*5. Factor v(h).
2*h**2*(h + 1)**3
Determine b, given that 8*b - 16/3 + 2/3*b**3 - 4*b**2 = 0.
2
Let a = -20 - -8. Let w(g) = -g**2 - 13*g - 9. Let u be w(a). Factor -1/2*d**u - 3/2*d + 1/2 + 3/2*d**2.
-(d - 1)**3/2
Let f be 5/2*(-1 - 1). Let s(v) = -2*v - 7. Let c be s(f). Factor 0 + 1/3*h**c + 0*h**2 + 0*h.
h**3/3
Suppose 5*a - 2 + 27 = 0, 8 = -4*y - 4*a. Find r such that 5/2*r + 1/2*r**2 - 1/2*r**y + 3/2 = 0.
-1, 3
Let s(y) be the first derivative of -y**3/21 - 3*y**2/14 - 2*y/7 - 7. Factor s(m).
-(m + 1)*(m + 2)/7
Let r be ((6 - 4) + -1)/((-2)/(-3)). Factor 3/2*u**4 - u**3 - u**2 + r*u - 1/2 - 1/2*u**5.
-(u - 1)**4*(u + 1)/2
Let r(z) be the first derivative of -z**4/16 - z**3/2 - 3*z**2/2 - 2*z + 20. Factor r(l).
-(l + 2)**3/4
Let o(b) = -b**3 - 2*b**2 + 2*b - 3. Let f be o(-3). Let h = 4 - f. Determine j so that -h*j**2 + 2*j + 0 + 0 + 2*j**3 = 0.
0, 1
Let k(n) be the second derivative of n**7/399 - n**6/285 - n**5/190 + n**4/114 - 18*n. Find p such that k(p) = 0.
-1, 0, 1
Factor -1/4*x - 1/2*x**2 + 1/2*x**4 + 0*x**3 + 0 + 1/4*x**5.
x*(x - 1)*(x + 1)**3/4
Let j(g) be the first derivative of -g**4/4 - 2*g**3 - g**2/2 + g + 2. Let m be j(-6). Solve -3*d + m + 2*d**3 - 3*d + 0 - 3 = 0.
-2, 1
Let i = -381 + 383. Solve i - 6*l + 5/2*l**2 = 0 for l.
2/5, 2
Let b = -5/31 + 118/155. Suppose -1/5*n**4 + 2/5 + b*n**2 - 1/5*n**3 + n = 0. What is n?
-1, 2
Let x be (-3 - -3)*3/(-6). Determine h so that x + 0 - 36*h**2 + 33*h**2 = 0.
0
Let q(g) be the third derivative of g**5/15 + 2*g**4/3 + 2*g**3 - 24*g**2. Factor q(a).
4*(a + 1)*(a + 3)
Factor 78*g + 12 + 69*g**2 + 33/2*g**3.
3*(g + 2)**2*(11*g + 2)/2
Let i be (-20 + 19)*(-1)/3. Let p(r) be the first derivative of i*r**2 + 3 + 1/6*r**4 + 4/9*r**3 + 0*r. Determine x, given that p(x) = 0.
-1, 0
Let r(l) be the third derivative of l**8/112 + 11*l**7/70 + 43*l**6/40 + 73*l**5/20 + 7*l**4 + 8*l**3 + 19*l**2. Solve r(c) = 0.
-4, -1
Suppose -13*m**2 + m + 8*m**2 + 2*m + 8*m**2 = 0. Calculate m.
-1, 0
Let q(w) be the second derivative of 0*w**2 + 7/75*w**6 - 3*w + 0 - 1/21*w**7 + 0*w**4 + 0*w**3 - 1/25*w**5. Let q(c) = 0. What is c?
0, 2/5, 1
Let t(d) = -12*d - 4*d**2 + 0*d**2 + 2*d + d**2. Let y(m) = m**2 + 3*m. Let p(h) = -h**2 + h + 7. Let r be p(0). Let v(i) = r*y(i) + 2*t(i). Factor v(o).
o*(o + 1)
Solve 0*d + 9/7*d**3 + 0 - 3/7*d**4 - 6/7*d**2 = 0 for d.
