*o**5 - 11*o**4 - 12*o**3 + 20*o**2 - o - 7. Let u(z) = 2*z**5 - 6*z**4 - 6*z**3 + 10*z**2 - 4. Let r(m) = 4*g(m) - 7*u(m). Factor r(j).
2*j*(j - 1)**3*(j + 2)
Solve -12*r - 12*r**4 + 10*r**2 - 8 + 18*r**3 - 8*r**5 - 2*r**3 + 10*r**2 + 4*r**3 = 0 for r.
-2, -1, -1/2, 1
Factor 2*c**2 + 2*c**2 + 2*c**3 + 0*c**2 - 2*c - 2*c**2 - 2*c**4.
-2*c*(c - 1)**2*(c + 1)
Let q(x) be the first derivative of 56/9*x**3 + 16/3*x - 8*x**2 - 1/18*x**6 + 3 - 8/3*x**4 + 3/5*x**5. Let q(v) = 0. Calculate v.
1, 2
Let g(b) = 15*b**5 - 20*b**4 + 5*b**3 - b**2 + 1. Let y(p) = p**5 - p**3 + p**2 - 1. Let o(i) = g(i) + y(i). What is t in o(t) = 0?
0, 1/4, 1
Let o(l) = -36*l**4 - 60*l**3 - 24*l**2 + 16*l. Let p(y) = -7*y**4 - 12*y**3 - 5*y**2 + 3*y. Let v(s) = 3*o(s) - 16*p(s). Factor v(w).
4*w**2*(w + 1)*(w + 2)
Let s = -19/2 + 10. Let d be ((-5)/20*0)/(-2). Find x such that 0 + 1/2*x + d*x**2 - s*x**3 = 0.
-1, 0, 1
Let g(w) = w**4 + w**3 + w**2 + w. Let s(z) = 7*z**4 + 5*z**3 + 6*z**2 + 8*z. Let y(k) = 24*g(k) - 3*s(k). Suppose y(c) = 0. What is c?
-2, -1, 0
Let u(k) = k**3 + 11*k**2 - 13*k - 11. Let f be u(-12). Suppose -f = -4*j + 7. Find s such that j*s**2 + s - 3*s + 3*s - s**2 = 0.
-1, 0
Let r(h) be the first derivative of -5*h**3/3 + 25*h**2/2 - 11. Factor r(x).
-5*x*(x - 5)
Let r(y) be the second derivative of y**5/150 - y**4/15 + 4*y**3/15 + 2*y**2 - 2*y. Let w(o) be the first derivative of r(o). Let w(t) = 0. What is t?
2
Let -b + 0*b**2 + 2 - 3*b**2 + b**3 - 3 + 4*b**2 = 0. What is b?
-1, 1
Let v = -1/70 + 37/140. Let z(c) be the first derivative of 0*c - v*c**4 - 1/3*c**3 - 1 + 2/5*c**5 + 0*c**2. Factor z(b).
b**2*(b - 1)*(2*b + 1)
Let i(y) = -5*y + 4*y + 2 + 1. Let x be i(0). Let -4*v - 4*v**2 + 2*v**x + 5*v**2 - 3*v**2 = 0. What is v?
-1, 0, 2
Let h(b) be the third derivative of b**6/24 + b**5/3 + 25*b**4/24 + 5*b**3/3 - 7*b**2. Factor h(m).
5*(m + 1)**2*(m + 2)
Let q(w) be the first derivative of -w**3/4 + 5*w**2/8 - w/2 + 4. Determine n, given that q(n) = 0.
2/3, 1
Let u(v) be the first derivative of -v**4/6 + 4*v**3/9 - v**2/3 - 1. Factor u(l).
-2*l*(l - 1)**2/3
Let i(w) be the second derivative of 2*w**6/15 + w**5/5 - 10*w**4/3 + 16*w**3/3 - 61*w. Find c such that i(c) = 0.
-4, 0, 1, 2
Let c(y) be the third derivative of y**10/75600 - y**9/15120 - y**5/15 - 5*y**2. Let r(z) be the third derivative of c(z). Factor r(l).
2*l**3*(l - 2)
Let o(u) = -2*u**2 - 4*u + 4. Let j(t) = t. Let k(d) = 6*j(d) + o(d). Factor k(h).
-2*(h - 2)*(h + 1)
Let g(p) be the first derivative of -p**5/20 - 15. Find w such that g(w) = 0.
0
Let v(k) be the third derivative of -3*k**7/280 + k**6/160 + k**5/16 - k**4/32 - k**3/4 + 39*k**2 - 2. Solve v(z) = 0 for z.
