 1)/3
Factor -3*c - 3/2*c**2 + 0 + 3/2*c**4 + 3*c**3.
3*c*(c - 1)*(c + 1)*(c + 2)/2
Factor 3*t**2 + 7*t**3 + 3 + 6*t**2 + 3*t + 6*t - 4*t**3.
3*(t + 1)**3
Suppose -w - 2 = 2*g, g + 0*g = -4*w + 6. Let b(m) be the first derivative of -2/3*m**w - 2/9*m**3 - 2/3*m - 1. Determine y, given that b(y) = 0.
-1
Let t(b) be the second derivative of -b**6/30 + b**5/20 - b**3/24 + b**2/2 + 5*b. Let k(h) be the first derivative of t(h). Solve k(v) = 0 for v.
-1/4, 1/2
Let q(a) be the third derivative of a**5/12 + 5*a**4/24 + 7*a**2. Factor q(s).
5*s*(s + 1)
Let n(p) = -p + 4. Let g be ((-8)/10)/(4/(-10)). Let a be n(g). Determine r, given that 4/5*r + 2/5*r**a + 2/5 = 0.
-1
Suppose 2*m = m. Let n(g) be the third derivative of 0*g**5 - g**2 + 1/63*g**7 + 0*g + 0*g**4 + 0*g**3 + 1/90*g**6 + m. Let n(v) = 0. Calculate v.
-2/5, 0
Factor -98*t - 3*t**2 + 143*t + 8*t**2.
5*t*(t + 9)
Let s(l) be the first derivative of -l**4/48 + l**3/6 - l**2/2 + l - 3. Let b(x) be the first derivative of s(x). Let b(z) = 0. Calculate z.
2
Let i(q) be the third derivative of -1/210*q**5 - 1/168*q**4 + 0*q + 1/735*q**7 + 0*q**3 + 0 + 1/2352*q**8 - 4*q**2 + 0*q**6. Factor i(k).
k*(k - 1)*(k + 1)**3/7
Let c(s) be the first derivative of s**6/300 + s**5/75 - s**4/15 - 8*s**3/15 + 5*s**2/2 + 1. Let r(i) be the second derivative of c(i). Let r(y) = 0. What is y?
-2, 2
Let y(w) be the first derivative of -1/9*w**6 - 3/2*w**4 - 2/3*w**2 + 4 + 0*w - 14/9*w**3 - 2/3*w**5. Let y(v) = 0. What is v?
-2, -1, 0
Let z(l) be the third derivative of -l**6/360 + l**5/180 + l**4/36 - 10*l**2. Factor z(x).
-x*(x - 2)*(x + 1)/3
Let w = -30/7 - -118/21. Factor -4*y + 3 + w*y**2.
(2*y - 3)**2/3
Let o(f) = -f**2 - 7*f - 4. Let n be o(-6). Suppose -3*i - 2*k + 8 = 0, 3*k + 18 = i + n*i. Suppose 0*q**i + q - 2*q**4 + q**5 - 2*q + 2*q**2 = 0. Calculate q.
-1, 0, 1
Let l(q) be the first derivative of -q**5/10 - 5*q**4/8 - 3*q**3/2 - 7*q**2/4 - q - 3. Determine j, given that l(j) = 0.
-2, -1
Let i(y) be the third derivative of -y**6/180 - y**5/45 - 4*y**2. Factor i(t).
-2*t**2*(t + 2)/3
Suppose -16*o - 12 = -19*o. Factor 0*k**2 - 2/9*k**3 + 2/3*k**o + 0*k + 0.
2*k**3*(3*k - 1)/9
Let k = 5/4 - 31/28. Let s(v) be the first derivative of -10/21*v**3 - 2/5*v**5 - 2/21*v**6 - k*v**2 - 9/14*v**4 + 3 + 0*v. Factor s(i).
-2*i*(i + 1)**3*(2*i + 1)/7
Let z(s) be the third derivative of -s**7/1155 - s**6/660 + s**5/165 - 11*s**2. Determine r so that z(r) = 0.
-2, 0, 1
Let m(o) be the first derivative of -o**4/10 - 2*o**3/15 + 2*o**2/5 - 38. Factor m(k).
-2*k*(k - 1)*(k + 2)/5
Let j(z) = z**5 - z**3 + z**2 + z + 1. Let b(w) = 2*w**5 - w**4 - 2*w**3 + 4*w**2 + 3*w + 3. Let g(o) = b(o) - 3*j(o). Factor g(f).
-f**2*(f - 1)*(f + 1)**2
Suppose 0 = 19*m + 2 - 97. Suppose -4/5*o**4 + 6/5*o**3 - 8/5*o + 8/5*o**2 - 2/5*o**m + 0 = 0. What is o?
-2, 0, 1
Let d = 12 - 7. Let z be 3/(d/(30/9)). What is p in -1/2*p**z + 1/2*p**3 + 0*p + 0 = 0?
