*t**3 = 0.
0, 1
Let f(y) = y**4 + y. Let s(n) = n**4 + n**3 + n**2 + n. Let m = 7 - 1. Let x = 0 - 4. Let z(k) = m*s(k) + x*f(k). Determine j so that z(j) = 0.
-1, 0
Factor 0 + 3/2*c - 1/2*c**3 + c**2.
-c*(c - 3)*(c + 1)/2
Let m(z) = z**2 + z + 1. Let q(n) = 2*n**3 + 16*n**2 + 16*n + 20. Let s(o) = -36*m(o) + 2*q(o). Factor s(j).
4*(j - 1)**2*(j + 1)
Factor -12/5*m**4 - 4/5*m**5 - 8/5*m**3 + 8/5*m**2 + 4/5 + 12/5*m.
-4*(m - 1)*(m + 1)**4/5
Let h(f) = -f**2 + f + 1. Let q be 3*4/(-2)*1. Let o(s) = -3*s**2 + 9*s + 6. Let p(v) = q*h(v) + o(v). Factor p(l).
3*l*(l + 1)
Let i(y) be the first derivative of -y**5/5 - y**4/2 + 5*y**3/3 + 3*y**2 - 10. Factor i(t).
-t*(t - 2)*(t + 1)*(t + 3)
Let o(j) = j**2 - 5*j + 7. Suppose 3*d + 7 = -5*v, -v + 6*d - d - 7 = 0. Let f = 5 + v. Let q(r) = -2*r**2 + 14*r - 20. Let g(s) = f*q(s) + 8*o(s). Factor g(u).
2*(u - 1)*(u + 2)
Factor -8/7 + 8*s**3 + 36/7*s - 24/7*s**4 + 4/7*s**5 - 64/7*s**2.
4*(s - 2)*(s - 1)**4/7
Determine d, given that -3*d**4 + 19*d**4 + 33*d + 48*d**3 + 64*d**2 - d + 2*d**5 = 0.
-2, 0
Let x(t) be the first derivative of -t**4/28 - t**3/21 - 1. Factor x(d).
-d**2*(d + 1)/7
Let f(s) be the second derivative of s**5/5 - s**4/3 - 4*s**3/3 + 25*s. Factor f(b).
4*b*(b - 2)*(b + 1)
Suppose 4*c - 86 - 54 = 0. Let h = -33 + c. What is k in -3/4*k**3 - 5/4*k**4 + 0 + 1/2*k**h + 0*k = 0?
-1, 0, 2/5
Let i = -92/45 - -22/9. Factor -8/5*u**2 + i*u - 2*u**3 + 0.
-2*u*(u + 1)*(5*u - 1)/5
Factor 1/5 + 1/5*n**4 + 6/5*n**2 + 4/5*n + 4/5*n**3.
(n + 1)**4/5
Let c(p) = -2 - 1 + 0*p - 2*p + p - 3*p**2. Let k(o) be the second derivative of -o**4/6 - o**2 + o. Let m(x) = 4*c(x) - 5*k(x). Solve m(f) = 0 for f.
-1
Let r(s) = -s**2 - 6*s - 5. Let a be r(-3). Let v(w) be the third derivative of w**2 - 1/12*w**a + 0 - 1/20*w**5 + 1/6*w**3 + 0*w. Factor v(n).
-(n + 1)*(3*n - 1)
Let p(x) be the first derivative of 2/5*x**5 + 1/6*x**6 + 0*x**3 - 2 + 0*x + 1/4*x**4 + 0*x**2. Factor p(a).
a**3*(a + 1)**2
Determine q, given that 1/2 + 1/3*q**3 - 1/6*q - q**2 - 1/6*q**5 + 1/2*q**4 = 0.
-1, 1, 3
Let s(r) be the first derivative of r**6/45 + r**5/15 + r**4/18 + 2*r - 4. Let v(h) be the first derivative of s(h). Factor v(w).
2*w**2*(w + 1)**2/3
Let v(d) = 3*d - 4. Let m be v(2). Suppose -4 + m = -o. Factor 0 + 2*t**o + 1/2*t**3 + 2*t.
t*(t + 2)**2/2
Let m(h) be the first derivative of 0*h - 1/4*h**4 - 3 - 1/3*h**3 + 1/2*h**2 + 1/5*h**5. Find o such that m(o) = 0.
-1, 0, 1
Factor 31*c**4 + 41*c**2 + 11*c**2 + 5*c**5 + 14*c**4 + 28*c**2 + 120*c**3.
5*c**2*(c + 1)*(c + 4)**2
Factor 0*p - 2/17*p**2 + 0.
-2*p**2/17
Solve -2/17*a**5 - 12/17*a**3 - 2/17*a - 8/17*a**4 - 8/17*a**2 + 0 = 0.
-1, 0
Let b(r) = 9*r + 3. Let x be b(-2). Let j be (-1)/1 + x/(-5). Solve -18/7*c**j - 4/7*c - 2/7*c**3 + 0 + 24/7*c**4 = 0.
