 7. Let q be j(-3). Let d be 4/(-24)*q/4. Factor 0 - l**3 + d*l**4 - 1/3*l + l**2.
l*(l - 1)**3/3
Suppose -2*k = 2*k - 8. Let n be k - (0/(-1) - 2). What is j in -3*j**4 - 3*j**n + 3*j**3 - 2*j**2 + 5*j**3 = 0?
0, 1/3, 1
Let h(a) be the third derivative of a**6/30 - a**5/3 + 7*a**4/6 - 2*a**3 + 16*a**2. Factor h(r).
4*(r - 3)*(r - 1)**2
Let u(g) be the second derivative of g**5/30 - 5*g**4/18 + 8*g**3/9 - 4*g**2/3 + g. Factor u(r).
2*(r - 2)**2*(r - 1)/3
Let v = 470/13 - 36. Determine p, given that 4/13*p**2 + 0*p + 6/13*p**3 + v*p**4 + 0 = 0.
-2, -1, 0
Let w(p) = p**2 - p. Let m(u) = -2 - 3*u**2 + 4 + u + 8*u. Let f(i) = m(i) + 5*w(i). Factor f(t).
2*(t + 1)**2
Suppose 0 + 2 = d. Let u = d + -5. Let k(y) = -2*y**2 - 6*y + 9. Let b(w) = -3*w**2 - 12*w + 18. Let h(c) = u*b(c) + 5*k(c). What is j in h(j) = 0?
3
Let o = 468 + -1390/3. Factor 0 - 10/3*b**4 - 2/3*b**5 - 4/3*b - o*b**2 - 6*b**3.
-2*b*(b + 1)**3*(b + 2)/3
Let h(l) = l**2 + 7*l + 3. Let k be h(-7). Factor 5*g**3 - 4*g**k + g**2 + 0*g**3.
g**2*(g + 1)
Determine w so that 3/2*w - 3/2 + 9/2*w**2 - 3/2*w**3 - 3*w**4 = 0.
-1, 1/2, 1
Suppose m = i, 0 = 4*m - m - 15. Solve 1/2*c**2 + 1/4*c**i - 1/4*c + 0*c**3 + 0 - 1/2*c**4 = 0 for c.
-1, 0, 1
Let o be 3/9 + 2*(-1)/6. Factor o*i**2 + 0 - 1/3*i**4 + 1/3*i**3 + 0*i.
-i**3*(i - 1)/3
Let c(n) = n**2 + 3. Let z be c(0). Suppose -y = 3*k + 5, -5*y + 23 = -z*k + 2*k. Let -1/4*t**2 + 0 - 3/4*t**y - 3/4*t**3 - 1/4*t**5 + 0*t = 0. Calculate t.
-1, 0
Let k be 2/(4/6) - 1. Let l = -18 - -164/9. Factor l*m**k + 0 + 0*m.
2*m**2/9
Let y(j) = -15*j**5 + 9*j**4 + 9*j**3 - 11*j**2 - 11*j - 11. Let b(t) = 3*t**5 - 2*t**4 - 2*t**3 + 2*t**2 + 2*t + 2. Let q(u) = -11*b(u) - 2*y(u). Factor q(p).
-p**3*(p - 2)*(3*p + 2)
Let h(w) = w**2. Let o(j) = -4*j**2 + 10*j - 15. Let t(a) = -5*h(a) - o(a). Let m be t(-11). Factor -2/5*c**2 + 0*c + 4/5*c**3 - 2/5*c**m + 0.
-2*c**2*(c - 1)**2/5
Let h(q) = 3*q**2 + q. Suppose 0*d + 10 = 5*d. Let f(r) = -r**2 - 1. Let n(l) = d*f(l) + h(l). Solve n(j) = 0 for j.
-2, 1
Let t = 19/24 - 1/8. Determine w so that 1/3*w - 1/3*w**3 + 2/3*w**4 + 0 - t*w**2 = 0.
-1, 0, 1/2, 1
Let j = -160 + 167. Let x(b) be the third derivative of 0*b - 1/120*b**6 - 1/90*b**5 + 1/1008*b**8 + b**2 + 0*b**j + 0*b**4 + 0*b**3 + 0. Solve x(v) = 0.
-1, 0, 2
Factor 24/5*v - 21/5 - 3/5*v**2.
-3*(v - 7)*(v - 1)/5
Factor 0 - 1/4*m**2 - 3/4*m.
-m*(m + 3)/4
Let n = -152/3 - -51. Factor -4/3*a + n - 1/3*a**2 + 4/3*a**3.
(a - 1)*(a + 1)*(4*a - 1)/3
Let d(v) be the second derivative of v**4/120 + v**3/60 - v**2/10 + 50*v. Factor d(z).
(z - 1)*(z + 2)/10
Let i(l) be the third derivative of l**5/15 + 5*l**4/6 + 8*l**3/3 + 16*l**2. Determine p, given that i(p) = 0.
