
Let o(b) = 23*b**4 + 22*b**3 - 15*b**2 - 38*b - 8. Let d(z) = 8*z**4 + 7*z**3 - 5*z**2 - 13*z - 3. Let j(i) = 8*d(i) - 3*o(i). Factor j(a).
-5*a*(a - 1)*(a + 1)*(a + 2)
Let g(t) be the first derivative of t**7/840 + t**6/120 + t**5/60 + 2*t**3/3 + 1. Let x(h) be the third derivative of g(h). Determine b so that x(b) = 0.
-2, -1, 0
Let m(p) = -p**3 + 5*p**2 + 3*p - 3. Let o(h) = -h**2 - h + 1. Let n(i) = -4*m(i) - 12*o(i). Factor n(b).
4*b**2*(b - 2)
Let j(a) = -4*a**2 - 8*a. Let y(c) = 5*c**2 + 9*c. Let r(l) = -4*j(l) - 3*y(l). Suppose r(b) = 0. Calculate b.
-5, 0
Suppose 0 = -3*a + 3, 2*a - 6*a = 2*m - 10. Suppose 7*f - 16 = m*f. Factor -f*s - 2*s**3 + 5 - 1 + 5*s**2 - 3.
-(s - 1)**2*(2*s - 1)
Let o = -37 + 371/10. Let j(c) be the second derivative of 1/2*c**4 + c**2 - 4*c - o*c**5 + 0 - c**3. Find s, given that j(s) = 0.
1
Let m(z) = 105*z**2 - 95*z + 25. Let u(f) = -53*f**2 + 48*f - 13. Let q(h) = -3*m(h) - 5*u(h). Let q(r) = 0. Calculate r.
2/5, 1/2
Let g be 2/(-7) + 18/14. Let l(b) = 3*b**2 - b + 1. Let z be l(g). Let u**3 - 7*u + 3*u + z*u = 0. What is u?
-1, 0, 1
Let m be 207/540 - (-3)/(-8). Let p(t) be the second derivative of 0*t**2 - 1/168*t**7 - 1/48*t**4 + m*t**6 + 1/80*t**5 + 0 + 0*t**3 + 3*t. Factor p(n).
-n**2*(n - 1)**2*(n + 1)/4
Find m such that -3/2*m**4 - 1/4*m + 3*m**2 + 1/2*m**3 - 1/4*m**5 - 3/2 = 0.
-6, -1, 1
Determine g so that 75*g + 210*g - 185*g**3 - 25*g**4 - 90 + 155*g**2 + 60*g**4 = 0.
-1, 2/7, 3
Suppose -2*s = s - 15. Suppose s*q**3 + 3*q**5 + 2*q**5 - 2*q**4 - 7*q**5 - q**3 = 0. Calculate q.
-2, 0, 1
Let y(b) = b + 10. Let k be y(-8). Suppose h**3 + 5*h**4 - 2*h**5 + k - 2*h + 4*h**3 - h**3 - 3*h**4 - 4*h**2 = 0. What is h?
-1, 1
Let o(z) = 2*z**2 - 2*z - 2. Let a(m) = m**2 - m - 1. Let t(d) = -a(d) + o(d). Let s be t(-2). Factor 3*x + x**3 - s*x + x.
x*(x - 1)*(x + 1)
Let j(q) be the first derivative of 5*q**6/2 - 21*q**5/5 - 39*q**4/4 + 11*q**3 + 12*q**2 - 12*q - 4. Solve j(s) = 0.
-1, 2/5, 1, 2
Let u(m) be the first derivative of -1/3*m**3 - 16*m + 1 + 4*m**2. Factor u(d).
-(d - 4)**2
Factor 2*j - 4*j + 14*j + 4*j**3 + 16*j**2.
4*j*(j + 1)*(j + 3)
Let y be 230/225 + 4/6. Let z = y + -8/9. Suppose -2/5*j + 2/5*j**5 + 0 - z*j**4 + 4/5*j**2 + 0*j**3 = 0. What is j?
-1, 0, 1
Let r(t) be the first derivative of -49*t**5/5 + 77*t**4/4 - 32*t**3/3 + 2*t**2 - 5. Find i such that r(i) = 0.
0, 2/7, 1
Let h = -573/4 + 144. Factor h*f + 9/4*f**2 - 3/2.
3*(f + 1)*(3*f - 2)/4
Let b(l) be the third derivative of 0*l - 3/448*l**8 + 0 + 1/70*l**7 - 1/20*l**5 + 2*l**2 + 0*l**3 + 1/96*l**6 + 1/24*l**4. Find s, given that b(s) = 0.
-1, 0, 2/3, 1
Factor -2/7*r**2 + 12/7 - 10/7*r.
-2*(r - 1)*(r + 6)/7
Let l be 4/(164/12 + (-2)/(-6)). Factor l - 2/7*c**3 - 2/7*c**2 + 2/7*c.
