*u**2 + 19*u - 11. Let m be 3/6 - 11/2. Let v(p) = 12*p**3 - 6*p**2 - 9*p + 6. Let g(k) = m*v(k) - 3*f(k). Factor g(q).
3*(q - 1)*(q + 1)*(4*q - 1)
Let l(a) = 2*a**2 + 2*a - 5. Let x = -26 - -44. Let y = x + -25. Let h(q) = 3*q**2 + 3*q - 7. Let z(g) = y*l(g) + 5*h(g). Find o, given that z(o) = 0.
-1, 0
Let n(a) = a - 3. Let h be n(6). Let v(l) be the second derivative of -1/4*l**4 + 0 + 2*l**2 + 2*l + 0*l**h + 1/20*l**5. What is d in v(d) = 0?
-1, 2
Let h(j) be the first derivative of j**7/147 - 2*j**6/105 + j**4/21 - j**3/21 - 2*j + 2. Let r(c) be the first derivative of h(c). What is p in r(p) = 0?
-1, 0, 1
Let o = -2374/9 - -265. Let d = o - 7/9. Determine q, given that 2/9*q**4 + 2/9 + 2/9*q - d*q**2 + 2/9*q**5 - 4/9*q**3 = 0.
-1, 1
Let i(d) be the first derivative of 5*d**6/6 + 5*d**5 + 15*d**4/2 - 10*d**3/3 - 35*d**2/2 - 15*d - 11. Factor i(s).
5*(s - 1)*(s + 1)**3*(s + 3)
Let y = -7 + 10. Let o(f) = -f**3 + 8*f**2 + f - 8. Let z be o(8). Let 0*b + 1/3*b**y + z + 1/3*b**5 - 2/3*b**4 + 0*b**2 = 0. What is b?
0, 1
Suppose -4*v = 2 - 6. Let k(r) = r**3 - v + 7 + 2*r + r**3 - 9*r**2 - 1. Let j(z) = z**3 - 1. Let t(p) = 5*j(p) + k(p). Determine u, given that t(u) = 0.
0, 2/7, 1
Find d, given that 2/7*d**5 + 0*d + 0 + 0*d**2 - 4/7*d**3 + 2/7*d**4 = 0.
-2, 0, 1
Let v(c) be the third derivative of 1/54*c**4 + 1/135*c**6 + 0*c - 4*c**2 + 0*c**3 - 1/945*c**7 - 1/54*c**5 + 0. Factor v(s).
-2*s*(s - 2)*(s - 1)**2/9
Let k be ((1 - -3)*1)/(79 + -77). Factor 2/5 - 9/5*o**k - 7/5*o.
-(o + 1)*(9*o - 2)/5
Factor -10 - 36*l**3 + 5*l**4 - 33*l**3 + 54*l**3 + 4*l**2 + l**2 + 15*l.
5*(l - 2)*(l - 1)**2*(l + 1)
Let r be (-3)/21 - (-76)/(-420)*-3. Factor 4/5 - r*m - 2/5*m**2.
-2*(m - 1)*(m + 2)/5
Let v(o) be the first derivative of -o**4/4 + o**3 - 3*o**2/2 + o + 7. Factor v(w).
-(w - 1)**3
Suppose 10 = -5*g + 4*h, 5*g - 40 = -5*h - 5. Let q = g + 0. Determine x, given that 4*x - 2*x - q*x**2 - x**2 = 0.
0, 2/3
Suppose 2*q + 15 = 3*s, s = q + 4*s - 15. What is w in q + 8*w**3 - 4/3*w + 10/3*w**2 = 0?
-2/3, 0, 1/4
Let x(q) = 5*q**3 + q**2 - 3*q - 3. Suppose -8*l - 15 = -3*l. Let u(r) = -r**4 - 6*r**3 - r**2 + 4*r + 4. Let i(b) = l*u(b) - 4*x(b). Find c such that i(c) = 0.
-1/3, 0, 1
Let a(u) be the first derivative of -u**4/10 + 2*u**3/5 + u**2/5 - 6*u/5 - 6. Let a(p) = 0. What is p?
-1, 1, 3
Factor -3*n + n**2 - 21*n**2 + 32*n**3 - 2*n - 7*n**3.
5*n*(n - 1)*(5*n + 1)
Let w be 18/8 + 6/8. Find p such that p + p**w - p + 2*p - 3*p**2 = 0.
0, 1, 2
Let r(s) be the third derivative of 5*s**8/336 + s**7/21 - s**6/24 - s**5/6 + s**2. Let r(x) = 0. Calculate x.
-2, -1, 0, 1
Let m be -8 - -9 - -4*1. Determine d so that 6*d**2 - 3*d**2 + d**m - 3*d**3 - 3*d**4 + 6*d**3 - 4*d**5 = 0.