0, 1
Factor -5*k + 15/4 + 5/4*k**2.
5*(k - 3)*(k - 1)/4
Let n(k) be the first derivative of -2*k**5/5 + k**4 - 2*k**2 + 2*k + 1. Factor n(r).
-2*(r - 1)**3*(r + 1)
Let l(b) = b - 2*b**2 + 8*b - 6 + 0 + b**2. Let n be l(8). Factor -5*v**3 + 3*v**3 + 0 + n*v**4 + 0.
2*v**3*(v - 1)
Let h = 21 - 13. Let s(r) be the third derivative of r**2 + 1/525*r**7 + 0*r**6 - 1/280*r**h + 0*r**4 + 0*r**3 + 0*r**5 + 0*r + 0. Factor s(k).
-2*k**4*(3*k - 1)/5
Find k such that 14*k**3 - 13*k**3 + 3 - 3 = 0.
0
Let m(n) = -6*n**2 + n + 9. Let q(j) = -j**2 + j. Let u(c) = -4*m(c) + 28*q(c). Factor u(r).
-4*(r - 3)**2
Determine o so that 4*o**4 + 0*o**4 + o**4 - 5*o**5 = 0.
0, 1
Let k be (-4)/6*6/(-2). Find w such that -8*w**3 - 7*w - w - 4*w**2 + 3*w**k - 19*w**2 = 0.
-2, -1/2, 0
Let l(m) be the first derivative of -m**3 + 0*m - 3/4*m**4 - 1/5*m**5 - 1/2*m**2 - 5. What is g in l(g) = 0?
-1, 0
Let f(z) = -7*z**3 + z**2 + 5*z + 5. Let a(g) = 2 + g**3 - 2 - g - 1. Let l(u) = -u**2 - 7*u - 1. Let o be l(-6). Let v(b) = o*a(b) + f(b). Factor v(r).
-r**2*(2*r - 1)
Factor -13/5*r - 4*r**2 - 2/5.
-(4*r + 1)*(5*r + 2)/5
Suppose 2*w = x - 4, -5*x = -3*w + 11 - 3. Let g(v) = v**3 - v - 1. Let z(f) = -46*f**3 - 6 - 17 - 92*f + 3 - 140*f**2. Let h(p) = w*g(p) + z(p). Factor h(d).
-2*(d + 2)*(5*d + 2)**2
Let u(j) = -j**4 + 1. Let h = 23 + -25. Let p(c) = -c**4 + 10*c**3 - 2*c**2 - 10*c + 3. Let v(q) = h*p(q) + 14*u(q). What is n in v(n) = 0?
-1, -2/3, 1
Find t, given that 4*t**3 + 0*t + 0*t - 8*t**2 + 4*t**2 = 0.
0, 1
Let w = 20 + -18. Let f = 4 - w. Solve 1/4*t**f - 1/4*t**3 + 0*t + 0 = 0 for t.
0, 1
Factor 1/4*n**3 + 0 - 1/2*n + 1/4*n**2.
n*(n - 1)*(n + 2)/4
Let a(f) be the first derivative of 21/5*f**5 + 2 + 0*f**2 + 6*f**4 - 49/6*f**6 + 0*f + 4/3*f**3. Factor a(r).
-r**2*(r - 1)*(7*r + 2)**2
Let w(r) be the third derivative of -3*r**7/175 + r**6/10 - 13*r**5/150 - r**4/3 - 4*r**3/15 + 8*r**2. Factor w(f).
-2*(f - 2)**2*(3*f + 1)**2/5
Let j(i) be the third derivative of -i**8/448 + i**7/105 - i**5/24 + i**4/32 + i**3/12 - 8*i**2. Determine x so that j(x) = 0.
-1, -1/3, 1, 2
Let v(q) = 8*q**5 + 7*q**4 - 47*q**3 + 41*q**2 + 2*q. Let t(j) = -3*j**5 - 2*j**4 + 16*j**3 - 14*j**2 - j. Let a(s) = 11*t(s) + 4*v(s). Factor a(p).
-p*(p - 3)*(p - 1)**3
Let m(v) = -3*v**3 + 19*v**2 - 11*v. Let k(r) = 2*r**3 - 10*r**2 + 6*r. Let s(i) = 11*k(i) + 6*m(i). Factor s(l).
4*l**2*(l + 1)
Let h(l) be the third derivative of 1/135*l**5 + 2*l**2 + 0 + 1/108*l**6 + 0*l + 0*l**4 + 0*l**3. Factor h(q).
2*q**2*(5*q + 2)/9
Let k(h) = -h**3 + 1. Let l(p) = p - 4. Let m be l(10). Let x(w) = -4*w**3 + w + 3. Let a(u) = m*k(u) - 2*x(u). Factor a(c).
