*m**3 - 2/3*m**2 + 1/3.
-(m - 1)**3*(m + 1)**2/3
Let z(l) = -3*l**2 - 7*l - 2. Let j be z(-5). Let x be (-3)/12 - j/8. Determine y, given that 18*y**3 + y + y - 5*y**4 + 4*y**x - 9*y**4 - 10*y**2 = 0.
0, 1/2, 1
Let x(h) be the third derivative of 0 + h**2 + 0*h - 1/84*h**7 - 1/6*h**3 + 11/48*h**4 + 17/240*h**6 - 7/40*h**5. Let x(i) = 0. What is i?
2/5, 1
Find f such that 31*f**2 + 2*f + 9 - 2*f - 32*f**2 = 0.
-3, 3
Let i(w) be the third derivative of -w**2 + 0*w**3 + 0 + 1/840*w**7 + 1/160*w**6 + 0*w + 1/80*w**5 + 1/96*w**4. Factor i(r).
r*(r + 1)**3/4
Let w(a) be the first derivative of 3/5*a**2 + 0*a - 3/20*a**4 + 1/5*a**3 + 2. Factor w(z).
-3*z*(z - 2)*(z + 1)/5
Suppose -j = -5*k + 1 - 18, 0 = -3*j - 2*k. Factor 14/9*s**j + 4/9 - 2*s.
2*(s - 1)*(7*s - 2)/9
Solve 5*q**3 - 3*q**3 - 3*q - 4*q**2 + 5*q = 0.
0, 1
Let o(g) be the first derivative of 5/4*g**3 - 3/2*g + 9/8*g**4 - 9/8*g**2 - 3. Solve o(z) = 0 for z.
-1, -1/2, 2/3
Suppose b - 3*b - 3*j = 5, 0 = 5*b - 3*j - 19. Let w be b/(-6)*(-5)/5. Factor 0 + 1/3*p**5 - 1/3*p**3 + w*p**2 + 0*p - 1/3*p**4.
p**2*(p - 1)**2*(p + 1)/3
Factor 0 - 8/5*g**2 - 6/5*g - 2/5*g**3.
-2*g*(g + 1)*(g + 3)/5
Let v(i) be the third derivative of -i**5/105 - i**4/21 - 2*i**3/21 - 5*i**2. Factor v(u).
-4*(u + 1)**2/7
Solve -2/7*y + 6/7*y**2 + 2/7*y**3 - 2/7*y**4 - 4/7 = 0.
-1, 1, 2
Let b(i) = i - 10. Let n be b(13). Determine u so that -26*u**2 - 8*u - 1 + 6 - 10*u**n + 3 = 0.
-2, -1, 2/5
Suppose 0 = 4*x + 2*x - 3*x. Factor 0 + 0*g**3 - 1/3*g**4 + x*g + 1/3*g**2.
-g**2*(g - 1)*(g + 1)/3
Determine u, given that 95*u**3 + 66*u**2 + 12*u - 28*u**2 + 127*u**2 + 33*u + 15*u**4 = 0.
-3, -1/3, 0
Suppose 4*b - 7 = 9. Find u such that -3 + 6 - 2*u - 6 - 3*u**2 - b*u = 0.
-1
Let j be (0 - -1)/(2/4). Suppose j*d + 14/5*d**2 - 4/5 = 0. Calculate d.
-1, 2/7
Let 144*r + 162 + 592 + 542 + 4*r**2 = 0. What is r?
-18
Let a be (-9)/2*(15 - 13). Let o be a/(-6) + (-22)/(-12). What is j in -o*j**2 - 16/3*j - 2/3*j**3 - 8/3 = 0?
-2, -1
Let g(c) be the first derivative of -c**4/4 + 2*c**3/3 - c**2/2 + 6. Factor g(p).
-p*(p - 1)**2
Let z(a) = -12*a + 1. Let x be z(-1). Factor 90*w**2 + 18*w - 6*w + 36*w + 8 + 63*w**3 - x*w**3.
2*(w + 1)*(5*w + 2)**2
Let p(y) be the third derivative of -y**5/30 + y**4/4 + 3*y**2. Factor p(f).
-2*f*(f - 3)
Let c be (-88)/(-28) + (-3)/21. Factor -8/5*i**4 - 8/5 + 24/5*i - 24/5*i**c - 2/5*i**2.
-2*(i + 2)**2*(2*i - 1)**2/5
Let f be (-2)/28*(3 + -7). Factor 0 - 4/7*o + 2/7*o**2 + f*o**3.
2*o*(o - 1)*(o + 2)/7
Suppose 4*k - 20 = -k. Let j be 5/20 + 1/k. Factor -1/2 - w - j*w**2.
-(w + 1)**2/2
Suppose -15 - 111 = -9*m. Let -8/5*o + 0 - 52/5*o**2 - m*o**3 + 49/5*o**4 = 0. What is o?