0, 1, 2
Let w(m) be the first derivative of 0*m**3 - 2 - 1/2*m**2 + 1/20*m**5 + 0*m + 3/16*m**4. Factor w(b).
b*(b - 1)*(b + 2)**2/4
Let r = -36 + 182/5. Let -3/5*u - r + 1/5*u**3 + 0*u**2 = 0. Calculate u.
-1, 2
Let q(f) be the second derivative of -1/21*f**3 - 1/210*f**5 - 2*f - 1/42*f**4 + 3/2*f**2 + 0. Let r(m) be the first derivative of q(m). Factor r(b).
-2*(b + 1)**2/7
Let b(a) be the second derivative of 5*a**4/6 - 13*a**3/3 - 6*a**2 - 6*a. Find r, given that b(r) = 0.
-2/5, 3
Let a = 314/3 - 2093/20. Let n(b) be the third derivative of -a*b**5 + 0*b + 2*b**2 + 0 - 1/12*b**4 + 0*b**3. Factor n(u).
-u*(u + 2)
Suppose 2*z**3 - 4*z**2 + 7*z**2 + 0*z**3 - 6*z + z**3 = 0. What is z?
-2, 0, 1
Let r(i) be the first derivative of -i**5/180 + i**4/24 - i**3/9 + i**2 - 7. Let v(n) be the second derivative of r(n). Let v(h) = 0. Calculate h.
1, 2
Let s = 720 + -3564/5. Let c be -5 - (-32)/12*3. Factor 2*r**4 - s*r**c + 0 + 24/5*r**2 + 16/5*r.
2*r*(r - 2)**2*(5*r + 2)/5
Let b = 6 + -4. Factor 0*a - 3*a**3 + 6*a**b - 4*a + a**3.
-2*a*(a - 2)*(a - 1)
Solve -4*b**2 - b**2 + 0*b**2 + 6*b**2 = 0.
0
Suppose 3*h - 2 = 4. Factor -f**2 + 0*f**4 + 0*f**4 + h*f - f**3 - f + f**4.
f*(f - 1)**2*(f + 1)
Let a(j) be the first derivative of -2*j**5/5 - j**4/8 - 6. What is s in a(s) = 0?
-1/4, 0
Let d(s) be the second derivative of -s**7/8820 - s**6/2520 - s**4/12 + s. Let f(g) be the third derivative of d(g). Factor f(a).
-2*a*(a + 1)/7
Suppose 0 = -5*n + 10, -n + 3 = -c + 5. Factor 0*i + 0 + 3/5*i**5 - 6/5*i**2 + 0*i**c - 9/5*i**3.
3*i**2*(i - 2)*(i + 1)**2/5
Let y(l) = -l**3 + 7*l**2 - 6*l + 4. Let p be y(6). Let z(c) = 2*c**2 - c + 3. Let d(j) = -3*j**2 + j - 4. Let m(s) = p*z(s) + 3*d(s). Factor m(x).
-x*(x + 1)
Let l(x) be the first derivative of -2 - 15/4*x**4 + 6*x**3 + 3/5*x**5 + 6*x**2 - 24*x. Factor l(p).
3*(p - 2)**3*(p + 1)
Determine k, given that -1/7*k**2 - 4/7*k**5 + k**4 + 0 - 2/7*k**3 + 0*k = 0.
-1/4, 0, 1
Suppose 0 = 2*k + 4*d - 24, -18 = -3*k + 4*k - 4*d. Suppose 4*n - 8 = k*j + 8, -5*n = -3*j - 20. Find a, given that 0*a**3 + 5*a**n - 6*a**4 + a**3 = 0.
0, 1
Let y(k) be the second derivative of -k**6/1620 - k**5/270 - k**4/108 + k**3/2 - 2*k. Let g(c) be the second derivative of y(c). Find t, given that g(t) = 0.