2*c*(c - 1)*(c + 1)
Suppose 4/9 - 2/9*j - 2/9*j**2 = 0. What is j?
-2, 1
Let g be (-6)/1 + (-510)/(-60). Factor 0*d - d**2 - 1/2*d**5 - 2*d**4 - g*d**3 + 0.
-d**2*(d + 1)**2*(d + 2)/2
Let i(p) be the first derivative of 0*p**2 + 5 + 1/7*p**4 + 0*p**3 + 1/21*p**6 + 0*p + 6/35*p**5. Solve i(f) = 0.
-2, -1, 0
Let u = 3 - 3. Let f(r) be the third derivative of 1/210*r**5 + u - r**2 + 1/84*r**4 + 0*r**3 + 0*r. What is j in f(j) = 0?
-1, 0
Let q = 4 + -8. Let h be (-1 + (-5)/q)*2. Factor h + 3*v**2 - 2*v + 1/2*v**4 - 2*v**3.
(v - 1)**4/2
Suppose 0 = -h + 2*f + 3 + 3, 4*h - 6 = -f. Let y(r) = 2*r**2. Let k be y(-2). Determine o, given that 0*o**3 - 3*o**2 + o**h - k*o**4 + 10*o**3 = 0.
0, 1/4, 1
Let x(t) = 10*t - 27. Let d(q) = 3*q - 9. Let l(j) = -7*d(j) + 2*x(j). Let v be l(6). Factor -4 - 6*f + 4*f**3 + 4*f**2 + 4*f - 2*f**v.
2*(f - 1)*(f + 1)*(f + 2)
Let i(n) be the third derivative of -n**6/210 + n**5/35 - 12*n**2. Factor i(u).
-4*u**2*(u - 3)/7
Factor 0*m + 0 - 1/2*m**3 - 1/2*m**2.
-m**2*(m + 1)/2
Let a(i) be the second derivative of i**7/14 + i**6/5 + 3*i**5/20 + 7*i. Factor a(w).
3*w**3*(w + 1)**2
Let m be (1 + 1)*20/130. Suppose 2/13*d - 14/13*d**5 - 68/13*d**3 + 4*d**4 + 32/13*d**2 - m = 0. What is d?
-2/7, 1
Let f(l) = 2*l**2 + 29*l - 43. Let n(x) = 3*x**2 + 57*x - 87. Let h(v) = -9*f(v) + 5*n(v). Factor h(q).
-3*(q - 4)**2
Factor 6*k**2 - 1 + 11 - k**2 + 15*k.
5*(k + 1)*(k + 2)
Let b = -4 + 6. Factor 5*a + 5 + 68*a**2 - 1 - 41*a + 13*a**b.
(9*a - 2)**2
Let k(i) = 3*i**3 - 17*i**2 + 11. Let f(t) = 2*t**3 - 18*t**2 + 12. Let y(c) = -3*f(c) + 4*k(c). Factor y(m).
2*(m - 2)*(m - 1)*(3*m + 2)
Solve 10/3*k + 2/3 - 10/3*k**3 - 2/3*k**2 = 0 for k.
-1, -1/5, 1
Let z(f) be the third derivative of f**4/24 - f**3/6 + f**2. Let u(a) = -a**2 + 4*a - 1. Let d(g) = 2*u(g) - 6*z(g). Factor d(k).
-2*(k - 2)*(k + 1)
Let a be (-4)/6 + (-6)/(-36). Let t = 1 + a. Suppose 0*b - 1/2*b**2 - t*b**4 - b**3 + 0 = 0. What is b?
-1, 0
Factor -14/9*n**2 + 2*n**3 + 0 - 4/9*n.
2*n*(n - 1)*(9*n + 2)/9
Let z(b) be the first derivative of 0*b**2 + 2 + b - 1/3*b**3. Factor z(u).
-(u - 1)*(u + 1)
Let l be (-28)/(-12) - (-4)/6. Factor -l*o**2 + 0 + 5 + 6*o**3 - 5 - 3*o**4.
-3*o**2*(o - 1)**2
Let i = 254/305 + -2/61. Suppose -4*o = -5*o + 4. Find q, given that 4/5*q**3 + 2/5*q**o + 0*q**2 - 2/5 - i*q = 0.
-1, 1
Let q(o) be the third derivative of -2*o**7/245 + 13*o**6/280 - 3*o**5/28 + o**4/8 - o**3/14 - 3*o**2. Factor q(p).
-3*(p - 1)**3*(4*p - 1)/7
Suppose 4/3 + 2*x**3 - 2*x - 2/3*x**2 - 2/3*x**4 = 0. Calculate x.
-1, 1, 2
Let n(u) = -u**2 - 2*u + 4*u**2 - 3 - 2*u**2. Let d be n(-2). Find v, given that -2/5*v**3 - 2/5*v**d + 0 + 0*v + 0*v**2 