-4, -1
Let p(y) be the third derivative of 0*y**3 - 6*y**2 + 1/420*y**7 + 0*y**4 - 1/120*y**5 + 0 + 0*y**6 + 0*y. Suppose p(o) = 0. Calculate o.
-1, 0, 1
Let u(m) be the first derivative of m**3 + 3*m**2 + 6. Factor u(r).
3*r*(r + 2)
Let n be 6/(-21) - 354/(-14). Let f be n/9 - 2/(-9). Suppose 5*w**2 + 2*w**f - w**3 - 4*w**2 = 0. Calculate w.
-1, 0
Let f(n) = n**5 + n**4 - 4*n**3 - 4*n**2 + 5*n - 5. Let w(i) = -i + 1. Let j(s) = -3*f(s) - 15*w(s). Let j(b) = 0. Calculate b.
-2, -1, 0, 2
Let v(k) be the second derivative of 1/7*k**3 - 2*k + 0 - 1/42*k**4 - 2/7*k**2. Factor v(s).
-2*(s - 2)*(s - 1)/7
Let i(c) = -c**3 - 5*c**2 + c + 8. Let y be i(-5). Let o(k) be the second derivative of 0 - 1/8*k**2 - 1/12*k**y - k - 1/48*k**4. Factor o(g).
-(g + 1)**2/4
Let w = 14 - 10. Suppose 0 = w*v + z - 8, -v + 10 = -3*v - 4*z. Factor 0 + 6/7*s**v + 0*s - 10/7*s**4 + 4/7*s**2.
-2*s**2*(s - 1)*(5*s + 2)/7
Factor -28 + 18 + 10 + s - 2*s**3 - s**2.
-s*(s + 1)*(2*s - 1)
Let a be (-130)/4 + (-6 - -7). Let i = -437/14 - a. Solve -2/7*b**2 + 4/7 + i*b = 0 for b.
-1, 2
Let m(u) be the second derivative of -u**7/7 - u**6/3 - u**5/5 - 7*u. Factor m(t).
-2*t**3*(t + 1)*(3*t + 2)
Solve 1/2*a + 3/4*a**2 + 0 + 1/4*a**3 = 0 for a.
-2, -1, 0
Let s = 10 - 6. Suppose -t = 1 - s. Factor -o**3 + 0*o - 2*o + 2*o**3 - 2*o**5 + 3*o**t.
-2*o*(o - 1)**2*(o + 1)**2
Let d(r) be the third derivative of r**6/40 + 6*r**5/5 + 24*r**4 + 256*r**3 + 12*r**2. Factor d(t).
3*(t + 8)**3
Solve 0*o**5 + 18*o**3 - 4*o**5 + 7*o**5 - 15*o**4 = 0 for o.
0, 2, 3
Let s(r) be the second derivative of r**7/56 + r**6/20 - 3*r**5/16 - 5*r**4/8 + r**3/2 + 3*r**2 - 24*r + 2. Determine a so that s(a) = 0.
-2, -1, 1, 2
Let o(l) be the third derivative of -2/735*l**7 + 1/105*l**6 - 2/21*l**3 + 9*l**2 + 0 + 0*l - 1/588*l**8 + 2/105*l**5 - 1/42*l**4. Factor o(k).
-4*(k - 1)**2*(k + 1)**3/7
Let g(w) be the third derivative of w**8/1848 - w**7/1155 - w**6/220 + w**5/66 - w**4/66 - 10*w**2. Let g(t) = 0. What is t?
-2, 0, 1
Let c(w) be the third derivative of -2*w**7/105 - w**6/30 - 8*w**2. Factor c(f).
-4*f**3*(f + 1)
Let n(f) be the first derivative of 3*f**4/10 - 2*f**3/15 - 8*f**2/5 - 8*f/5 - 7. Factor n(j).
2*(j - 2)*(j + 1)*(3*j + 2)/5
Factor 33*c**4 + 3*c**2 - 3*c**2 - 35*c**4 + 2*c**3.
-2*c**3*(c - 1)
Let i(w) be the first derivative of -w**4/2 - 4*w**3/3 + w**2 + 4*w - 2. Determine p so that i(p) = 0.
-2, -1, 1
Let 3/4*u**2 + 3/4*u - 3/2 = 0. What is u?
-2, 1
Suppose -4*i - 14 = 5*y - 7, -4*i - 2*y + 2 = 0. Let -5*s**2 - 4*s**i - 8*s - 4*s**3 + 10*s**4 + 12*s - s**2 = 0. What is s?
-1, 0, 2/5, 1
Let b(h) = -h**2 + 2 + 4*h**2 - 5*h**2 + h**2 + 4*h. Let z be b(4). Factor 2/7 + 6/7*p**z + 6/7*p + 2/7*p**3.
