0*r**3 + 0*r + 0*r**4 + 0 - 4*r**2. Factor q(a).
-3*a**4*(5*a + 2)
Let t(l) be the first derivative of 5*l**4/12 - 25*l**3/9 + 35*l**2/6 - 5*l + 20. Factor t(o).
5*(o - 3)*(o - 1)**2/3
Factor -1/9 + 0*t + 1/9*t**2.
(t - 1)*(t + 1)/9
Suppose 5*w - 3*w = -6. Let p be (-8)/(-40) - w/5. Factor p + 6/5*c - 2*c**2.
-2*(c - 1)*(5*c + 2)/5
Let b(f) = -3*f**3 - 24*f**2 + 55*f - 39. Let d(p) = p**3 + 12*p**2 - 27*p + 19. Let k(x) = 3*b(x) + 7*d(x). Let k(v) = 0. What is v?
2
Let s be (-6)/((-6)/9*3). Suppose 3*k - 3*k**3 + 2*k**2 + 4*k**2 - 6 + 3*k**2 - s*k**2 = 0. Calculate k.
-1, 1, 2
Factor -t - t + 4*t**4 - 16*t**2 + 24*t**2 - 10*t**3.
2*t*(t - 1)**2*(2*t - 1)
Let k(a) be the second derivative of a**8/6720 - a**6/720 + a**4/4 + 4*a. Let x(z) be the third derivative of k(z). Factor x(d).
d*(d - 1)*(d + 1)
Suppose 0 - 3 = -n. Suppose n*z = -2*z. Solve -2*f**3 + 6*f**2 + 2 + z + 0 - 6*f = 0 for f.
1
Let q(l) be the third derivative of -l**5/90 + l**4/36 + 2*l**3/9 + 6*l**2. Solve q(t) = 0 for t.
-1, 2
Let d(i) be the first derivative of 0*i**2 + 0*i**4 + 1/180*i**6 + i**3 - 1/60*i**5 + 3 + 0*i. Let c(m) be the third derivative of d(m). Factor c(y).
2*y*(y - 1)
Let c(t) = -2*t - 6. Let u be c(-4). Determine q, given that -3*q**u - 22*q**3 - q + 7*q + 20*q**5 + 2*q - 6*q + 3*q**4 = 0.
-1, -2/5, 0, 1/4, 1
Factor 2*m - 20*m**4 + 23*m**5 - 19*m - 18*m**5 + 20*m**2 + 15*m**3 - 3*m.
5*m*(m - 2)**2*(m - 1)*(m + 1)
Let x = 3907/5 - 781. Factor -x*n**2 + 2/5 + 9/5*n**3 - 9/5*n.
(n - 1)*(n + 1)*(9*n - 2)/5
Suppose -j = 12*j - 2*j. Factor j + 2/3*x**2 + 0*x.
2*x**2/3
Let u(r) be the third derivative of -r**5/40 + r**4/16 + 3*r**3 + r**2 - 12. Suppose u(h) = 0. What is h?
-3, 4
Let h(d) = d + 7. Let z be h(-3). Suppose 0 = -5*v + 10 + 10. Solve z*f**3 + v*f**3 - 2*f**2 - 6*f**3 = 0 for f.
0, 1
Let u be (-2 + 3)/((-2)/4). Let q be (4 - (-58)/(-14))*u. Factor -2/7*t + 0 - q*t**3 + 4/7*t**2.
-2*t*(t - 1)**2/7
Let f(z) be the third derivative of -z**8/1008 - z**7/105 - z**6/30 - z**5/18 - z**4/24 - 3*z**2 + 2. Factor f(p).
-p*(p + 1)**3*(p + 3)/3
Let i(j) = j**2 + j - 304. Let s be i(-18). Factor -4/3 + 4*w + 4/3*w**3 - 4*w**s.
4*(w - 1)**3/3
Let q be -4*(0 + (-15)/12). Let r(w) be the third derivative of -1/135*w**6 - 1/18*w**4 - 1/27*w**3 + 0 - 1/30*w**q + 0*w + w**2. Find b such that r(b) = 0.
-1, -1/4
Let -4*j**2 + 0*j**2 - 2*j**5 - 4*j**2 + 4*j**4 - 8*j + 6*j**3 = 0. What is j?
-1, 0, 2
Let z(i) be the third derivative of i**6/900 + i**5/75 + i**4/15 + 8*i**3/45 + 2*i**2. Factor z(m).
2*(m + 2)**3/15
Let s = 1 - 5. Let i(m) = -2*m - 2. Let t(l) = -l**2 - 8*l - 9. Let w(c) = 9*i(c) - 2*t(c). Let y(g) = -3*g**2 + 3*g. Let z(k) = s*w(k) - 3*y(k). Factor z(v).
v*(v - 1)
Determine x so that 7*x + 2 - 3*x + 2*x**2 - x**2 + x**2 = 0.