-2/7, 0, 2
Let v(y) be the first derivative of y**4/24 + 2*y**3/9 + y**2/3 + 11. Factor v(f).
f*(f + 2)**2/6
Let r(t) = -t**3 + 5*t**2 + t - 1. Let w be r(5). Factor 3*p**3 + 6*p**4 - w*p**2 - 2 - 6*p + p**5 + p**5 + p**3.
2*(p - 1)*(p + 1)**4
Let h(x) be the first derivative of x**6/63 + 2*x**5/105 - x**4/21 - 4*x**3/63 + x**2/21 + 2*x/21 + 25. Factor h(j).
2*(j - 1)**2*(j + 1)**3/21
Suppose -3*l - 54 = -7*l - 2*f, 0 = -l - 3*f + 6. Suppose 0 = 3*d + 2*d - l. Find b such that -5*b**2 - 1 + 3*b - 3 + b**d + 0*b**3 + 5*b = 0.
1, 2
Let r be (-34)/(-8) - 2/8. Let n be r/(-3)*(-6)/2. Factor -6 + a**2 - a**5 + 6 + a**3 - a**n.
-a**2*(a - 1)*(a + 1)**2
Let u(r) = 6*r**2 - 19*r - 25. Let a(w) = -w**2 + 3*w + 4. Suppose -1 - 23 = -4*m. Let f(g) = m*u(g) + 39*a(g). Factor f(t).
-3*(t - 2)*(t + 1)
Let m(k) = 5*k**4 - 3*k**3 - 2*k**2 + 4*k. Let o(z) = -4*z**4 + 2*z**3 + 2*z**2 - 3*z. Let a(p) = -3*m(p) - 4*o(p). Factor a(d).
d**2*(d - 1)*(d + 2)
Let b(i) be the first derivative of i**6/10 - 6*i**5/25 + 2*i**3/5 - 3*i**2/10 + 2. Factor b(z).
3*z*(z - 1)**3*(z + 1)/5
Let q(u) be the first derivative of 12*u**5/5 + 15*u**4 + 33*u**3 + 30*u**2 + 12*u - 7. Factor q(j).
3*(j + 2)**2*(2*j + 1)**2
Let q(r) be the first derivative of r**7/280 - r**6/60 - r**5/40 + r**4/4 - 5*r**3/3 - 5. Let x(u) be the third derivative of q(u). Factor x(s).
3*(s - 2)*(s - 1)*(s + 1)
Let w(i) be the second derivative of 0 - 1/9*i**4 - 1/60*i**5 - 2/9*i**3 + 0*i**2 + 3*i. What is j in w(j) = 0?
-2, 0
Let t(n) be the second derivative of n**5/5 - 10*n**4/3 + 50*n**3/3 + 16*n. Factor t(d).
4*d*(d - 5)**2
Let p be (-1 + (-1)/(-2))/(-1). Let s(z) be the second derivative of -1/8*z**4 + p*z**3 + 0 + z - 3/4*z**2. Factor s(t).
-3*(t - 1)**2/2
Factor 0 + 0*p + 0*p**2 + 2/3*p**3.
2*p**3/3
Let g = -17 + 23. Let t(u) be the third derivative of 1/840*u**7 + 1/480*u**g - 2*u**2 + 0*u + 0 + 0*u**3 - 1/96*u**4 - 1/240*u**5. What is j in t(j) = 0?
-1, 0, 1
Let x(y) be the third derivative of -y**5/240 + y**4/48 - y**3/24 - 2*y**2. Determine h, given that x(h) = 0.
1
Suppose -4*z = 34 - 2. Let g = -3 - z. Solve 5*f**2 - 6*f**4 + 15*f**g - 18*f + 27*f**3 + 19*f**3 - 43*f**5 + 4 - 3*f**2 = 0 for f.
-1, 2/7, 1/2, 1
Let y = 256 - 254. Determine j so that 1/2*j**y - 3/4*j**3 + 0*j + 0 - 5/4*j**4 = 0.
-1, 0, 2/5
Let c be 2 + -7 - 996/(-192). Let h(q) be the first derivative of c*q**4 - 1/4*q**3 + 0*q - 2 - 3/8*q**2 + 3/20*q**5. Determine u so that h(u) = 0.
-1, 0, 1
Let p(t) be the first derivative of 1 - 4/3*t**2 + 2/9*t**3 + 8/3*t. Find q such that p(q) = 0.
2
Let t(o) be the third derivative of 5*o**8/336 + o**7/6 + 5*o**6/12 - o**5/6 - 55*o**4/24 - 25*o**3/6 + 11*o**2. Factor t(s).
5*(s - 1)*(s + 1)**3*(s + 5)
Factor -1/2 - 1/2*m + 1/2*m**3 + 1/8*m**4 + 3/8*m**2.
(m - 1)*(m + 1)*(m + 2)**2/8
Let o = -2/27 - -176/189. Suppose -2/7 + 2/7*q**3 + o*q - 6/7*q**2 = 0. What is q?