-1, 0, 1
Solve 0*h - 5/6*h**5 + 0*h**2 + 0 - 10/3*h**3 - 10/3*h**4 = 0 for h.
-2, 0
Let x(s) = 9*s**4 - 6*s**3 - 3*s**2 + 3*s + 3. Let l(p) = p**5 + 8*p**4 - 5*p**3 - 4*p**2 + 2*p + 2. Let n(h) = 3*l(h) - 2*x(h). Determine i so that n(i) = 0.
-2, -1, 0, 1
What is s in 0 + 3*s**2 - 33*s**3 + 3*s + 30*s**3 - 3 = 0?
-1, 1
Suppose 5*s - 10 = 4*t + 6, 3*t = -2*s + 11. Solve -2/3*x**3 + 2/9*x**s - 2/9*x + 0 + 2/3*x**2 = 0.
0, 1
Factor 2*m + m - 4*m**2 + 10*m - 9*m + 24.
-4*(m - 3)*(m + 2)
Let n(k) = k**3 + 7*k**2 + 6*k + 4. Let i be n(-6). Suppose -3*y + 9 = -0. Factor -y + i + 3*x + 3*x**3 - 1 - 6*x**2.
3*x*(x - 1)**2
Let l = -3 + 1. Let g(c) = 24*c**4 + 11*c**3 - 19*c**2 - 11*c - 5. Let h(v) = 12*v**4 + 5*v**3 - 10*v**2 - 5*v - 2. Let s(b) = l*g(b) + 5*h(b). Factor s(a).
3*a*(a - 1)*(a + 1)*(4*a + 1)
Suppose 6*j - 17 - 1 = 0. Factor -15/4*h - 3*h**2 - 3/4*h**j - 3/2.
-3*(h + 1)**2*(h + 2)/4
Let x(d) = -3*d**2 - d - 5. Let k(n) = n**2 + 2. Let h(g) = -5*k(g) - 2*x(g). Factor h(y).
y*(y + 2)
Determine c so that -8*c**2 + 4*c**3 - 15*c**4 - 7*c**2 - 73*c**3 - 54 + 153*c = 0.
-3, 2/5, 1
Let w(k) = -1 - k - k**2 + 6*k + 4. Let j be w(5). Find y, given that 3*y**2 - 5*y**4 + 2*y**2 + 2*y + 7*y**5 - 9*y**j + 0*y**4 = 0.
-1, -2/7, 0, 1
Let t(z) be the third derivative of -2*z**7/245 - z**6/105 + z**5/35 + z**4/21 + 33*z**2. Find i such that t(i) = 0.
-1, -2/3, 0, 1
Let d be 2/3*(-18)/(-3). Suppose 5*o - a - 10 = -3*a, 20 = d*a. Factor 0*q + o - 1/3*q**2.
-q**2/3
Let m(n) be the third derivative of -n**6/180 + n**5/10 - 5*n**4/12 + 7*n**3/9 + 29*n**2. Suppose m(a) = 0. What is a?
1, 7
Let p(s) be the third derivative of s**6/30 - 4*s**5/15 + 5*s**4/6 - 4*s**3/3 - 3*s**2. Factor p(a).
4*(a - 2)*(a - 1)**2
Let n(q) be the second derivative of -q**7/105 - 4*q**6/75 - 3*q**5/25 - 2*q**4/15 - q**3/15 + 3*q. Factor n(z).
-2*z*(z + 1)**4/5
Let x(f) be the first derivative of f**5/25 - 3*f**4/10 + 13*f**3/15 - 6*f**2/5 + 4*f/5 - 7. Suppose x(w) = 0. What is w?
1, 2
Let b(t) = t**3 + 5*t**2 - 4*t - 4. Let w be b(-4). Let f be w/24 + 4/(-6). Factor -f*p**2 + 1/2*p**4 - 1/2*p**5 + 0*p + 0 + 1/2*p**3.
-p**2*(p - 1)**2*(p + 1)/2
Let x(n) be the third derivative of -n**8/30240 + n**7/7560 + n**5/30 + 2*n**2. Let f(o) be the third derivative of x(o). Factor f(c).
-2*c*(c - 1)/3
Determine c so that 90*c**3 + 35*c**4 - 56*c - 59*c + 75*c**4 + 25*c**5 - 30 - 80*c**2 = 0.
-3, -1, -2/5, 1
Solve 6*d - 4*d**2 + 2*d**3 + 2*d**2 - 6*d**2 = 0.
0, 1, 3
Factor -4/13 - 10/13*t - 2/13*t**3 - 8/13*t**2.
-2*(t + 1)**2*(t + 2)/13
Let t be (6/(-4))/(3/(-6)). Suppose 0*q + 6 = 5*q - 4*u, 0 = t*q + 5*u - 11. Find h, given that 1/4*h + 0 + 1/4*h**q = 0.
