10 - 2*k**2. Factor n(f).
f**2*(f + 2)*(4*f - 1)/7
Let n(r) be the first derivative of r**6/51 + 11. Suppose n(l) = 0. What is l?
0
Let l(f) = -2*f - 9*f**3 + 11 + 72*f**2 + 2*f - 59*f**2. Let s(t) = 6 - 2*t**2 + 5*t**2 + 4*t**2 - 5*t**3. Let m(w) = -6*l(w) + 11*s(w). Factor m(x).
-x**2*(x + 1)
Suppose 3*a + 2*g + 4 = 0, 11 + 1 = 2*a + 5*g. Let c(w) = -2*w**2 + 6. Let s(t) = -4*t**2 + 13. Let h(o) = a*s(o) + 9*c(o). Find z, given that h(z) = 0.
-1, 1
Find v, given that 4*v**4 + 4*v - 6*v + 4*v - 2*v**5 - 4*v**2 = 0.
-1, 0, 1
Suppose 4*h - h - 3*q = 18, 0 = 4*q + 12. Let u(i) be the first derivative of 0*i**2 + 1 - 3/2*i**4 + 0*i - 2/3*i**h - 1/3*i**6 - 6/5*i**5. Factor u(k).
-2*k**2*(k + 1)**3
Factor 0*p**2 + 0 - 4/9*p**4 + 0*p**3 + 0*p - 2/3*p**5.
-2*p**4*(3*p + 2)/9
Let a(s) be the first derivative of s**5/110 + s**4/33 + 2*s + 3. Let q(n) be the first derivative of a(n). Factor q(j).
2*j**2*(j + 2)/11
Let w = -14 - -16. What is h in 0*h - 4*h**w - 4*h + 14 + 4*h**3 - 10 = 0?
-1, 1
Let x(g) be the second derivative of 7*g**6/720 + g**5/48 - g**4/24 - 7*g**3/6 + 3*g. Let s(l) be the second derivative of x(l). Determine t so that s(t) = 0.
-1, 2/7
Let a(h) = h**3 - 4*h**2 + 4*h. Let t be a(3). Find d such that -2*d**2 + 5*d**2 + 3*d**t + d**2 + 2*d**2 + 3*d = 0.
-1, 0
Let p(b) be the second derivative of -1/24*b**4 + 0 - 1/12*b**3 + 1/40*b**5 + 0*b**2 - 2*b + 1/60*b**6. Factor p(w).
w*(w - 1)*(w + 1)**2/2
Factor -16/11*c**3 + 2/11*c**2 + 0 + 4/11*c + 10/11*c**4.
2*c*(c - 1)**2*(5*c + 2)/11
Factor 0*y - 2/3*y**2 + 1/3*y**4 - 1/3*y**3 + 0.
y**2*(y - 2)*(y + 1)/3
Let q(h) be the third derivative of h**7/630 - h**6/72 - 7*h**5/180 + 5*h**4/72 + h**3/3 - 25*h**2. Factor q(c).
(c - 6)*(c - 1)*(c + 1)**2/3
Let i(h) be the first derivative of -2*h**5/5 + 2*h**3/3 + 3. Factor i(k).
-2*k**2*(k - 1)*(k + 1)
Let n = -1016 - -1019. Suppose 0*b - 3/5*b**2 + 0 + 3/5*b**n = 0. Calculate b.
0, 1
Let -4*g**4 - 4*g**2 + 2*g**2 - 4*g + 2*g**5 + 6*g**2 + 2*g = 0. What is g?
-1, 0, 1
Factor f**3 + 1/3*f + 0 - f**2 - 1/3*f**4.
-f*(f - 1)**3/3
Let b(a) be the second derivative of 0*a**2 - 1/18*a**4 + 0 + 0*a**3 + 7*a. Factor b(p).
-2*p**2/3
Let y(w) be the third derivative of 0*w - 2/525*w**7 - 1/120*w**4 - 1/100*w**6 - 1/75*w**5 + 0*w**3 - 3*w**2 - 1/1680*w**8 + 0. Factor y(g).
-g*(g + 1)**4/5
Let y(w) be the first derivative of -4/3*w**3 - 8*w + 4 - 6*w**2. Factor y(m).
-4*(m + 1)*(m + 2)
Let g(h) be the third derivative of -7*h**5/24 - 17*h**4/48 - h**3/6 - 7*h**2. Factor g(y).
-(5*y + 1)*(7*y + 2)/2
Let u(k) = k - 5. Let v be u(5). Solve v - 2*m**2 - 2 + 2 = 0.
0
Let q = -11 - -11. Let h(r) be the third derivative of 1/240*r**5 + 0*r**6 - 1/840*r**7 + 0*r**3 + 0*r**4 + 0 - 2*r**2 + q*r. Factor h(w).