-2/3, -1/4, 0, 1
Let s(n) be the second derivative of 11*n**4/24 - 3*n**3/4 - n**2/2 + 3*n. Factor s(i).
(i - 1)*(11*i + 2)/2
Let p(u) = -u - 13. Let b be p(0). Let c = 17 + b. Suppose -20/3*m**2 - 20/3*m**3 - 10/3*m**c - 2/3 - 10/3*m - 2/3*m**5 = 0. What is m?
-1
Suppose -2 = n, 2*n = 3*o - 2*n - 35. Let t = o + -7. Factor -2*h**3 + 2*h**2 - t*h**2 + 5*h**2 - 2*h.
-h*(h - 2)*(2*h - 1)
Suppose -i = -3*t + 3*i + 22, -5*t + 3*i = -22. Solve 2/7*w**4 + 0 + 6/7*w**t + 6/7*w**3 + 2/7*w = 0 for w.
-1, 0
Let k(h) be the third derivative of 2*h**7/315 - 2*h**5/15 - 4*h**4/9 - 2*h**3/3 + 12*h**2. Factor k(i).
4*(i - 3)*(i + 1)**3/3
Determine b so that b**2 + 1 + 7*b + 1 - 4*b = 0.
-2, -1
Suppose 11 - 1 = 5*i. Let l(q) be the second derivative of -1/36*q**4 + 0 + 3*q - 1/20*q**5 + 0*q**3 + 0*q**i + 2/45*q**6. Factor l(u).
u**2*(u - 1)*(4*u + 1)/3
Let w be -7 - 42/(3 - 9). What is v in 0*v - 6/7*v**2 - 9/7*v**3 - 3/7*v**4 + w = 0?
-2, -1, 0
Let h(d) = -d**3 + 2*d**2 + d - 5. Let a(n) = n**3 - 2*n**2 - n + 6. Let l(k) = -3*a(k) - 4*h(k). Determine j so that l(j) = 0.
-1, 1, 2
Let a(q) be the first derivative of -1/6*q**3 + 1/4*q**2 + 0*q - 2. Factor a(x).
-x*(x - 1)/2
Let i = 2/7 + 8/21. Let g be (-9)/(-15) - (-256)/240 - 1. Find f such that -i*f**3 - g*f**2 + 0*f + 0 = 0.
-1, 0
Let z(h) be the third derivative of -h**5/300 + h**4/30 - 24*h**2. Factor z(a).
-a*(a - 4)/5
Let z = -93/2 + 49. Factor z*k**2 - 2 - 4*k.
(k - 2)*(5*k + 2)/2
Let q(i) = i**3 + i**2 + 4*i + 3. Let c be q(-2). Let n be (-1)/(-2) - c/2. Find r, given that -n*r + r**2 + 2*r**2 + 2*r - r**3 + 1 = 0.
1
Suppose -4*i = -d - 7, 8 = 4*d - 12. Factor 0*r**3 + r**2 - 9*r**i - 2*r**2 - 3*r**5 + 9*r**4 + 4*r**2.
-3*r**2*(r - 1)**3
Let h(a) = -a**2 + 7*a - 2. Let n be h(6). Let g be ((-6)/n + 0)*-6. Let q - g*q**3 + q**2 + 1 - 2*q**2 + 8*q**3 = 0. Calculate q.
-1, 1
Factor 0*b + 10/13*b**2 + 14/13*b**4 + 2/13*b**5 + 22/13*b**3 + 0.
2*b**2*(b + 1)**2*(b + 5)/13
Suppose -5*f + 10 = 0, 3*x = 2*x + 2*f - 4. Factor 1/3*p**3 + x + 4/3*p - 4/3*p**2.
p*(p - 2)**2/3
Let q(o) = o**2 + 5*o - 3. Let l be q(-6). Suppose 3*r + 0*r - 4*g = 0, 0 = 3*r - l*g. Factor r + 0*w**2 + 0*w - 1/4*w**3 - 1/4*w**4.
-w**3*(w + 1)/4
Let w(a) = -5*a**2 + 20. Let s(l) = -85*l**2 + 340. Let h(o) = -2*s(o) + 35*w(o). Factor h(p).
-5*(p - 2)*(p + 2)
Let n(b) = -8 - 5*b**2 + 4 + 2 - 3*b**3. Let m(a) = -4*a**3 - 6*a**2 + a - 3. Let t(f) = 2*m(f) - 3*n(f). Factor t(w).
w*(w + 1)*(w + 2)
Let n(w) be the third derivative of w**9/4536 + w**8/2520 - w**7/1260 - w**6/540 - w**3/6 - 5*w**2. Let x(b) be the first derivative of n(b). Factor x(j).
2*j**2*(j - 1)*(j + 1)**2/3
Let k(b) be the second derivative of b**4/50 - 4*b**3/15 - 7*b**2/25 + 8*b + 1. Factor k(m).
