -5*q + 7 + 3 = 0. Solve -1/3 - 1/3*l**3 - l**q - l = 0 for l.
-1
Suppose 38 = 2*h - 4*x, -x - 40 = -5*h - 2*x. Let d be 8/(-36) - (-5)/h. Factor 1/3*a**2 - d + 0*a.
(a - 1)*(a + 1)/3
Let f(d) = 36*d**2 - 132*d + 72. Let h(y) = -9*y**2 + 33*y - 18. Let r(a) = 4*f(a) + 15*h(a). Suppose r(o) = 0. What is o?
2/3, 3
Let t be (12/24)/((-2)/(-8)). Factor 8/9*p + 8/9 + 2/9*p**t.
2*(p + 2)**2/9
Let v(h) be the third derivative of h**5/42 - h**4/42 - h**3/7 + 24*h**2. Factor v(o).
2*(o - 1)*(5*o + 3)/7
Solve 0*d - 22/9*d**4 - 8/9*d**5 - 10/9*d**3 + 4/9*d**2 + 0 = 0.
-2, -1, 0, 1/4
Let w be (-6*(-2)/(-3))/(-2). Suppose w + 6 = 2*x. Suppose -k**x + 10*k**4 + 8*k**3 - 2*k**3 + 21*k**5 + 18*k**4 = 0. What is k?
-1, -2/7, 0
Let g be -2*(2 + (-1)/2). Let v be (-14)/(-10) - (-3)/g. Factor -4/5*c - v - 2/5*c**2.
-2*(c + 1)**2/5
Suppose 4*w + 3*l - 11 = 0, 4*w - 19 = 5*l + 16. Factor 9*f**2 + 9*f + 0 + 3*f**3 + w - 2.
3*(f + 1)**3
Factor -2/3*m + 0 + 0*m**2 + 2/3*m**3.
2*m*(m - 1)*(m + 1)/3
Let r(g) = -92*g**5 - 16*g**4 + 61*g**3 + 47*g**2 - 11. Let q(n) = -31*n**5 - 5*n**4 + 20*n**3 + 16*n**2 - 4. Let b(i) = 11*q(i) - 4*r(i). Factor b(x).
3*x**2*(x - 1)*(3*x + 2)**2
Suppose -3*c + 2 = -2*z, -2*c = z + 2 - 8. Let h = 61/6 - 10. What is p in 0 - h*p**z + 0*p = 0?
0
Suppose 3*v + 4*i = 40, 2*v + 3*v - 2*i = 84. What is r in -12*r**2 + 32*r + 4*r**3 - 11*r**2 - v + 3*r**2 = 0?
1, 2
Factor 20/7*f - 16/7*f**2 + 4/7*f**3 - 8/7.
4*(f - 2)*(f - 1)**2/7
Let m(j) = 21*j**2 + 41*j - 7. Let w(q) = 21*q**2 + 40*q - 8. Let d(k) = 4*m(k) - 5*w(k). Factor d(x).
-3*(x + 2)*(7*x - 2)
Suppose 3*f - 3 = 5*m, -5*m - 2*f = -7*f + 5. Find p such that 1/3 - 1/3*p**2 + m*p = 0.
-1, 1
Let r(i) be the first derivative of -1/3*i**2 + 0*i**4 + 4/15*i**5 + 0*i - 4/9*i**3 + 1/9*i**6 - 3. Factor r(h).
2*h*(h - 1)*(h + 1)**3/3
Let r(u) = 3*u**2 + 24*u - 6. Let d(p) = -6*p**2 - 47*p + 11. Let g(f) = 6*d(f) + 11*r(f). Factor g(j).
-3*j*(j + 6)
Let t(k) be the third derivative of k**7/630 - k**6/360 + 6*k**2. Factor t(p).
p**3*(p - 1)/3
Solve -1/2 - 5/8*y**2 - 1/8*y**3 - y = 0 for y.
-2, -1
Let r = -208/9 - -70/3. Let k = r + 8/45. Let 2/5*s**5 + 4/5*s**2 - 4/5*s**3 - k + 2/5*s - 2/5*s**4 = 0. Calculate s.
-1, 1
Suppose 3*y = g + 3, -2*y = g - 3*g - 6. Let u(c) be the second derivative of c + 0*c**3 + 3/70*c**5 + y*c**2 + 0 - 1/21*c**4. Let u(r) = 0. What is r?
0, 2/3
Let f be 217/108 + 0 + -2. Let q(w) be the third derivative of w**2 + 0*w**5 + f*w**4 + 0*w + 0*w**3 + 0 - 1/540*w**6. Factor q(z).
-2*z*(z - 1)*(z + 1)/9
Let c = 4 - 1. Factor 0*s**3 - 3*s**4 + s**3 - c*s**3 + s**4.
-2*s**3*(s + 1)
Let m(a) = a**3 - 6*a**2 + 3. Let f be m(6). Factor 4 - 6*p**2 - 2 - 3*p**3 - p**f.
-2*(p + 1)**2*(2*p - 1)
Let n(d) = 3*d - 109. Let m be n(37). Suppose -2/3*o - 8/3*o**m + 0 = 0. What is o?
-1/4, 0
Let o(s) be the third derivative of -s**7/35 - s**6/8 - s**5/5 - s**4/8 - 8*s**2. Factor o(u).
-3*u*(u + 1)**2*(2*u + 1)
Let j = 1102 - 13211/12. Let w(b) be the first derivative of -2 + 1/3*b**2 + j*b**4 - 13/9*b**3 + 28/15*b**5 + 0*b. What is k in w(k) = 0?
-1, 0, 1/4, 2/7
Let t(c) be the second derivative of c**7/420 - 5*c**3/6 + c. Let p(l) be the second derivative of t(l). Suppose p(m) = 0. What is m?
0
Let g(h) = -2*h - 5. Let n be g(-7). Factor -2*s**4 + 3*s**4 + 12*s**2 + 2*s**4 - s**4 + 4*s + n*s**3.
s*(s + 2)*