-1, -2/3, 1
Let b be (-1)/(5 + -4) - -3. Determine y, given that 0*y + 1/2*y**4 + 1/2 - y**b + 0*y**3 = 0.
-1, 1
Let k(a) = 6*a**3 - 2*a**2 - 6*a + 10. Suppose -1 = -5*t + y - 5, 4*t = -5*y - 9. Let b(q) = -q**3 + q - 1. Let i(v) = t*k(v) - 8*b(v). What is m in i(m) = 0?
-1, 1
Factor -4/3*d**2 - 64/3*d - 256/3.
-4*(d + 8)**2/3
Let q = 1167 - 105029/90. Let s(a) be the second derivative of 0 - 1/27*a**3 + 0*a**2 + q*a**5 - 3*a + 0*a**4. Factor s(b).
2*b*(b - 1)*(b + 1)/9
Let p(f) be the third derivative of f**6/600 + f**5/100 - f**4/120 - f**3/10 - 3*f**2. Factor p(w).
(w - 1)*(w + 1)*(w + 3)/5
Suppose -2/5*k**2 - 4/5*k + 0 + 2/5*k**3 = 0. What is k?
-1, 0, 2
Let w be (-6)/21 + 46/14. Suppose 5/6*f**w + 1/3 - 5/6*f + 1/6*f**2 - 1/2*f**4 = 0. Calculate f.
-1, 2/3, 1
Let k(q) = q**2 - 3*q + 3. Let o be k(3). Let f(j) be the first derivative of 1 - 3*j**3 + 0*j**2 + o*j + 3/2*j**4. Factor f(c).
3*(c - 1)**2*(2*c + 1)
Suppose 5 = 3*o - 4. Let y be (-1 + 27/o)/1. Let 1 - 4*f**4 - 4*f**5 + 7*f**2 + 4*f**4 - y*f**4 - f**3 + 5*f = 0. What is f?
-1, -1/2, 1
Let c(a) be the third derivative of a**7/1120 - a**6/240 - a**3/2 + 2*a**2. Let i(p) be the first derivative of c(p). Let i(b) = 0. Calculate b.
0, 2
Let r = 1 + 10. Let k(g) = g**3 - g**2 + 4*g. Let q(u) = 3*u**3 - 3*u**2 + 11*u. Let h(t) = r*k(t) - 4*q(t). Factor h(x).
-x**2*(x - 1)
Let j(l) = -l**2 + 7*l + 11. Let b be j(8). What is z in -b*z**2 + z + z**2 + z - 4*z = 0?
-1, 0
Let a(m) be the second derivative of m**6/1980 + m**5/330 + m**4/132 + m**3/2 - 4*m. Let o(u) be the second derivative of a(u). Factor o(j).
2*(j + 1)**2/11
Determine p, given that -153/7*p**3 + 36/7*p**2 - 27*p**5 - 366/7*p**4 + 12/7*p + 0 = 0.
-1, -2/9, 0, 2/7
Let t(f) be the first derivative of 32*f - 120*f**2 + 98/3*f**6 + 472/3*f**3 - 504/5*f**5 - 1 + 11*f**4. Find a, given that t(a) = 0.
-1, 2/7, 1, 2
Let q(g) = 12*g**4 - 12*g**3 + 24*g**2 + 12*g + 9. Let s(p) = p**4 - p**3 + p**2 + p + 1. Let v(o) = q(o) - 15*s(o). Factor v(n).
-3*(n - 2)*(n - 1)*(n + 1)**2
Suppose 0 - 14/17*j**4 + 2/17*j**5 - 10/17*j**2 + 0*j + 22/17*j**3 = 0. What is j?
0, 1, 5
Let o be -10*-1*4/8. Let g(n) be the second derivative of 0*n**3 - 1/35*n**o + 0*n**2 + 0 - 2*n - 1/42*n**4 - 1/105*n**6. Factor g(x).
-2*x**2*(x + 1)**2/7
Let h be (12/11)/(9/(-6)). Let q = -5/22 - h. Factor q*y**2 + 0*y + 0*y**3 - 1/4 - 1/4*y**4.
-(y - 1)**2*(y + 1)**2/4
Let q(w) be the first derivative of 0*w**3 + 0*w + 3 - 1/10*w**4 + 1/5*w**2. Determine d so that q(d) = 0.
-1, 0, 1
Let h be 36/16 + (-2)/8. Determine b, given that -27*b + 11 + 12*b**2 - 5 + 11*b - h*b**4 = 0.
-3, 1
Let l(y) be the third derivative of -y**8/1008 + y**7/315 - y**5/90 + y**4/72 - 11*y**2. Factor l(c).
-c*(c - 1)**3*(c + 1)/3
Suppose 1/4*l**2 + 9/4*l + 2 = 0. What is l?
