**2 - 6*q**2 + 4 + 18*q + p*q**3 + 8*q**3 + 8*q**2.
2*(q + 2)*(2*q + 1)**2
Suppose -9 = 8*h - 25. Factor 1/4*r**h + 0 + 1/4*r.
r*(r + 1)/4
Let o(m) = -10*m**3 - 4*m**2 - 5*m - 5. Suppose -l + 1 + 4 = 0. Let w(t) = -5*t**3 - 2*t**2 - 2*t - 2. Let r(u) = l*w(u) - 2*o(u). Factor r(p).
-p**2*(5*p + 2)
Let k(s) be the third derivative of s**7/2100 - s**6/900 - s**5/150 - s**3/2 - 4*s**2. Let l(o) be the first derivative of k(o). Find h, given that l(h) = 0.
-1, 0, 2
Suppose -16 = -4*x - 0*x. Suppose 0*g - 5*g + 2*g**2 + g - 2*g**x + 4*g**3 = 0. What is g?
-1, 0, 1, 2
Factor 0 - 48/7*x**2 + 6/7*x**3 + 96/7*x.
6*x*(x - 4)**2/7
Let v(o) = o**3 + 6*o**2 + 5*o + 2. Let z be v(-5). Let j = -1 + 2. Factor 1 - 2*s + s**z + j - s.
(s - 2)*(s - 1)
Let m(d) = d**2 + 5*d + 4. Let l be m(-5). Find f, given that -6*f**2 + 4*f**l + 9*f**3 - f - 7*f**4 + f = 0.
0, 1, 2
Let m(f) = f**2 - 3*f - 4. Let q be m(5). Suppose -q*b + 16*b = 20. Factor 0 + 3/5*o**b + 3/5*o.
3*o*(o + 1)/5
Let b(z) be the third derivative of z**6/160 - z**5/80 + 26*z**2. What is g in b(g) = 0?
0, 1
Let f(w) be the second derivative of w**5/10 - 2*w**4/3 + w**3 + 22*w. Factor f(k).
2*k*(k - 3)*(k - 1)
Let m(q) be the first derivative of 1/27*q**6 + 4/45*q**5 + 3 + 0*q**4 + 0*q - 4/27*q**3 - 1/9*q**2. Factor m(j).
2*j*(j - 1)*(j + 1)**3/9
Let b(k) = 10 + 4 - 4*k**3 - 3 - 5*k + 5*k**2. Let q(r) = 2*r**3 - 2*r**2 + 2*r - 6. Let l(w) = 4*b(w) + 7*q(w). Factor l(m).
-2*(m - 1)**3
Let v(a) be the second derivative of a**7/126 + a**6/90 - a**5/20 - a**4/36 + a**3/9 - a. Factor v(p).
p*(p - 1)**2*(p + 1)*(p + 2)/3
Let z = -980 + 983. Solve 2/17*o**z - 4/17*o - 2/17*o**2 + 0 = 0.
-1, 0, 2
Let q(k) be the first derivative of -2/15*k**3 + 1/30*k**6 + 3 + 2/25*k**5 + 0*k**4 - 1/10*k**2 + 0*k. Factor q(l).
l*(l - 1)*(l + 1)**3/5
Let n = 83 + -81. Let f(c) be the third derivative of -1/2*c**3 - 3*c**n + 1/20*c**5 + 0 - 1/8*c**4 + 0*c + 1/40*c**6. Factor f(d).
3*(d - 1)*(d + 1)**2
Let g(s) = -s + 3. Let a be g(-3). Let x = 10 - a. Determine c, given that 6*c - 2*c + 2*c**3 - x*c - 2*c**2 = 0.
0, 1
Let i(d) be the third derivative of -d**5/70 + 5*d**4/84 + 2*d**3/21 + 42*d**2. Factor i(j).
-2*(j - 2)*(3*j + 1)/7
Let x(r) be the first derivative of -2*r**3/9 - 2*r**2 - 6*r + 10. Suppose x(k) = 0. What is k?
-3
Suppose -143 = 2*m - 143. Solve 4/3*i**5 + m + 0*i + 0*i**2 + 1/3*i**3 - 5/3*i**4 = 0.
0, 1/4, 1
Let a(u) be the third derivative of 0*u - 1/39*u**3 - 1/39*u**5 - 5/156*u**4 - 1/273*u**7 + 0 + 3*u**2 - 1/2184*u**8 - 1/78*u**6. Factor a(l).
-2*(l + 1)**5/13
Suppose -5 = -8*l + 19. Solve -2/7 + 2/7*n**l + 2/7*n**2 - 2/7*n = 0.
-1, 1
Let i(b) be the second derivative of -16*b**6/75 + 12*b**5/25 + b**4/2 + 2*b**3/15 + 8*b. Determine p, given that i(p) = 0.