-2*(c - 1)*(c + 1)**2/7
Let v(h) be the second derivative of h**5/5 - 4*h**4/3 - 2*h**3/3 + 8*h**2 + 5*h. Find y such that v(y) = 0.
-1, 1, 4
Let q = -138 + 1657/12. Let a(k) be the second derivative of k - q*k**3 + 1/8*k**2 + 1/48*k**4 + 0. Factor a(t).
(t - 1)**2/4
Let p(q) = -2*q**4 - 6*q**3 + 3*q**2 - 4*q + 3. Let l(v) = 3*v**4 + 7*v**3 - 3*v**2 + 5*v - 4. Let w(h) = 3*l(h) + 4*p(h). Find m such that w(m) = 0.
0, 1
Let b(l) be the second derivative of 9*l**5/80 + 5*l**4/16 + l**3/8 - 3*l**2/8 - 6*l. Factor b(s).
3*(s + 1)**2*(3*s - 1)/4
Let k(p) be the third derivative of -p**8/1848 - 2*p**7/385 - 7*p**6/330 - 8*p**5/165 - 3*p**4/44 - 2*p**3/33 + 3*p**2. What is o in k(o) = 0?
-2, -1
Let x = 2387/38 + 51/19. Let s = -64 + x. Solve 3/2*d**2 + 0 + s*d = 0 for d.
-1, 0
Let n(a) be the third derivative of -a**7/210 + a**6/120 + a**5/60 - a**4/24 + 6*a**2. Factor n(d).
-d*(d - 1)**2*(d + 1)
Let k(i) be the first derivative of 1/4*i**2 - 1/12*i**3 + 3 - 1/4*i. Determine x, given that k(x) = 0.
1
Let q(d) = -d**3 + 5*d**2 - 3*d. Let y(w) = w - 5. Let p be y(9). Let r be q(p). Find l such that 0 + 1/4*l**2 - 1/4*l**r + 1/4*l - 1/4*l**3 = 0.
-1, 0, 1
Let a be 52/(-16) + 1/4. Let x(j) = j**3 - 3*j**2 - 2*j + 2. Let f(s) = -3*s**2 - 3*s + 3. Let u(h) = a*x(h) + 2*f(h). Find y such that u(y) = 0.
0, 1
Let l(c) be the first derivative of -1/5*c**3 + 5 + 0*c**2 - 3/20*c**4 + 0*c. Find f such that l(f) = 0.
-1, 0
Let l be (18/27)/(16/4). Factor -l*h**4 + 1/6*h**3 + 0 - 1/6*h + 1/6*h**2.
-h*(h - 1)**2*(h + 1)/6
Factor 2/11*p**2 + 4/11 + 6/11*p.
2*(p + 1)*(p + 2)/11
Let o(k) = -k**3 - 3*k**2 + 4*k + 3. Suppose -3*y - 5 = 7. Let m be o(y). Determine q, given that -q - 5*q**2 - q + q**2 + m*q**2 = 0.
-2, 0
Let o(x) be the third derivative of 0 - 1/180*x**5 - 8*x**2 + 0*x - 1/18*x**3 - 1/36*x**4. Factor o(n).
-(n + 1)**2/3
Let 16 - d**3 + 6*d**2 - 11 - 9*d - 5 = 0. Calculate d.
0, 3
Let p(m) be the third derivative of m**6/20 - m**5/15 - m**4/4 + 2*m**3/3 - 13*m**2. Factor p(t).
2*(t - 1)*(t + 1)*(3*t - 2)
Let f(x) = -x**2 + 3*x - 5. Let b(h) = -2*h**2 + 8*h - 12. Let s(m) = 5*b(m) - 12*f(m). Factor s(c).
2*c*(c + 2)
Let q(a) be the third derivative of a**6/30 + 2*a**5/15 - 2*a**4/3 - 16*a**3/3 - 3*a**2. Factor q(w).
4*(w - 2)*(w + 2)**2
Solve 10*k**3 - 6*k**3 + 8*k - 3*k**2 + 10*k**2 + 5*k**2 = 0.
-2, -1, 0
Let u(w) be the second derivative of w**7/357 - 7*w**6/1020 + w**5/255 - 4*w**2 + 9*w. Let v(x) be the first derivative of u(x). Suppose v(a) = 0. What is a?
0, 2/5, 1
Let v(l) = l**2 + 4*l. Let d(g) = -4*g**2 - 16*g. Let h(u) = 6*d(u) + 22*v(u). Factor h(w).
-2*w*(w + 4)
Let n(d) = -6*d**4 + 10*d**2 + 8*d - 4. Let b(g) be the second derivative of -g**5/20 - g**4/12 - g**3/6 + g**2/2 + 4*g. Let s(m) = 4*b(m) + n(m). Factor s(x).