-1, 0
Let j(r) = -r**2. Let p be (3 + -5)*-1*1. Let v(h) = -p + 10*h**2 + 2 - 2*h**3. Let b(l) = -8*j(l) - v(l). Find k, given that b(k) = 0.
0, 1
Let d(o) be the third derivative of -o**6/240 + o**5/120 - 17*o**2. Solve d(g) = 0.
0, 1
Let k(h) be the second derivative of 0*h**4 + 0*h**2 - 1/3*h**3 + 0 + 1/10*h**5 + 2*h. Solve k(g) = 0 for g.
-1, 0, 1
Let k(d) be the second derivative of d**4/30 - d**2/5 - 3*d. Factor k(m).
2*(m - 1)*(m + 1)/5
Factor 8*q - 29*q**3 + q**4 - 5*q**4 + 45*q**3 - 20*q**2.
-4*q*(q - 2)*(q - 1)**2
Let z(n) be the second derivative of n**6/120 - n**5/80 - 15*n. Factor z(r).
r**3*(r - 1)/4
Let n = 7 + -6. Factor -2*u**2 - u + u**4 + u**4 - u**4 + 2*u**3 - u**5 + n.
-(u - 1)**3*(u + 1)**2
Let l = -2 + 5. Let n = 6 - l. Suppose -1/2*a**4 + a**n - 1/2*a**2 + 0*a + 0 = 0. What is a?
0, 1
Let h(r) be the second derivative of r**8/13440 - r**6/480 - r**5/120 - r**4/12 - 3*r. Let w(x) be the third derivative of h(x). Factor w(d).
(d - 2)*(d + 1)**2/2
Let m(k) be the third derivative of k**8/20160 - k**7/5040 - k**6/360 - k**5/30 - 3*k**2. Let p(t) be the third derivative of m(t). Factor p(s).
(s - 2)*(s + 1)
Let l(u) be the first derivative of -u**4/14 + 8*u**3/21 + 3*u**2/7 - 36*u/7 + 3. Let l(m) = 0. What is m?
-2, 3
Let d(g) be the second derivative of g**7/147 - 2*g**6/105 - 3*g**5/70 + 2*g**4/21 + 4*g**3/21 + 4*g. Factor d(p).
2*p*(p - 2)**2*(p + 1)**2/7
Suppose -3*l - 4 + 31 = 0. Let i = l - 5. Let 4*b**2 + 1 - 2*b**i + 1 - 4 = 0. What is b?
-1, 1
Let j(t) be the first derivative of t + 0*t**2 + 0*t**3 - 2 - 1/33*t**4 + 1/110*t**5. Let q(d) be the first derivative of j(d). Factor q(i).
2*i**2*(i - 2)/11
Let z(b) = -3*b**5 - 18*b**4 - 42*b**3 - 48*b**2 - 23*b - 2. Let a(t) = t + 1. Let s(h) = 4*a(h) - z(h). Factor s(j).
3*(j + 1)**4*(j + 2)
Let c(t) be the first derivative of 2/35*t**5 - 2 + 0*t**2 - 4/21*t**3 + 0*t**4 + 2/7*t. Factor c(r).
2*(r - 1)**2*(r + 1)**2/7
Let u(s) be the first derivative of -s**6 + 38*s**5/5 - 33*s**4/2 + 6*s**3 + 8. Suppose u(j) = 0. What is j?
0, 1/3, 3
Let u(j) be the third derivative of 3/245*j**7 - 1/210*j**5 + 0*j**4 + 0*j**3 + 0*j + 0 - 1/140*j**6 + 9/392*j**8 - 2*j**2. Let u(i) = 0. What is i?
-1/3, 0, 1/3
Suppose -5*s - 3*o + 5 = -o, o + 5 = 0. Let f be (2 + -32)/(s/(-2)). What is k in k**5 - 20*k**4 + f*k**4 = 0?
0
Suppose -5*j - 2*m = -4 - 3, 5*j - 5*m = 35. Let y(q) = q**3 - 4*q**2 + q + 7. Let g be y(j). Factor g + 3/2*f**2 + 5/2*f.
(f + 1)*(3*f + 2)/2
Let m = -125 - -130. Factor -4/7*c**3 + 2/7*c + 2/7*c**m - 2/7 - 2/7*c**4 + 4/7*c**2.
2*(c - 1)**3*(c + 1)**2/7
Let j be (-5)/((-240)/8) + 57/90. Factor j*v**3 - 3/5*v**4 + v**2 - 2/5*v + 0.
-v*(v - 2)*(v + 1)*(3*v - 1)/5
Let r(y) = y**3 - 5*y**2 - 5*y - 4. Let i be r(6). Determine l so that 9*l**3 + 5*l**2 + 16*l**i + 32*l - 26*l = 0.
-2, -1/3, 0
Let q be (3/3*6)/2. Factor 