-8, -1
Let s(i) be the second derivative of i**8/1680 - i**7/840 - i**6/360 + i**5/120 + i**3 - 7*i. Let x(v) be the second derivative of s(v). Factor x(u).
u*(u - 1)**2*(u + 1)
Suppose 4*v + 5 = -39. Let f(c) = -4*c**3 - 12*c**2 - 19*c - 11. Let n(p) = 2*p**3 + 6*p**2 + 10*p + 6. Let k(l) = v*n(l) - 6*f(l). Factor k(d).
2*d*(d + 1)*(d + 2)
Let q = 8639 - 328309/38. Let t = -4/19 - q. Determine o, given that o**2 + 0 + 1/2*o + t*o**3 = 0.
-1, 0
Let u be -2*(-3)/(-237)*1. Let a = 83/158 + u. Factor 0 - a*v**3 + 0*v - 1/4*v**2 - 1/4*v**4.
-v**2*(v + 1)**2/4
Let v(o) be the first derivative of -2 - 4/7*o**3 - 3/7*o - 6/7*o**2. Determine c so that v(c) = 0.
-1/2
Let l be 68/(-340)*20/(-6). Factor l*u**2 + 2/9*u**3 + 0 + 4/9*u.
2*u*(u + 1)*(u + 2)/9
Let r(a) be the second derivative of -a**4/60 + a**3/10 - a**2/5 - 22*a. Determine h so that r(h) = 0.
1, 2
Let q(n) be the first derivative of 2/21*n**3 + 2 + 0*n + 1/7*n**2. Factor q(c).
2*c*(c + 1)/7
Let u(r) be the second derivative of r**10/2016 + r**9/720 + r**8/1120 + 7*r**4/12 + 6*r. Let m(a) be the third derivative of u(a). Factor m(j).
3*j**3*(j + 1)*(5*j + 2)
Let c(v) be the third derivative of v**6/420 - v**5/70 + v**4/42 + 7*v**2. Suppose c(u) = 0. What is u?
0, 1, 2
Solve 3/7*o - 3/7*o**4 + 1/7 + 2/7*o**2 - 2/7*o**3 - 1/7*o**5 = 0.
-1, 1
Let z(y) be the first derivative of 1 - 8/5*y**5 - 4*y**3 + 0*y - 9/2*y**4 - y**2. Find o such that z(o) = 0.
-1, -1/4, 0
Let o be 8/56*(-28)/(-8). Factor 1/2*s**2 - o + 0*s.
(s - 1)*(s + 1)/2
Suppose 2*z + 25 - 2 = -5*j, 2*z + 4*j + 18 = 0. Let q = z - -1. Factor -3*g**q - 2*g - 2*g**3 - 1/2*g**4 - 1/2.
-(g + 1)**4/2
Let l(b) be the second derivative of 3*b**5/20 - b**4/6 - b**3/2 + b**2 + 3*b. Let l(w) = 0. What is w?
-1, 2/3, 1
Suppose -7*s - 4 = -3*s, 2*q + 13 = -3*s. Let g be (6 + q)/(2/10). Determine v so that 0 - v**g + 0*v + 0*v**2 + 2/5*v**3 + 3/5*v**4 = 0.
-2/5, 0, 1
Suppose -7 = j - 3*x, -5*j + 27 + 18 = 5*x. Factor -5*m**j - m**3 + 0*m**4 - 2*m**2 + 3*m**4 + 5*m**4.
-m**2*(m - 1)**2*(5*m + 2)
Suppose 4*q = 2 + 2. Let m(g) = 5*g**3 + 2*g**2 + g + 1. Let o(r) = -r**3 - r - 1. Let d(z) = q*m(z) + 3*o(z). Factor d(h).
2*(h - 1)*(h + 1)**2
Let s(h) be the third derivative of -h**6/210 + h**5/105 - 25*h**2. Factor s(c).
-4*c**2*(c - 1)/7
Determine k, given that -4/3*k + 5/6*k**3 - 1/6*k**4 - 1/6*k**5 + 1/6*k**2 + 2/3 = 0.
-2, 1
Let q(m) be the second derivative of m**5/10 - m**4/3 - m**3/3 + 2*m**2 - m + 16. Factor q(z).
2*(z - 2)*(z - 1)*(z + 1)
Let i = 8 - 3. What is l in 0*l**i - 5*l**5 + 3*l**5 = 0?
0
Let i(c) be the second derivative of c**7/5040 - c**6/360 + c**5/60 + c**4/12 + 2*c. Let n(k) be the third derivative of i(k). Factor n(m).
(m - 2)**2/2
Let r(j) = 8*j**2 + 8*j - 5. Let a(b) = b**2 + b - 1. 