-1/4, 0, 2
Determine f so that 2*f - 3*f**2 - 2*f - 6 + 9*f = 0.
1, 2
Let j(v) = v**3 + v**2 - 1. Let b(z) = -3*z**3 - z**2 + 2*z + 1. Let f(u) = 2*b(u) + 2*j(u). Find n, given that f(n) = 0.
-1, 0, 1
Suppose j + 1 = 0, -4*h + 0*h - 79 = -5*j. Let l = h + 24. Factor 0 - 3/2*u - l*u**2 - 3/2*u**3.
-3*u*(u + 1)**2/2
Factor 3*o**3 - o - 47*o**4 - 3*o + 9*o**2 + 38*o**4 + 3*o**5 - 2*o.
3*o*(o - 2)*(o - 1)**2*(o + 1)
Let t(c) = -c**4 + 4*c - 1. Let z(d) = 4*d**4 - d**3 - 13*d + 3. Let m(r) = 21*t(r) + 6*z(r). Suppose m(a) = 0. What is a?
-1, 1
Let f(n) be the third derivative of n**5/30 + n**4/6 - 3*n**2. Find b such that f(b) = 0.
-2, 0
Let x(w) be the third derivative of -1/9*w**3 + 0*w + 3*w**2 + 0 - 1/315*w**7 - 1/9*w**4 - 1/45*w**6 - 1/15*w**5. Let x(p) = 0. Calculate p.
-1
Factor -1/6*r**5 + 4/3*r**2 - 1/3*r**4 + 7/6*r + 1/3*r**3 + 1/3.
-(r - 2)*(r + 1)**4/6
Factor 5*l**4 - 24*l**3 - 2*l**4 - 238*l**5 + 241*l**5 - 36*l**2.
3*l**2*(l - 3)*(l + 2)**2
Suppose 2*l - 7 = -3. Factor -3*g**3 + 6*g - 3*g**3 + 3*g**2 + 3*g**3 - 6*g**l.
-3*g*(g - 1)*(g + 2)
Let 0 - 1/2*o - o**4 + 1/2*o**5 + o**2 + 0*o**3 = 0. What is o?
-1, 0, 1
Let u(v) = v**2 + 6*v - 6. Let c be u(-7). Factor d**5 - d**4 - 1 + c.
d**4*(d - 1)
Suppose v - 4*w - 2 = 2*v, 0 = -v + w + 3. Factor 16*x**2 - 8*x**v + 3*x**3 - 6*x**2.
x**2*(3*x + 2)
Let a(s) be the second derivative of s**7/6 - 3*s**6/10 - s**5/4 + 3*s**4/4 - s**3/3 - 9*s. Factor a(r).
r*(r - 1)**2*(r + 1)*(7*r - 2)
Let i(a) be the third derivative of 0*a + 0*a**3 - 1/672*a**8 + 1/30*a**5 - 1/48*a**4 + a**2 + 1/105*a**7 + 0 - 1/40*a**6. Factor i(l).
-l*(l - 1)**4/2
Let 2/11*w**2 + 0 + 0*w + 2/11*w**4 - 4/11*w**3 = 0. What is w?
0, 1
Let f(n) = -5*n**4 - 6*n**2 - 8*n + 3. Let v(y) = 4*y**4 + y**3 + 6*y**2 + 7*y - 2. Let r(k) = 3*f(k) + 4*v(k). What is l in r(l) = 0?
-1
Let t(a) be the first derivative of 2*a**3/3 + a**2 - 6. Find b, given that t(b) = 0.
-1, 0
Suppose 5*o + 17 = -4*l, 2*l - 3*o - 7 = 6*l. Factor -i**2 - l*i + 2*i.
-i**2
Let x(l) be the third derivative of -l**8/1680 + l**7/2520 + l**6/180 - l**5/120 - l**4/24 + l**2. Let z(i) be the second derivative of x(i). Factor z(f).
-(f - 1)*(f + 1)*(4*f - 1)
Factor -14*b**3 - 208*b + 4*b**3 + 7*b**3 + 64 + 49*b**2.
-(b - 8)**2*(3*b - 1)
Suppose -162 + 158 = -c. Factor -1/3*k + 1/3*k**3 - 1/3*k**2 + 1/3*k**c + 0.
k*(k - 1)*(k + 1)**2/3
Let n be 4*8/(-96)*3/(-2). Let g be 5*(39/30 + -1). Factor g*j - n*j**2 - 1.
-(j - 2)*(j - 1)/2
Suppose 2 = u - 1. Let y(c) be the first derivative of -27/2*c**2 - 27*c + 3 - 1/4*c**4 - 3*c**u. Factor y(h).
-(h + 3)**3
Let u(a) = 2*a**2 + 14*a - 1. Let f be 4/(-6) - (-13)/(-3). Let k(x) = 9*x**2 + 69*x - 6. Let j(q) = f*k(q) + 24*u(q). Factor j(m).
