c - 13. Suppose -5*f + 44 = -4*q, -5*f + 3*f + 32 = -4*q. Let h(b) = q*l(b) + 26*a(b). Factor h(s).
2*s*(s + 1)
Find s, given that 0 + 0*s + 0*s**2 + 5/3*s**3 = 0.
0
Factor -16*p + 7*p**2 + p**2 + 3 + 3 + 2*p**2.
2*(p - 1)*(5*p - 3)
Let m(s) = -s**4 + s + 1. Let f(d) = 6*d**4 - 3*d - 3. Let y(u) = f(u) + 3*m(u). Let y(p) = 0. Calculate p.
0
Let g(j) be the first derivative of -3*j**4/16 - j**3 - 3*j**2/2 - 10. Solve g(t) = 0 for t.
-2, 0
Let z(m) = -4*m**3 + 12*m - 3. Let r(v) = -v**3 - v**2 + v. Let d(h) = -3*r(h) + z(h). Let k(i) be the first derivative of d(i). Find c such that k(c) = 0.
-1, 3
Let j(c) be the first derivative of 1/21*c**3 - c + 0*c**2 + 1/42*c**4 + 2. Let q(a) be the first derivative of j(a). Factor q(y).
2*y*(y + 1)/7
Let j(k) be the first derivative of -k**4/2 + 2*k**3 - 8*k - 38. Let j(m) = 0. Calculate m.
-1, 2
Let s(o) be the third derivative of -o**6/300 - o**5/30 + 13*o**4/60 - 7*o**3/15 - 3*o**2. Factor s(k).
-2*(k - 1)**2*(k + 7)/5
Let a(d) be the first derivative of d**3/15 - 2*d**2/5 + 3*d/5 - 19. Suppose a(s) = 0. Calculate s.
1, 3
Factor 4*w**3 + 5*w**2 - 5*w**3 - 4*w**3.
-5*w**2*(w - 1)
Factor -1/2*q + 0 + 1/2*q**2.
q*(q - 1)/2
Let j(p) = p**2 - 9*p + 12. Let o be j(8). Factor 1/2*z**3 + 0*z**2 - 1/4*z**o + 0*z + 0 - 1/4*z**5.
-z**3*(z - 1)*(z + 2)/4
Let f be ((-8)/16)/(1*-2). Factor -f*j**2 - 1/4*j + 0.
-j*(j + 1)/4
Factor 0 + 0*j + 4/9*j**2 - 2/9*j**3.
-2*j**2*(j - 2)/9
Let r(p) be the third derivative of -p**10/907200 + p**8/120960 - p**5/60 - 8*p**2. Let o(x) be the third derivative of r(x). Factor o(u).
-u**2*(u - 1)*(u + 1)/6
Let i be 6*(-5)/(-5) + -4. Factor -1/2*d + 1/2*d**i - 1.
(d - 2)*(d + 1)/2
Let u(h) be the first derivative of -h**7/21 + 2*h**6/15 - h**5/10 + 4*h - 4. Let f(k) be the first derivative of u(k). Find n such that f(n) = 0.
0, 1
Let d(v) be the first derivative of 1/4*v**4 + 2/9*v**3 + 0*v**2 - 2 + 1/15*v**5 + 0*v. Factor d(z).
z**2*(z + 1)*(z + 2)/3
Let j(r) = 2*r**2 - r + 10. Let l be j(0). Let n be (l/(-45))/(4/(-24)). Suppose -2*t - 2/3*t**2 - n = 0. Calculate t.
-2, -1
Let b(t) = t - 3. Let o be b(5). Let h(u) be the third derivative of 1/30*u**4 + 1/150*u**5 - u**o + 0 + 1/15*u**3 + 0*u. Factor h(x).
2*(x + 1)**2/5
Let g(f) = -f**3 - 6*f**2 - 7*f - 7. Let i be g(-5). Let a be (-11)/33*i/(-4). Determine l so that 1/4*l**2 + 0 + a*l**3 - 1/4*l - 1/4*l**4 = 0.
-1, 0, 1
Let a be (-242)/77*(-5 - 2). Let f = -20 + a. Factor 4/3*n**4 + 0*n**f - 2/3*n**5 + 0 + 0*n - 2/3*n**3.
-2*n**3*(n - 1)**2/3
Let c = 4343 + -30459/7. Let d = c - -230/21. Determine m so that -d*m - 2/3*m**2 - 8/3 = 0.
-2
Let p(n) be the second derivative of n**6/90 - n**5/30 + n**4/36 + 2*n. Let p(g) = 0. Calculate g.
0, 1
Let c be (2/(-2))/(34/(-102)). Factor -20/7*x**2 - 2/7*x**c + 8/7*x + 8/7*x**4 + 16/7 - 2/7*x**5.
