(i - 1)*(i + 1)/3
Let v(b) = -b**3 - 7*b**2 + 3. Let c be v(-7). Factor -m**3 + c*m**3 - m**3 + m - 2*m**2.
m*(m - 1)**2
Let f(o) = 2*o**2 + 2*o + 2. Let w(y) be the second derivative of y**3/6 - 8*y. Let d(k) = -2*f(k) + 12*w(k). Factor d(u).
-4*(u - 1)**2
Let u be 345/138 - 2/4. Let -5/2*i**3 + 1 + 0*i**4 + 1/4*i**5 - 15/4*i + 5*i**u = 0. What is i?
-4, 1
Suppose -j = 0, -4*j - 11 + 1 = -5*s. Let u be 24/s*4/36. Factor -2 - u*q - 2/9*q**2.
-2*(q + 3)**2/9
Let k(h) be the third derivative of -h**4/24 + 7*h**3/6 + 3*h**2. Let j be k(3). Factor -2/3*r**2 - 2*r**j - 2*r**3 + 0 - 2/3*r**5 + 0*r.
-2*r**2*(r + 1)**3/3
Let r = 5 + -3. Factor c**2 - 4 - c**2 + 2*c**2 + 6*c - 4*c**r.
-2*(c - 2)*(c - 1)
Suppose 5*x - n + 7 = 10, 2*n + 6 = 3*x. Factor -2/5*h**5 + 0*h**2 - 2/5*h + 4/5*h**3 + x + 0*h**4.
-2*h*(h - 1)**2*(h + 1)**2/5
Let v(w) be the first derivative of -3 + 1/4*w**4 + 0*w**2 + 1/6*w**3 + 0*w + 1/10*w**5. Let v(a) = 0. Calculate a.
-1, 0
Let p(k) be the second derivative of 2*k**7/21 + 4*k**6/15 - 2*k**4/3 - 2*k**3/3 + k - 1. Suppose p(f) = 0. What is f?
-1, 0, 1
Let z(x) be the first derivative of -x**5/20 - x**4/8 + x**2/4 + x/4 - 1. Factor z(n).
-(n - 1)*(n + 1)**3/4
Factor -3/7*o + 1/7*o**3 + 2/7 + 0*o**2.
(o - 1)**2*(o + 2)/7
Solve -3/7*c - 3/7*c**2 + 6/7 = 0.
-2, 1
Let w = -18/11 + 191/110. Let f(q) be the second derivative of 1/10*q**3 + 0 + 1/15*q**4 + q - w*q**2. Let f(i) = 0. What is i?
-1, 1/4
Let q = -14 + 71/5. Find j such that 1/5*j**3 + 3/5*j**2 + 3/5*j + q = 0.
-1
Let c(q) = -q**2 + 18*q - 30. Let a be c(16). Suppose -8/3*k + 3*k**3 - k**a + 4/3 = 0. What is k?
-1, 2/3
Let h be (-4)/(-8) + (-3)/(-2). Factor -4*b**h + 2*b**2 + 2*b**2 + 1 - b**2.
-(b - 1)*(b + 1)
Let n(c) be the first derivative of 2*c**5/25 + c**4/5 + 2*c**3/15 - 9. Factor n(h).
2*h**2*(h + 1)**2/5
Let p = -5 - -1. Let w be 1 - 5/((-25)/p). Determine h, given that -w*h**3 + 1/5*h**2 + 0 + 0*h = 0.
0, 1
Find b such that 5/6*b**2 + 1/3*b + 1/6*b**3 - 4/3 = 0.
-4, -2, 1
Factor 4*r**2 - 4*r + 2*r + r + 4*r**3 - 4 - 3*r.
4*(r - 1)*(r + 1)**2
Let s(g) be the third derivative of -g**8/1176 + g**7/735 + g**6/84 - g**5/210 - 2*g**4/21 - 4*g**3/21 - 5*g**2. Factor s(b).
-2*(b - 2)**2*(b + 1)**3/7
Let q(a) be the third derivative of 0 + 0*a**3 - 1/8*a**4 + 0*a + 1/10*a**5 - 1/40*a**6 + 4*a**2. Factor q(s).
-3*s*(s - 1)**2
Let o(j) be the second derivative of j**6/360 + j**5/120 + j**3/2 + j. Let q(k) be the second derivative of o(k). Factor q(z).
z*(z + 1)
Let g(v) be the second derivative of -2*v + 0 + 0*v**2 - 1/3*v**4 + 1/6*v**3. Factor g(q).
-q*(4*q - 1)
Let s = 61/21 - 5/21. Let j = -25/3 + 9. Suppose 0 - 4/3*v**2 + j*v - 14/3*v**3 - s*v**4 = 0. Calculate v.
-1, 0, 1/4
Let t(k) be the first derivative of -3/16*k**4 + 0*k + 0*k**2 + 3/20*k**5 - 1/24*k**6 + 2 + 1/12*k**3. Suppose t(l) = 0. Calculate l.