2*(m - 7)*(3*m + 1)/25
Determine n, given that 3*n**2 - 9*n**3 - 3*n**4 + 0*n**2 + 20*n - 14*n + 3*n**5 = 0.
-1, 0, 1, 2
Let u(f) be the third derivative of 3*f**5/20 - f**4/8 - f**3 + 2*f**2. Let u(j) = 0. Calculate j.
-2/3, 1
Let a = -19/2 + 11. Let o(h) be the first derivative of -3/4*h**4 + 0*h + 0*h**3 + 3 + a*h**2. Solve o(w) = 0.
-1, 0, 1
Let j be (-4)/(-12) - (-39)/(-144). Let z(m) be the first derivative of 2 + 1/6*m**3 + 0*m + 1/8*m**2 - j*m**4 - 1/10*m**5. Factor z(p).
-p*(p - 1)*(p + 1)*(2*p + 1)/4
Determine b so that 4/7*b**3 + 8/7*b**4 + 0 + 4/7*b**5 + 0*b**2 + 0*b = 0.
-1, 0
Let c(y) = -9*y**3 + y - y**2 - 1 + 2*y**2 + 0*y**2. Let l(i) = -3*i**3. Suppose 2*v = a - 13, 0 = -2*v + 5*a - a - 4. Let f(u) = v*l(u) + 3*c(u). Factor f(g).
-3*(g - 1)**2*(g + 1)
Find s such that 2/3 + 8/3*s**4 - 2*s**3 - 10/3*s**2 + 2*s = 0.
-1, -1/4, 1
Suppose -6*x**3 - 5*x - x**5 + 4*x - 28*x**2 + 24*x**2 - 4*x**4 = 0. What is x?
-1, 0
Let n(a) be the third derivative of a**8/6720 + a**7/1260 - a**4/6 + 2*a**2. Let o(y) be the second derivative of n(y). Let o(u) = 0. What is u?
-2, 0
Let x = 25 - 25. Let u be ((-1)/3)/((-1)/6). Let x - 2/3*k**3 + 0*k**u + 2/3*k = 0. What is k?
-1, 0, 1
Factor -t**2 - 3*t**2 + 6*t**2 + 3*t - 2*t - 3*t**3.
-t*(t - 1)*(3*t + 1)
Let f(z) be the second derivative of z**5/18 - z**4/3 - 8*z**3/27 + 15*z. Suppose f(q) = 0. Calculate q.
-2/5, 0, 4
Let h(r) = 2*r**3 - r + 1. Suppose 5*l = -2*f - f + 13, 7 = 3*f + 2*l. Let m be h(f). Factor 2*c**2 + 2/3*c**3 + 2/3 + m*c.
2*(c + 1)**3/3
Let q = 20 + -6. Suppose a + 3*i - q + 2 = 0, 5*a = 2*i - 8. Factor 0*y - 2/3*y**2 + a.
-2*y**2/3
Let k(u) be the third derivative of 1/120*u**6 + 1/360*u**5 + 0*u**4 + u**2 + 0*u + 1/140*u**7 + 0 + 0*u**3. Factor k(d).
d**2*(3*d + 1)**2/6
Suppose 4/7*w**3 + 8/7 - 2/7*w**4 - 16/7*w + 6/7*w**2 = 0. Calculate w.
-2, 1, 2
Suppose n = 2*c + 1, 7*c = n + 3*c + 1. Let f = 6 - n. Find s such that 3*s**2 + s - 4*s**2 + 2*s**3 - 4*s**f = 0.
-1, 0, 1/2
Let n(f) = -f**3 - 3*f**2 + 3. Suppose -5 = 3*a + 4. Let u be n(a). Factor u*t**2 + 2*t - 6*t - 8*t**3 - t**3 + 9*t**2.
-t*(3*t - 2)**2
Let h = 6 + -4. Suppose -5*t = 15, h*w = -t - 4*t - 15. Let w*y - 3/2*y**3 + 0 + 1/2*y**2 = 0. Calculate y.
0, 1/3
Let d(c) be the third derivative of -2*c**7/105 + 2*c**6/15 - c**5/5 - 2*c**4/3 + 8*c**3/3 - 4*c**2. Determine q so that d(q) = 0.
-1, 1, 2
What is r in 16/23*r**2 - 14/23*r + 4/23 - 4/23*r**4 - 4/23*r**3 + 2/23*r**5 = 0?
-2, 1
Let a(m) be the second derivative of -m**7/231 + m**5/22 - 4*m**3/33 + m. Solve a(b) = 0.
-2, -1, 0, 1, 2
Suppose 3*l + 5*b - 16 = 0, 12 = 4*l + 5*b - 3*b. Suppose -2*y - j + 4 = 0, -4*y + 1 = -5*y - l*j. Factor z**4 + z**4 - 2*z**3 - 2*z**2 + 2*z + 0*z**y.
2*