-2*(x - 2)**3*(x + 1)**2/7
Factor 44*s**2 - 13*s**2 - 8 - 13*s**2 - 16*s**2.
2*(s - 2)*(s + 2)
Let u be 4/2 + 0*2/2. Factor 0 + 0*f + 0*f**u + 0*f**4 + 0*f**3 + 1/5*f**5.
f**5/5
Let w be 4/(-30) + 366/45. Let g = -8 + w. Factor g - 2/3*h**2 + 2/3*h.
-2*h*(h - 1)/3
Let 33/4*l - 1/4*l**5 + 19/2*l**2 + 0*l**4 + 5/2 + 4*l**3 = 0. What is l?
-2, -1, 5
Let f(x) be the second derivative of x**6/160 - x**5/240 - 5*x**3/6 - 4*x. Let u(v) be the second derivative of f(v). Factor u(r).
r*(9*r - 2)/4
Let o = 80 - 78. Solve 3/5*i**o - 1/5*i + 1/5*i**4 + 0 - 3/5*i**3 = 0 for i.
0, 1
Let c(h) be the second derivative of 0 - 4*h + 0*h**2 - 2/9*h**3 + 7/30*h**5 + 5/18*h**4. Find u such that c(u) = 0.
-1, 0, 2/7
Let s(q) = -9*q**2 + 21*q - 16. Let a(b) = 5*b. Let z be a(1). Let r(h) = 4*h**2 - 10*h + 8. Let w(x) = z*r(x) + 2*s(x). Suppose w(o) = 0. What is o?
2
Solve 359*r + 4107*r**2 - 158*r + 243*r + 7 + 5 = 0.
-2/37
Let i(n) be the first derivative of n**4/6 - 2*n**3/3 + n**2 - 2*n/3 - 12. Suppose i(b) = 0. What is b?
1
Let b(s) = 3*s**3 - 5*s**2 + 4*s + 1. Suppose 2*i - 3*i = 3*a - 13, 5 = -i. Let k(f) = 6*f**3 - 11*f**2 + 9*f + 1. Let t(r) = a*k(r) - 10*b(r). Factor t(u).
2*(u - 1)**2*(3*u - 2)
Let -110*w**2 + 112*w**2 + 1 + 10*w + 7 = 0. What is w?
-4, -1
Let a = -1 - -1. Let h(m) = 0*m + a*m - m - m**2. Let z(f) = -f**2 - 7*f + 2. Let k(g) = 3*h(g) - z(g). Factor k(o).
-2*(o - 1)**2
Let v(z) be the third derivative of -z**6/24 - z**5/6 + 5*z**4/24 + 5*z**3/3 - 9*z**2. Factor v(k).
-5*(k - 1)*(k + 1)*(k + 2)
Let q(y) = y**3 + y**2 - 3*y - 1. Let s be q(-2). Let u be s + 2 + (-11)/5. Factor u + 1/5*h**2 - 4/5*h.
(h - 2)**2/5
Let h(d) be the third derivative of -d**11/332640 + d**10/151200 - 2*d**5/15 + 2*d**2. Let j(f) be the third derivative of h(f). Solve j(y) = 0.
0, 1
What is l in -9/4*l**2 + 3/8*l + 9/4 - 3/8*l**3 = 0?
-6, -1, 1
Factor -1/5*p**2 - 1/5*p**5 + 1/5*p**4 + 0*p + 1/5*p**3 + 0.
-p**2*(p - 1)**2*(p + 1)/5
Let 3*a**3 + 24/5*a**2 + 12/5*a + 0 + 3/5*a**4 = 0. What is a?
-2, -1, 0
Let u(i) = -i**2 + 12*i - 13. Let o be u(10). Let c = o - 4. Find z, given that 2/3 + 5/3*z**c - 2/3*z**2 - 5/3*z = 0.
-1, 2/5, 1
Let n(y) = y**2 - 2*y + 1. Let v be n(1). Suppose v = -0*l + 3*l - 24. Factor 2*k**2 + k**4 + 6*k**4 - k**4 + l*k**3.
2*k**2*(k + 1)*(3*k + 1)
Let h(c) be the second derivative of 4/75*c**6 - 1/105*c**7 - 1/15*c**3 + 2/15*c**4 + 0 - 3/25*c**5 - c + 0*c**2. Factor h(n).
-2*n*(n - 1)**4/5
Let d(r) be the second derivative of r**7/840 - r**6/120 + r**4/3 + r. Let q(y) be the third derivative of d(y). Determine m, given that q(m) = 0.
0, 2
Factor 0*m + 0 + 5/2*m**3 - 5/4*m**2 - 5/4*m**4.
-5*m**2*(m - 1)**2/4
Let n(s) = -3*s - 3. Let d be n(-4). Factor 6*o + d - 1 + 10*o + 3*o**2 + 3*o**2.