0, 1
Let r(w) be the second derivative of 2/21*w**3 + 0 + 0*w**2 + 2/35*w**5 + 5/42*w**4 - w + 1/105*w**6. Factor r(o).
2*o*(o + 1)**2*(o + 2)/7
Suppose -j - 6*j = -21. Factor -1/4*z**j + 0*z + 0 + 0*z**2.
-z**3/4
Let m be 16/(-20)*((-10)/44)/1. Factor -m*a**3 + 2/11 + 2/11*a - 2/11*a**2.
-2*(a - 1)*(a + 1)**2/11
Factor -2/5*v**3 + 2/5*v - 3/5*v**2 + 0 + 3/5*v**4.
v*(v - 1)*(v + 1)*(3*v - 2)/5
Let g = 12 - 10. Solve 4*x**g - x**2 + x - 3 - x = 0 for x.
-1, 1
Let r(j) be the third derivative of -j**5/90 - j**4/12 - 2*j**3/9 - 26*j**2. Factor r(k).
-2*(k + 1)*(k + 2)/3
Let n(w) = 3*w**5 - 5*w**4 + 2*w**3 + 2*w**2 + 2*w. Let o(q) = -30*q**5 + 51*q**4 - 21*q**3 - 21*q**2 - 21*q. Let p(y) = 21*n(y) + 2*o(y). Factor p(h).
3*h**4*(h - 1)
Let j = 5 + -5. Factor -3*s**3 + s**3 + 4*s**2 - 2*s + j*s.
-2*s*(s - 1)**2
Suppose -f - 11 = -5*c, c + 3*f = f. Find d such that 7*d**2 + 2 + 8*d**3 - 2*d**5 + 2*d**4 - 2*d - 3*d**2 - 8*d**c - 4*d**3 = 0.
-1, 1
Suppose 6*w = 4*w + 10. Suppose 3*b = -w + 8. Let -z**2 - b + 1 = 0. Calculate z.
0
Let c(i) = -i**3 - i**2 - i - 3. Let y be 4/(12/9) - 1. Let t(u) = -3*u**3 - 3*u**2 - 2*u - 7. Let f(d) = y*t(d) - 5*c(d). Determine w so that f(w) = 0.
-1, 1
Let z(o) = -o**2 - 9*o + 4. Let j be z(-9). Solve f - 3*f + j*f + 2*f**2 = 0 for f.
-1, 0
Let c(j) = 0*j**2 + 2*j**2 - j + j**2 - 4*j**2. Let o(d) = 2*d**2 + 7*d - 4. Let k(g) = -3*c(g) - o(g). Suppose k(i) = 0. Calculate i.
2
Let o = 9452/9 + -1050. Factor 0 + 2/9*r**5 + 8/9*r**2 + 4/3*r**3 + o*r + 8/9*r**4.
2*r*(r + 1)**4/9
Factor 3/5*u**2 - 3/5 + 0*u.
3*(u - 1)*(u + 1)/5
Factor 20 + 69*z**3 - 71*z**2 + 431*z**2 + 107*z + 58*z + 11*z**3.
5*(z + 4)*(4*z + 1)**2
Let v(c) be the second derivative of 0 - 1/42*c**4 + 1/70*c**5 + 0*c**3 - 2*c + 0*c**2. Factor v(b).
2*b**2*(b - 1)/7
Suppose 1 + 1 = m. Factor 3 + 17*x**m - 2 - x**2 + 8*x.
(4*x + 1)**2
Let f(b) be the third derivative of -b**10/90720 - b**9/15120 - b**8/6720 - b**7/7560 + b**4/24 - b**2. Let q(p) be the second derivative of f(p). Factor q(m).
-m**2*(m + 1)**3/3
Suppose 0 = t + 21 - 7. Let p be (3/4)/(t/(-56)). What is n in 2/3*n**p - 2/3*n**2 + 2/3 - 2/3*n = 0?
-1, 1
Factor -20*q**3 + 9*q**4 + 8*q**4 + 4*q**2 - 12*q**4 + 16*q**2.
5*q**2*(q - 2)**2
Let v be ((-4)/(-2))/(-19 - -23). Factor -v*j**2 + 2 + 0*j.
-(j - 2)*(j + 2)/2
Suppose -5*r + 13 = -5*s - 22, -2*r - 36 = 3*s. Let k be ((-12)/s)/((-4)/(-5)). Factor 1/2*n + 0 - k*n**2 - 1/2*n**4 + 3/2*n**3.
-n*(n - 1)**3/2
Let k = 2 - -1. Let a(t) = 2*t**3 - 3*t**3 - t**2 + 0*t**3 - 5*t**k. Let p(g) = 5*g**3 + g**2. Let v(j) = 4*a(j) + 5*p(j). Determine n so that v(n) = 0.