2*(p + 1)**3/7
Let t be 0 - (-3 - (3 + -2)). Determine j, given that -t*j**4 - 4*j**5 - 4*j**4 + 8*j**2 + 0*j**2 + 4*j = 0.
-1, 0, 1
Let c(x) be the third derivative of x**2 + 0 - 1/2*x**3 + 0*x - 9/80*x**5 - 5/8*x**4. Suppose c(k) = 0. Calculate k.
-2, -2/9
Let k be (-105)/39 - (6 - 9). Find x such that 2/13*x + k - 2/13*x**2 = 0.
-1, 2
Let s(i) be the first derivative of -343*i**6/24 + 931*i**5/10 - 4039*i**4/16 + 1094*i**3/3 - 296*i**2 + 128*i + 7. Factor s(j).
-(j - 1)**2*(7*j - 8)**3/4
Let z(g) be the second derivative of 25*g**4/24 + 5*g**3/3 + g**2 - 2*g. Factor z(v).
(5*v + 2)**2/2
Let u(d) be the first derivative of 3 + 0*d + 4/3*d**3 + 49/30*d**5 + 7/3*d**4 + 1/2*d**2. Let z(c) be the second derivative of u(c). Factor z(g).
2*(7*g + 2)**2
Let n(s) be the second derivative of -s**7/189 - s**6/135 + s**5/30 + 5*s**4/54 + 2*s**3/27 - 34*s. Factor n(t).
-2*t*(t - 2)*(t + 1)**3/9
Let r(w) = -w**3 + w**2 + 4. Let v(i) = -i**3 + 2*i**2 + 4. Let n(x) = -5*r(x) + 4*v(x). Factor n(k).
(k - 1)*(k + 2)**2
Let d(g) = 5*g**2 - 18*g - 42. Let v(q) = q**2 - q - 1. Let n(u) = d(u) - 6*v(u). Suppose n(p) = 0. Calculate p.
-6
Solve 12*w**3 - 5*w**4 - 2*w**4 - 12*w**2 + 2*w**4 + w**4 + 4*w = 0.
0, 1
Suppose -2*p + 0*p = 0. Let m(y) be the third derivative of 0 + 0*y + p*y**5 + 3/20*y**4 + 2/15*y**3 - 4/175*y**7 + y**2 - 19/300*y**6. What is f in m(f) = 0?
-1, -1/4, 2/3
Suppose 0 = -3*z - 5*h - 0 - 6, 4*h + 8 = -4*z. Let q be 2*1 + (-1 - z). Let 9*k**2 - 7*k**2 + 5*k**3 - q*k**3 = 0. What is k?
-1, 0
Suppose -4*v = 4*r - 7 - 1, 4*r - 3*v - 1 = 0. Let a(n) be the first derivative of 13*n**2 + r - 8/3*n**3 - 6*n. Factor a(o).
-2*(o - 3)*(4*o - 1)
Let a(w) = -2*w**2 + w - 3. Let x(k) = k**2 + 2. Let n(q) = -4*a(q) - 6*x(q). Factor n(i).
2*i*(i - 2)
Suppose 5*c + 4*l = -38, 0 = -3*l - l - 8. Let u = c - -8. Let 8*r - r**2 + 3*r**2 - 10*r**u + 2*r**3 = 0. What is r?
0, 2
Let i be ((-52)/78)/((-4)/9). Factor 1/2 + f - i*f**2.
-(f - 1)*(3*f + 1)/2
Let d = 1442 - 1438. Factor 0 - 1/6*s**d + 0*s**2 + 0*s - 1/6*s**3.
-s**3*(s + 1)/6
Let l(y) be the second derivative of y**7/24 + y**6/24 - y**5/40 + 7*y. Factor l(j).
j**3*(j + 1)*(7*j - 2)/4
Let a = -22/3 + 8. Factor -y - 1/3*y**2 - a.
-(y + 1)*(y + 2)/3
Let b(f) = 4*f**2 + 3*f - 4. Let q(v) = -7*v**2 - 5*v + 8. Let c(s) = -5*b(s) - 3*q(s). Solve c(w) = 0.
-2, 2
Let b(t) be the third derivative of t**7/210 - t**6/120 - t**5/60 + t**4/24 - 2*t**2 - t. Factor b(r).
r*(r - 1)**2*(r + 1)
Let b = -4 - -4. Let y(g) be the third derivative of 0 - g**2 + 0*g**3 - 1/12*g**4 + b*g - 1/60*g**6 + 1/15*g**5. Determine h so that y(h) = 0.
0, 1
Let l(j) be the first derivative of 1/3*j**2 - 2/9*j**3 - 2/9*j + 1/18*j**4 + 1. Factor l(x).
2*(x - 1)**3/9
Let l(y) be the second derivative of -3*y**4 + 0 - 3/2*y**3 - 21/20*y**5 + 3*y**2 - 2*y. Factor l(f).
-3*(f