2*(o + 2)*(3*o + 2)
Let y(x) be the third derivative of 7/60*x**5 + 0 + 1/40*x**6 - 3*x**2 + 0*x**3 + 1/12*x**4 + 0*x - 1/30*x**7 - 5/336*x**8. Find k, given that y(k) = 0.
-1, -2/5, 0, 1
Solve 32*y - 128/3 - 8*y**2 + 2/3*y**3 = 0 for y.
4
Let a be (-94)/(-18) + (-2)/9. Let s(u) = -2*u**2 + 8*u - 13. Let z(q) = -q**2 + 4*q - 7. Let m(k) = a*z(k) - 3*s(k). Suppose m(t) = 0. Calculate t.
2
Let k**4 - 10*k**3 + 2*k**4 - 3*k**4 + 2*k**4 = 0. Calculate k.
0, 5
Let b(p) be the first derivative of -2*p**5/35 - p**4/7 + 2*p**3/21 + 2*p**2/7 - 1. Factor b(w).
-2*w*(w - 1)*(w + 1)*(w + 2)/7
Determine y, given that -5*y**2 + 0*y**2 + y**2 + 3*y + 9*y = 0.
0, 3
Let d be (1/(-130))/(15/(-60)). Let w(x) be the second derivative of 0 + 1/39*x**3 + 0*x**2 + 4*x - 5/78*x**4 + d*x**5. Let w(y) = 0. Calculate y.
0, 1/4, 1
Suppose 13*f - 8*f = -50. Let y(u) = u**3 + 11*u**2 + 11*u + 13. Let q be y(f). Suppose -1/3*t**4 + 1/3 + 0*t**2 + 2/3*t - 2/3*t**q = 0. Calculate t.
-1, 1
Let t(i) be the third derivative of 0 - 2*i**2 - 1/9*i**3 + 1/180*i**5 + 0*i + 1/72*i**4. Factor t(p).
(p - 1)*(p + 2)/3
Factor -3/5*m**3 + 12/5*m**2 - 9/5*m + 0.
-3*m*(m - 3)*(m - 1)/5
Suppose -3*y + 4*v + 14 = 0, 5*y - 3*v + 1 = 17. Let 0*z - 2/7*z**y + 0 = 0. Calculate z.
0
Let n = 169/6 - 28. Let x(y) be the first derivative of 0*y**3 + 0*y - 1/12*y**4 + n*y**2 - 1. Solve x(b) = 0.
-1, 0, 1
Let d = 5/18 - 1/36. Factor 0*z + 0*z**2 - 1/4*z**5 + 0 - d*z**4 + 0*z**3.
-z**4*(z + 1)/4
Let r(u) be the third derivative of 1/2*u**4 - 8*u**2 + 0 - 1/30*u**5 + 0*u - 3*u**3. Suppose r(m) = 0. What is m?
3
Suppose -2*m - 4*m**3 - 6*m**4 + 3*m**4 + 4*m**4 - 2*m**4 - 5*m**2 = 0. What is m?
-2, -1, 0
Let q(g) = -7*g**4 + 3*g**2. Let p(b) = -20*b**4 + 9*b**2. Let k(i) = -4*p(i) + 11*q(i). Determine d, given that k(d) = 0.
-1, 0, 1
Let z(r) be the third derivative of 1/735*r**7 - 1/210*r**5 + 0*r**3 + 3*r**2 + 0*r - 1/1176*r**8 + 0 + 1/420*r**6 + 0*r**4. Suppose z(h) = 0. Calculate h.
-1, 0, 1
Let j(g) be the first derivative of -2/9*g**3 + 3 + 1/18*g**6 + 0*g + 0*g**4 - 1/6*g**2 + 2/15*g**5. Factor j(r).
r*(r - 1)*(r + 1)**3/3
Suppose 2*r = -r + 9. Let u = r - 1. Factor -8*i**u - 4*i + i + 5*i.
-2*i*(4*i - 1)
Let z(f) = -6*f**2 - 8*f. Let u(a) = -4*a**2 - 5*a. Let q(n) = 8*u(n) - 5*z(n). Find v such that q(v) = 0.
0
Suppose 4 = -2*t - 12. Let s = t - -12. Find o such that -10*o + 4*o**3 + 3*o**3 - s*o**2 + 4 + 3*o**3 = 0.
-1, 2/5, 1
Suppose 3/5*h**3 - 6/5 + 0*h**2 - 9/5*h = 0. Calculate h.
-1, 2
Suppose 0 = 3*k - 3*a - 12, 3 = -2*k + 5*a + 17. Let w(f) be the first derivative of -3/2*f**4 + 0*f - 1 + 2/5*f**5 + 2*f**3 - f**k. Factor w(r).
2*r*(r - 1)**3
Let s(x) be the secon