-1
Let w = -5 - -1. Let m(n) = 16*n**3 + 5*n**2 - 5*n - 16. Let d(f) = 3*f**3 + f**2 - f - 3. Let l(t) = w*m(t) + 22*d(t). Suppose l(x) = 0. What is x?
-1, 1
Suppose 0*w**2 + 2/5*w**4 - 2/5 + 4/5*w**3 - 4/5*w = 0. Calculate w.
-1, 1
Factor -26*u**2 + 24*u + 3*u**5 + 4*u**2 - 21*u**4 + 54*u**3 - 38*u**2.
3*u*(u - 2)**3*(u - 1)
Let m(v) = v**5 - 9*v**4 - 9*v**3 + 9*v**2 - 4. Let a(c) = 2*c**5 - 8*c**4 - 8*c**3 + 8*c**2 - 3. Let o(z) = -4*a(z) + 3*m(z). Factor o(g).
-5*g**2*(g - 1)**2*(g + 1)
Let x(w) be the second derivative of -1/18*w**4 + 0*w**3 + 1/6*w**2 + 1/90*w**6 + 0 - 2*w + 0*w**5. Factor x(m).
(m - 1)**2*(m + 1)**2/3
Let r(h) be the third derivative of 0*h + 1/315*h**7 - 1/9*h**4 + 1/9*h**3 - 1/45*h**6 + 1/15*h**5 + 3*h**2 + 0. Factor r(m).
2*(m - 1)**4/3
Suppose 3*z = 3*v + 123, 3*v - 6*z = -4*z - 126. Let u be (-4 - 144/v)*-2. Factor 0 + 152/11*q**2 - 686/11*q**5 + 98/11*q**4 + u*q + 420/11*q**3.
-2*q*(q - 1)*(7*q + 2)**3/11
Let j(w) be the first derivative of -w**3/6 + 5*w**2/4 - 3*w + 6. Factor j(t).
-(t - 3)*(t - 2)/2
Let y = -171/2 + 78. Let k = y - -8. Let 0 + k*s - 1/2*s**2 = 0. What is s?
0, 1
Let z(s) be the first derivative of -18*s**5/55 + 3*s**4/11 + 2*s**3/3 - 4*s**2/11 - 8*s/11 + 1. Solve z(c) = 0.
-2/3, 1
Suppose 0 = k - 1 - 4. Let l = -2843/6 - -474. Solve -5/6*w - 5/6*w**4 - 1/6*w**k - l - 5/3*w**2 - 5/3*w**3 = 0 for w.
-1
Let z(i) be the first derivative of 0*i + 1/2*i**4 + 2 + i**2 + 4/3*i**3. Factor z(a).
2*a*(a + 1)**2
Let t be 2*(-2 - -3 - 63/105). Solve -t + 6/5*h - 2/5*h**2 = 0 for h.
1, 2
Let h = 5 - 3. Let l = -1/23 - -51/115. Factor 0 - l*w**h + 2/5*w - 2/5*w**3 + 2/5*w**4.
2*w*(w - 1)**2*(w + 1)/5
Find p such that -p**2 + 4*p**3 - 3*p**2 + p + 0*p**2 - 9*p = 0.
-1, 0, 2
Suppose 3*s = -3*o + 27, o + 0 = 3. Factor -3*p + 3*p**5 + 0*p**4 + s*p**4 + 0*p**5 - 6*p**2.
3*p*(p - 1)*(p + 1)**3
Suppose 5*q - 6 = 3*q. Find l, given that -l - 2*l**3 - 3*l**2 + q*l + 3 + 9*l**2 - 9 = 0.
-1, 1, 3
Let f(x) = -x**3 - 24*x**2 - 142*x - 28. Let s be f(-14). Factor -8/5*y**2 + s + 8/5*y + 2/5*y**3.
2*y*(y - 2)**2/5
Let m(q) be the second derivative of -2*q**6/5 + 14*q**5/5 - 16*q**4/3 + 4*q**3/3 + 6*q**2 + 8*q. Find r such that m(r) = 0.
-1/3, 1, 3
Let c(o) be the first derivative of -o**3 - 3*o**2 + 6. Solve c(g) = 0 for g.
-2, 0
Let g be (1/66)/(1/(-4 + 5)). Let m(h) be the second derivative of 0*h**3 - 1/110*h**5 - 2*h + 0*h**2 + 0 + g*h**4. Solve m(r) = 0.
0, 1
Suppose -4 + 16 = 2*b. Let f be (-5)/(-1) + (b - 9). Find q, given that 2/3*q**f + 0 - 2/3*q = 0.
0, 1
Suppose 0 = -x + 4*c - 6, 0 = 5*x + 3*c + 2*c - 20. Let g = x + -2. Suppose 2/5*l**4 + 2/5*l**3 + 0 + g*l**2 + 0*l = 0. What is l?