1
Factor -10 - 33*o**3 - 3*o**5 + 19*o**3 - 6*o**5 + 26*o**4 + 31*o - 24*o**2.
-(o - 1)**4*(9*o + 10)
Factor 4*x**2 - x**2 + 670*x - 676*x + 3*x**3.
3*x*(x - 1)*(x + 2)
Let k be 0 + 17 + (17 - 18). Suppose 0 = -5*w - 3*p + 18, -3*w + k = 2*w + p. Factor 1/3*o**5 + 2/3*o**4 + 1/3*o**w + 0 + 0*o + 0*o**2.
o**3*(o + 1)**2/3
What is w in 48*w**4 - 44*w + 154*w**3 - 1 + 291*w**2 + 152*w + 13 + 62*w**3 = 0?
-2, -1/4
Suppose -18*z = -17*z. Let c be (-4)/(-6)*(-12)/(-32). Find k such that z*k**3 + 0*k - 1/2*k**2 + 1/4*k**4 + c = 0.
-1, 1
Let h(t) be the first derivative of t**5/55 - t**4/11 + 4*t**3/33 - 35. Factor h(y).
y**2*(y - 2)**2/11
Let r(i) = 2*i - 34. Let f be r(19). Let u(h) be the first derivative of 1/6*h**3 + 1/10*h**5 + 0*h + 1/4*h**f - 2 + 0*h**2. Factor u(y).
y**2*(y + 1)**2/2
Let k be 5 - (((-10)/(-15) - 0) + 3). Find f, given that -k - 4/3*f - 1/3*f**2 = 0.
-2
Let u = 22 - 47. Let d be (-3)/5*u/30. Factor 0*b**2 + 0 - d*b**3 + 1/2*b.
-b*(b - 1)*(b + 1)/2
Factor -16 + z**3 - 32*z - 4*z**3 - z**3 + 0 - 20*z**2.
-4*(z + 1)*(z + 2)**2
Let g = -9/10 - -16/15. Let d(j) be the first derivative of -1/2*j + 1/2*j**2 - 3 - g*j**3. Let d(m) = 0. Calculate m.
1
Let z(c) be the third derivative of c**8/1260 - c**7/315 + c**6/270 - c**3/6 - 9*c**2. Let o(t) be the first derivative of z(t). Factor o(d).
4*d**2*(d - 1)**2/3
Let w(k) be the third derivative of 0*k**3 + 5*k**2 + 1/20*k**5 + 0 + 1/40*k**6 + 0*k**4 + 0*k. Factor w(v).
3*v**2*(v + 1)
Suppose 3*o - 2 = 2*o, 13 = 5*b + 4*o. Let l = 2 + b. Suppose 3*h + 2*h**l + 4*h**2 + 0*h - h = 0. Calculate h.
-1, 0
Let q = 2/127 - -240/889. Suppose q*y**2 + 2/7*y - 2/7 - 2/7*y**3 = 0. Calculate y.
-1, 1
Factor 4/11*p + 0 - 2/11*p**2 - 2/11*p**3.
-2*p*(p - 1)*(p + 2)/11
Factor j**2 - 5*j + 0 + 0 + 0*j.
j*(j - 5)
Let t(g) be the first derivative of g**6/24 - 3*g**5/20 + 3*g**4/16 - g**3/12 + 10. Solve t(i) = 0 for i.
0, 1
Factor -8/11*l + 0 + 10/11*l**2 - 2/11*l**3.
-2*l*(l - 4)*(l - 1)/11
Suppose -3*u - 13 = -4*a, -4*a + 12 = -4*u - 4. Suppose -a = -o + 2. Factor -1/3*p**o + 4/3*p**2 + 0 - 4/3*p.
-p*(p - 2)**2/3
Suppose r = -0*r + 3. Solve 9*y - 6*y**2 - 5*y - y**r + 3*y**3 = 0.
0, 1, 2
Let j(z) = -2*z**2 - 7*z + 6. Let m be j(-4). Suppose 0*h**3 + 0*h**m - 1/2*h**5 - 1/2*h**4 + 0*h + 0 = 0. Calculate h.
-1, 0
Let l(b) = -b**2 - b + 1. Let n(k) = 2*k**2 + 6*k. Let r(m) = 4*l(m) + n(m). Find q such that r(q) = 0.
-1, 2
Let u(i) be the third derivative of i**6/10 + 8*i**5/15 - i**4/2 - 15*i**2. Factor u(n).
4*n*(n + 3)*(3*n - 1)
Factor -162/5*b**4 + 0 + 18*b**3 + 64/5*b**2 + 8/5*b.
-2*b*(b - 1)*(9*b + 2)**2/5
Solve -24*i**2 - 16*i**4 + 13*i**3 - 8*i**3 + 4*i + 31*i**3 = 0 for i.
0