-2*x*(x - 1)*(x + 1)*(3*x + 2)
Let q be (-60)/(-45)*(-1)/(-4). Let t(y) be the first derivative of -2*y - 3 + 1/2*y**2 + q*y**3. Determine z so that t(z) = 0.
-2, 1
Let o be 5 - (-70)/(-15) - 2/(-6). Determine i so that 0 - 2*i**4 - 2*i**3 + 0*i - 2/3*i**2 - o*i**5 = 0.
-1, 0
Suppose 0*f - 1/2*f**3 + 1/2*f**5 + 0 - 1/2*f**4 + 1/2*f**2 = 0. Calculate f.
-1, 0, 1
Suppose 0 = -k + 5*t + 13, -7*k = -3*k + 2*t - 8. Suppose k*o = -3*l + 6, 2*l - 3 = 5*o + 1. Factor s**l + 4/3*s + 1/3.
(s + 1)*(3*s + 1)/3
Let p(s) be the second derivative of -27*s**4/14 + 6*s**3/7 - s**2/7 - 8*s. Factor p(x).
-2*(9*x - 1)**2/7
Let j be -4 - (-228)/28 - 4. Let r(a) be the first derivative of -2 + 0*a + j*a**2 - 2/21*a**3. Factor r(g).
-2*g*(g - 1)/7
Let d(o) be the second derivative of -o**4/16 + o**3/2 - 3*o**2/2 + 11*o. Solve d(t) = 0 for t.
2
Let m = 19002/11 - 6212048/3597. Let w = -2/981 + m. Let -10/9*i**3 - 14/9*i**2 + 0 - w*i = 0. What is i?
-1, -2/5, 0
Let u(b) = b**2 - 8*b + 11. Let p be u(7). Factor -3*x**3 + 2*x + x**p - 2*x - 27*x**5 + 29*x**5.
x**3*(x - 1)*(2*x + 3)
Suppose 0 = -11*z - 9 + 31. What is k in 0*k - 3/4*k**z + 0 = 0?
0
Let b be -10 + 11 + 194/(-4). Let q = 48 + b. What is h in -q*h**2 - 1/2*h + 0 = 0?
-1, 0
Let s(t) be the third derivative of t**8/1512 - t**7/945 - t**6/135 + 2*t**5/135 + 15*t**2. Suppose s(b) = 0. Calculate b.
-2, 0, 1, 2
Factor -3/2*n**3 + 3/2*n + 1/2*n**4 - 1 + 1/2*n**2.
(n - 2)*(n - 1)**2*(n + 1)/2
Let w = -2 - -16. Let d be 4/w - 95/(-35). Factor -2/5*z + 2/5*z**d - 2/5 + 2/5*z**2.
2*(z - 1)*(z + 1)**2/5
Let d(w) = 4*w**2 - 8*w - 8. Let k(z) = -12*z**2 + 24*z + 25. Let y(x) = 11*d(x) + 4*k(x). Factor y(b).
-4*(b - 3)*(b + 1)
Let p(s) = -s**5 + s**4 + s**3 + s**2. Let x(i) = -33*i**4 - 36*i**3 + 9*i**2 + 36*i + 12. Let y(w) = -6*p(w) - x(w). Suppose y(d) = 0. Calculate d.
-2, -1, -1/2, 1
Suppose -21*j = -26*j + 15. Let y(w) be the third derivative of -1/27*w**j - 3*w**2 + 0 + 0*w**4 + 1/270*w**5 + 0*w. Suppose y(o) = 0. What is o?
-1, 1
Let z(x) = -8*x**2 + 2*x. Let w(c) = 7*c**2 - c. Let g(b) = 5*w(b) + 4*z(b). Factor g(y).
3*y*(y + 1)
Let s(n) = n - 7. Let x be s(10). Factor -24/5*f**2 + 4/5*f**x + 48/5*f - 32/5.
4*(f - 2)**3/5
Let n(c) = 2*c + 12. Let w be n(-5). Factor 1/3*m**w - 1/3*m**3 + 1/3*m - 1/3.
-(m - 1)**2*(m + 1)/3
Let j(t) = -3*t**2 - 59*t - 35. Let a be j(-19). Let 0 - 2/3*i**a - 8/3*i + 8/3*i**2 = 0. Calculate i.
0, 2
Let h(f) = -2*f**2 - 6. Suppose 2*u - 24 = -4*j, 3*u = -2*j - 3 + 19. Let r(b) = -2*b**2 - b - 7. Let v(c) = j*h(c) - 4*r(c). Factor v(g).
-2*(g - 1)**2
Factor 0 + 8/3*g**2 + 4/3*g**4 - 4*g**3 + 0*g.
4*g**2*(g - 2)*(g - 1)/3
Let s = -6 - -6. Let t(m) be the second derivative of 1/24*m**3 + 