-w**2*(w - 1)*(w + 1)/4
Let m(d) be the third derivative of 0*d**3 + 1/35*d**7 + 1/30*d**5 + 0*d + 5*d**2 - 1/168*d**8 - 1/20*d**6 + 0*d**4 + 0. Factor m(w).
-2*w**2*(w - 1)**3
Suppose -2/3 + 2*p**3 - 2*p + 2/3*p**2 = 0. Calculate p.
-1, -1/3, 1
Let t(h) be the third derivative of 0*h - 1/210*h**5 + 1/84*h**4 + 0 + 5*h**2 + 0*h**3. Factor t(w).
-2*w*(w - 1)/7
Let v(m) be the third derivative of -1/120*m**4 + 9*m**2 + 2/525*m**7 + 0*m**3 + 0 - 1/100*m**6 + 1/75*m**5 - 1/1680*m**8 + 0*m. Find u such that v(u) = 0.
0, 1
Let i(w) = w + 2. Let h be i(-2). Suppose h*d - 3*d + 6 = 0. Factor 21*t**3 + 12*t**d + 4*t**2 - 2*t**4 + 11*t**4 + 4*t.
t*(t + 1)*(3*t + 2)**2
Let t(g) = g**3 - 4*g**2 - 6*g + 5. Let j be t(5). Suppose -4*h - b + 7 = j, 2*b + 0*b = 4*h - 22. Factor 0*s**2 + 0 - 2/5*s**h + 2/5*s**4 + 0*s.
2*s**3*(s - 1)/5
Let w(g) = 4*g**2 - 2*g - 6. Suppose -3*r = -r - 2. Let l(h) = -h**2 + 1. Let a(n) = r*w(n) + 6*l(n). Solve a(b) = 0 for b.
-1, 0
Let l(m) = -8*m**5 + 4*m**3 + 6*m**2 + 4*m - 6. Let u(y) = y**5 - y**2 - y + 1. Let s(j) = l(j) + 6*u(j). Factor s(x).
-2*x*(x - 1)**2*(x + 1)**2
Let t(z) = 10*z**4 + 12*z**3 - 8*z**2 - 4*z. Suppose 0 = 2*c - n + 5, 0*c + 4*n - 4 = 4*c. Let u(o) = o**3 + o. Let g(d) = c*u(d) - t(d). Factor g(h).
-2*h**2*(h + 2)*(5*h - 2)
Find l, given that -2/11*l**3 + 2/11*l**4 + 0 - 4/11*l**2 + 0*l = 0.
-1, 0, 2
Let m(o) = 3*o - 16. Let j be m(11). Solve -24*d - 7*d**3 + 6*d**2 + 5 + 3 + j*d**3 = 0 for d.
-2, 2/5, 1
Suppose t = -3 + 5. Let x(h) be the second derivative of 1/30*h**4 + 4/15*h**3 + 4/5*h**2 + 0 + t*h. Determine n so that x(n) = 0.
-2
Let z(n) be the third derivative of -n**9/15120 + n**8/6720 + n**4/6 + n**2. Let k(v) be the second derivative of z(v). Solve k(t) = 0 for t.
0, 1
Let l(a) = -2*a**2 - 4*a - 5. Let u(o) = 2*o**2 + 4*o + 4. Let q(x) = -2*l(x) - 3*u(x). Solve q(r) = 0.
-1
Let c(a) be the third derivative of -a**7/630 + 7*a**5/180 - a**4/12 - 44*a**2. Factor c(s).
-s*(s - 2)*(s - 1)*(s + 3)/3
Let m(b) be the second derivative of 0 - b**2 + 1/2*b**3 - 2*b - 1/12*b**4. Find g such that m(g) = 0.
1, 2
Factor 3*x - 2*x**2 + 0*x**2 - 11*x - 16 + x**2.
-(x + 4)**2
Find c, given that -32/7*c + 104/7*c**2 + 4*c**3 + 0 = 0.
-4, 0, 2/7
Suppose 4*l - 6 = 2. Let a = 5 - l. Suppose 0 + 2/9*w**2 + 2/9*w**a + 0*w = 0. Calculate w.
-1, 0
Let k = 14 - 12. Suppose 2*q - 4*j - 14 = 0, 10 = 3*q + 3*j + 2*j. Solve 1/4*a - 5/4*a**3 - 3/4*a**4 + 3/4*a**k + a**q + 0 = 0.
-1, -1/4, 0, 1
Let m(y) be the first derivative of -2/33*y**3 + 2/55*y**5 + 0*y**2 + 1 + 0*y**4 + 0*y. Factor m(k).
2*k**2*(k - 1)*(k + 1)/11
Factor 0 - 5/2*a - 5/6*a**2.