-1, 0
Let z(i) be the first derivative of i**8/1960 - i**7/588 + i**6/1260 + i**5/420 + i**3 - 3. Let k(r) be the third derivative of z(r). Factor k(p).
2*p*(p - 1)**2*(3*p + 1)/7
Suppose -3*g = 2*b - 24, 2*b = -3*g + 4*g. Let x(q) be the first derivative of -3/16*q**4 + 1/8*q**g - 1/4*q**3 + 3/20*q**5 - 4 + 0*q + 0*q**2. Factor x(l).
3*l**2*(l - 1)*(l + 1)**2/4
Let l be -4 + (-119)/(-13) + -5. Factor 0 + l*r**3 - 2/13*r**4 - 2/13*r + 2/13*r**2.
-2*r*(r - 1)**2*(r + 1)/13
Let j(g) be the third derivative of -g**6/10 + 11*g**5/30 + g**4/6 - 11*g**2. Factor j(r).
-2*r*(r - 2)*(6*r + 1)
Let a be 7*((-16)/(-7) - 2). Suppose 0 = -4*q + 2*q. Factor 2/9*t**4 + q*t**3 + 0*t - 4/9*t**a + 2/9.
2*(t - 1)**2*(t + 1)**2/9
Let u(t) = -t**3 - 6*t**2 - 5*t. Let p = 4 - -1. Suppose 0 = -0*r + 9*r - 54. Let k(s) = s**3 + 7*s**2 + 6*s. Let l(c) = p*k(c) + r*u(c). Factor l(w).
-w**2*(w + 1)
Let x(w) be the third derivative of w**9/7560 + w**8/3360 - w**7/1260 - w**6/360 - w**4/24 - w**2. Let d(b) be the second derivative of x(b). Factor d(h).
2*h*(h - 1)*(h + 1)**2
Let a(z) = 26*z**3 - 10*z**2 - 11*z - 5. Let q(i) = 27*i**3 - 9*i**2 - 12*i - 6. Let y = 14 + -9. Let g(n) = y*q(n) - 6*a(n). Factor g(t).
-3*t*(t - 1)*(7*t + 2)
Factor 8/3*d - d**2 + 1/3*d**4 - 2/3*d**3 - 4/3.
(d - 2)*(d - 1)**2*(d + 2)/3
Let r = -51 + 51. Factor 0 - 81/4*d**5 - 3/4*d**2 + r*d - 27/4*d**3 - 81/4*d**4.
-3*d**2*(3*d + 1)**3/4
Suppose -b = b. Factor 0*o + b*o**3 + 2/9*o**4 - 2/9*o**2 + 0.
2*o**2*(o - 1)*(o + 1)/9
Let i(j) = -j**2 + 5*j + 11. Let p(o) = -2*o**2 + 4*o + 12. Let a(b) = -4*i(b) + 3*p(b). Find h such that a(h) = 0.
-2
Suppose -4*y - y = -25. Suppose -2*q**3 + 2 + 2*q - 7 - 2*q**4 + 2*q**2 + y = 0. What is q?
-1, 0, 1
Let i(n) be the third derivative of -n**5/570 + n**4/114 - 17*n**2. Factor i(h).
-2*h*(h - 2)/19
Let k(x) be the third derivative of -x**5/120 - x**4/12 - x**3/3 - 7*x**2. What is q in k(q) = 0?
-2
Let p = 4 - -1. Factor 0*m - p*m**2 + 3*m + 2*m**2.
-3*m*(m - 1)
Let y(w) = 3*w**2 - 2*w - 1. Let z be y(-1). Suppose -a - z*a = 0. What is h in 1/4*h**5 + 0*h + 1/4*h**3 + a + 1/2*h**4 + 0*h**2 = 0?
-1, 0
Let k(f) be the first derivative of -f**3/6 - 15*f**2/4 - 7*f + 37. Factor k(a).
-(a + 1)*(a + 14)/2
Let c = 14 + -27/2. Solve 0 + 2*k**3 - 1/3*k - c*k**2 - 7/6*k**4 = 0 for k.
-2/7, 0, 1
Let o(t) be the third derivative of 4*t**7/315 + 7*t**6/180 - t**5/15 - 7*t**4/36 + 2*t**3/9 + 7*t**2. Determine m so that o(m) = 0.
-2, -1, 1/4, 1
Let y = -13 - -17. Suppose -3*g - 6 + 3*g**2 + 0*g + y*g + 6*g = 0. Calculate g.
-3, 2/3
What is x in 10*x**2 - 3*x**2 + 8*x**2 + 5*x**3 - 5*x**2 = 0?
-2, 0
Let 7*h**3 - 32*h + 12*h**2 - 2*h**3 + 16 + 4*h**3 - 4*h**4 - h**3 = 0. Calculate h.
-2, 1, 2
Let o be (-4)/6 - (-28)/6. Suppose -5 - 7 = -o*r. Factor -3*p +