-1, 0
Let o = 134 - 134. Determine c so that o*c**4 + 0*c - 1/2*c**3 + 0*c**2 + 0 + 1/2*c**5 = 0.
-1, 0, 1
Let u be (-4)/1*(-135)/20. Let z = -27 + u. Determine i, given that -1/4 - 1/2*i + z*i**2 + 1/4*i**4 + 1/2*i**3 = 0.
-1, 1
Let d(m) = m**2 + 5*m - 2. Let z be (-80)/14 - 6/21. Let g be d(z). Suppose -2*y + 2*y**2 + g*y - 4*y**2 = 0. What is y?
0, 1
Let m(f) = -f**4 - f**3 - f**2 + 1. Let q(l) = -6*l**4 - 4*l**3 - 4*l**2 - l + 5. Let w(p) = 10*m(p) - 2*q(p). Solve w(a) = 0 for a.
-1, 0, 1
Let z be 4/48*-2*(-10)/1. Find t, given that -3*t**2 + 7/3*t**4 + 5/3*t**3 + 2/3 - z*t = 0.
-1, 2/7, 1
Factor -62*j**3 + 7 - 2*j**5 - j**5 - 1 + 48*j**2 - 27*j + 20*j**3 + 18*j**4.
-3*(j - 2)*(j - 1)**4
Let b(f) be the second derivative of -3/4*f**3 + 1/16*f**4 + 0 + 27/8*f**2 - 6*f. Factor b(j).
3*(j - 3)**2/4
Let q(j) be the second derivative of 0*j**4 + 0 + 0*j**2 + 2*j + 1/60*j**5 + 0*j**3. Factor q(l).
l**3/3
Let t(j) = -2*j**2. Let a be t(1). Let h(g) = -4*g**3 - 4*g**2 - 3*g - 1. Let v be h(a). Factor 2*k**2 - v*k - 5*k**2 + 24*k.
-3*k*(k - 1)
Let z(m) be the second derivative of m**4/30 - m**3/3 + 4*m**2/5 + 20*m. Factor z(d).
2*(d - 4)*(d - 1)/5
Let v(h) be the second derivative of h**6/180 - h**2/2 - 2*h. Let x(t) be the first derivative of v(t). Determine m, given that x(m) = 0.
0
Suppose v = -0*v. Suppose -3*p = 4*z + 10, v*p + 2*p + 4 = -2*z. What is f in 4*f**p - 2*f**5 - 2*f - f**3 - 2 - 2*f**4 - f**3 + 6*f**3 = 0?
-1, 1
Suppose 6/7*b - 3/7 - 3/7*b**2 = 0. Calculate b.
1
Solve 5*d**3 + 2 - 9*d - 2*d**3 + 4 = 0 for d.
-2, 1
Let t(h) be the second derivative of -h**4/12 + 2*h**3/3 - 3*h**2/2 + 6*h. Factor t(c).
-(c - 3)*(c - 1)
Let l be ((-16)/(-48))/((-40)/(-66)). Let y(o) be the second derivative of 1/10*o**6 + l*o**5 + 11/12*o**4 - o**2 + 0 - o + 1/6*o**3. Factor y(x).
(x + 1)**2*(x + 2)*(3*x - 1)
Let c(b) = b**2 + 34*b - 109. Let n be c(-37). Let 16/11*g + 32/11 + 2/11*g**n = 0. Calculate g.
-4
Find v such that 16*v**2 - 3*v - 13*v**2 - 5 - 1 = 0.
-1, 2
Suppose 10*s - 30 = 5*s. Let j(m) be the second derivative of 0*m**4 + 2/5*m**5 + 0*m**2 + 25/21*m**7 + 0*m**3 + m + 0 + 4/3*m**s. Factor j(w).
2*w**3*(5*w + 2)**2
Let c be (28/8)/7*14. Factor t**3 - 3*t + 1 - 10 + c.
(t - 2)*(t + 1)**2
Let h be 4/7 + 96/28. Suppose -2*i - 3*i = 3*g + 19, -h*i - 30 = -5*g. Factor 8/3 + 8*l + 6*l**g.
2*(3*l + 2)**2/3
Let i(j) be the third derivative of -6*j**2 - 1/60*j**6 + 1/12*j**4 - 1/30*j**5 + 1/3*j**3 + 0*j + 0. Let i(q) = 0. Calculate q.
-1, 1
Suppose 4*l - 12 = 2*a, -4*a = 5*l + 10 - 38. Determine s, given that 15*s**3 + 14*s**5 + 4 - 2*s + 13*s**3 - 32*s**a + 40*s**3 - 52*s**4 = 0.
-2/7, 1
Let q(o) be the third derivative of -o**6/90 + 13*o**5/120 - o**4/8 + 2*o**3/3 + 8*o**2. Let l(v) be the first derivative of q(v). Factor l(p).
-(p 