-5*a*(a + 3)/6
Let l(d) be the third derivative of d**8/112 - 9*d**7/70 + 23*d**6/40 - 7*d**5/20 - 3*d**4 + 8*d**3 - 48*d**2. Suppose l(s) = 0. Calculate s.
-1, 1, 4
Let o be -1 - (3 - 5 - -1). Suppose o*v**2 - v**2 + 4 + 3*v**2 - 2*v + 8*v = 0. Calculate v.
-2, -1
Factor -4/5*k**2 + 0*k - 6/5*k**3 - 2/5*k**4 + 0.
-2*k**2*(k + 1)*(k + 2)/5
Let w(u) be the second derivative of 1/28*u**4 + 0*u**2 + 0 - 1/14*u**3 + 2*u. Factor w(r).
3*r*(r - 1)/7
Let d = -4 + 12. Suppose -d*r = -r. Let 1/2*i**3 - 1/2*i + 0 + r*i**2 = 0. Calculate i.
-1, 0, 1
Let s(d) = -3*d**4 + 5*d**3. Let j(t) = -20*t**4 + 35*t**3. Let h(q) = -2*j(q) + 15*s(q). Solve h(y) = 0.
0, 1
Let i(w) = w**3 + 3*w**2 - 3*w. Let p be i(-4). Let k be (-4)/2*p/36. Find a, given that k*a**3 - 2/9*a**2 + 0*a + 0 = 0.
0, 1
Suppose 3*s = 19*y - 16*y - 12, -y + 4 = s. Factor 0*a**3 + 1/6*a**y - 1/6*a**2 + 0 + 0*a.
a**2*(a - 1)*(a + 1)/6
Let -135/2*l**2 + 0 - 135/4*l - 45*l**3 - 10*l**4 = 0. Calculate l.
-3/2, 0
Suppose -4*u = y + 20, -14*u + 9*u - 25 = -3*y. Factor 0*s**2 - 2/3*s**3 + 0 + y*s.
-2*s**3/3
Let a(v) = -v**2 + v. Let x(o) = 6*o**2 - 3*o. Let r(u) = -3*a(u) - x(u). Determine b so that r(b) = 0.
0
Let d(v) be the third derivative of v**7/210 + v**6/40 - v**4/6 - 9*v**2. Find c such that d(c) = 0.
-2, 0, 1
Factor 3/2*c + 0 - 3/2*c**2.
-3*c*(c - 1)/2
Let o(w) be the first derivative of 3*w**5/25 + w**4/20 - 2*w**3/5 - 3*w**2/10 - 2*w - 2. Let b(m) be the first derivative of o(m). Factor b(c).
3*(c - 1)*(c + 1)*(4*c + 1)/5
Let n(c) = c**2 - 2*c - 4. Let v be n(4). Let u = 3 + 0. Factor 7*j**4 - 7*j**v + j**u - j**5.
-j**3*(j - 1)*(j + 1)
Let i(m) = m**2 + 37 - 28 - 28 + 11*m. Let x(g) = -4*g + 3 + 0 + 3. Let r(o) = -2*i(o) - 7*x(o). Factor r(h).
-2*(h - 2)*(h - 1)
Let d = -75/2 + 387/10. Find m such that 2/5*m**2 + 4/5 + d*m = 0.
-2, -1
Let d be ((-2)/(-10))/((-5)/(-5)). Let y(r) be the first derivative of -1 + 2/15*r**3 + d*r**2 + 0*r. What is n in y(n) = 0?
-1, 0
Let h be ((-272)/680)/(6/(-20)). Factor -1/3*b**2 - 1 + h*b.
-(b - 3)*(b - 1)/3
Find p such that -35*p**3 - 60*p**4 + 2*p - 4*p - 40*p**2 - 60*p**3 - 3*p = 0.
-1, -1/3, -1/4, 0
Let j(z) be the third derivative of z**6/180 - z**5/45 - z**4/12 - 19*z**2. Find a, given that j(a) = 0.
-1, 0, 3
Let l(m) be the first derivative of 0*m - 1/16*m**4 - 1/8*m**2 + 1 + 1/6*m**3. Determine k so that l(k) = 0.
0, 1
Let s be (-2)/(1 + 15/(-9)). What is n in n**4 - 14*n**s - 4*n**2 - n**4 - 6*n**4 = 0?
-2, -1/3, 0
Let u(m) be the third derivative of m**6/180 - m**5/30 + m**4/12 + m**3/2 + 2*m**2. Let n(b) be the first derivative of u(b). Find x, given that n(x) = 0.
1
Let m(g) be the third derivative of -g**5/270 + g**4/27 - 4*g**3/27 - 3*g**2. Factor m(b).
-2*(b - 2)**2/9
Let r = 16 + -16. Let b(a) be the second derivative of 0*a**4 + a + 0*a**3 + 1/70*a**5 + r + 0*a**2. Factor b(o).
2*o**3/7
Let t(j) 