3*(m - 2)*(m - 1)
Suppose 0 = -11*u + 5*u. Let q(l) be the third derivative of 4*l**2 - 1/6*l**3 - 1/60*l**5 - 1/12*l**4 + u + 0*l. Factor q(s).
-(s + 1)**2
Factor -8/9 - 8/9*i - 2/9*i**2.
-2*(i + 2)**2/9
Let a(l) be the third derivative of l**7/140 - l**6/18 + 7*l**5/45 - 2*l**4/9 + 7*l**3/6 - 6*l**2. Let k(s) be the first derivative of a(s). Factor k(v).
2*(v - 2)*(3*v - 2)**2/3
Let j(a) = a**2 - 3*a - 14. Let l be j(-3). Let y(t) be the first derivative of -3/4*t**l + 1/5*t**5 + t**3 + 3 + 0*t - 1/2*t**2. Solve y(h) = 0 for h.
0, 1
Let v = -7 + 10. Factor -4*k - k**3 + 2*k**3 + 0*k**2 - 2 + 3*k**v + 2*k**2.
2*(k - 1)*(k + 1)*(2*k + 1)
Let q(j) be the first derivative of 16*j**6/13 + 16*j**5/13 - j**4/2 - 8*j**3/39 + j**2/13 + 4. Solve q(n) = 0.
-1, -1/3, 0, 1/4
Let t = 4 - 4. Let h(k) be the second derivative of 0*k**3 + 1/50*k**5 + 2*k - 1/30*k**4 + 0*k**2 + t. Determine b, given that h(b) = 0.
0, 1
Find n, given that -2*n**2 + 47*n - 52*n + 5*n**3 + 5 - 3*n**2 = 0.
-1, 1
Suppose 4*c - 16 = 5*y - 3*y, -2*y = 4*c. Determine v, given that -2*v**2 + 0*v**2 + 0*v**2 + 4*v**c = 0.
0
Let w(h) = -6*h**3 + 2*h**2 - 12*h - 3. Let u(f) = 2*f**3 - f**2 + 4*f + 1. Let s(y) = -17*u(y) - 6*w(y). Determine t so that s(t) = 0.
-1, -1/2
Let -2/3*u**5 + 0*u + 0 - 2/3*u**4 + 2/3*u**2 + 2/3*u**3 = 0. Calculate u.
-1, 0, 1
Let f(b) be the first derivative of 9*b**4/14 + 68*b**3/21 + 4*b**2 - 16*b/7 + 3. Factor f(c).
2*(c + 2)**2*(9*c - 2)/7
Let z(a) be the second derivative of -a**5/4 + 25*a**4/12 - 20*a**3/3 + 10*a**2 - 16*a. Solve z(h) = 0.
1, 2
Let g(p) be the third derivative of 0 + 1/120*p**6 + 1/8*p**4 + 0*p - 1/6*p**3 - 1/20*p**5 + 5*p**2. Solve g(f) = 0.
1
Let q(m) be the second derivative of m**5/50 - m**4/15 + 7*m. Factor q(k).
2*k**2*(k - 2)/5
Let b(x) = -x**2 + 10*x - 6. Let k be b(8). Determine f, given that 0*f**3 + 3*f**4 - 3*f + 9*f**2 - k*f**3 + f**3 = 0.
0, 1
Let n(u) be the second derivative of -2*u + 1/3*u**4 + 32*u**2 - 16/3*u**3 + 0. Factor n(y).
4*(y - 4)**2
Suppose -6 = -3*t, -3*a - 3*t + t = -4. Factor -1/5*m**2 + a + 0*m.
-m**2/5
Suppose 2*z + 0 - 2 = -3*w, 0 = -5*w - 3*z + 4. Let s be -1 + -1 + 9/2 - 2. Solve 1/2*n**4 - s*n**w + 0 + 1/2*n**3 - 1/2*n = 0 for n.
-1, 0, 1
Let d(r) be the second derivative of -r**5/60 - r**4/36 - 3*r. Let d(m) = 0. Calculate m.
-1, 0
Let t be (9 - 4) + -3*1. Suppose -5*f = -t*f. Factor -2/3*j**3 + 2/3*j + f*j**2 + 0.
-2*j*(j - 1)*(j + 1)/3
Let m(t) be the third derivative of 1/84*t**4 - 5*t**2 + 1/210*t**5 + 0*t + 0 + 0*t**3. Factor m(u).
2*u*(u + 1)/7
Factor -1 + 38*k - 20*k + 2*k**3 + k**4 - 20*k.
(k - 1)*(k + 1)**3
Factor 2/11*r - 2/11*r**3 + 0*r**2 + 0.
-2*r*(r - 1)*(r + 1)/11
Suppose 3*j = 6 - 0. Let 0*n**4 - j*n**3 + 2*n - 7 + 7 - 2*n**2 + 2*n**4 = 0. Calcul