-1
Let o be (-20)/(-6)*(-21)/7. Let d = -8 - o. Factor 2/3*l - 2/3*l**3 + 0 + 0*l**d.
-2*l*(l - 1)*(l + 1)/3
Suppose -o = -2*o + 6. Suppose -2*j = -c - 9, -c + o*c = 4*j - 33. Factor -11*x**3 + 18*x**4 - 16*x**j - 3*x**3 + 12*x - 2 + 2*x**3.
2*(x - 1)*(x + 1)*(3*x - 1)**2
Suppose i + 18 = 3*c - 0*c, -5*c + 29 = -2*i. Let v(s) = s - 5. Let m be v(c). Factor 2*k + 2 - 2*k**3 + 2 - 2*k**2 + 0 - m.
-2*(k - 1)*(k + 1)**2
Factor 12/19*j + 2/19*j**2 - 14/19.
2*(j - 1)*(j + 7)/19
Let m be 4/2 + (1 - -5). Let i = m + -3. Find c, given that 5*c**2 + i*c + 4 - 2 + 2*c = 0.
-1, -2/5
Let g(y) be the third derivative of y**5/90 - 13*y**4/18 + 169*y**3/9 + 26*y**2 - 2*y. Determine o so that g(o) = 0.
13
Let z(d) be the first derivative of -7*d**4 + 16*d**3 - 6*d**2 - 8*d + 2. Find g such that z(g) = 0.
-2/7, 1
Let z(m) be the second derivative of m**6/70 - m**5/20 + 2*m**3/21 - 4*m. Factor z(c).
c*(c - 2)*(c - 1)*(3*c + 2)/7
Let c(j) = -84*j**3 - 410*j**2 - 330*j - 58. Let o(g) = 168*g**3 + 821*g**2 + 661*g + 117. Let l(u) = -11*c(u) - 6*o(u). Find z such that l(z) = 0.
-4, -2/3, -2/7
Factor 0 + 40/3*v**2 + 80/3*v + 5/3*v**3.
5*v*(v + 4)**2/3
Factor 0 + 1/2*g - 1/2*g**3 + 0*g**2.
-g*(g - 1)*(g + 1)/2
Let j(y) be the first derivative of -y**4/10 + 2*y**3/5 - 2*y**2/5 + 5. Factor j(m).
-2*m*(m - 2)*(m - 1)/5
Suppose 4*h = 3*p + 11, -6*p = 2*h - 5*p - 3. Factor 1/2 - 1/2*m**3 - 1/2*m**h + 1/2*m.
-(m - 1)*(m + 1)**2/2
Let s(x) = -x**2 - 5*x + 11. Let l(v) = -2*v**2 - 4*v + 12. Let y = 0 - 4. Let i(p) = y*s(p) + 3*l(p). Solve i(a) = 0.
2
Let p = -19/22 + 761/66. Let f = -487 + 1477/3. Find z, given that -f*z**2 - p*z**3 + 10*z + 6 = 0.
-3/4, 1
Let q = -24 - -21. Let r(g) = 23*g**3 + 65*g**2 + 64*g + 13. Let w(s) = -116*s**3 - 324*s**2 - 320*s - 64. Let t(k) = q*w(k) - 16*r(k). Factor t(v).
-4*(v + 1)*(v + 2)*(5*v + 2)
Suppose -j - 4 + 28 = -4*o, -5*j + 25 = -o. Factor 4*w**4 + 0*w + 4*w + j*w - 8*w**3 - 4.
4*(w - 1)**3*(w + 1)
Let w be -16 - -15 - (-4 - 0). Let w*f - 6*f**2 + f**2 + f - 2*f**3 + 7*f**2 = 0. What is f?
-1, 0, 2
Suppose -62 = 3*q - 236. Let h = q + -288/5. Find r such that 0*r - 2/5*r**3 - h*r**5 + 0 - 4/5*r**4 + 0*r**2 = 0.
-1, 0
Let -343/3*o**3 - 98/3*o**2 + 8/3 + 28/3*o = 0. What is o?
-2/7, 2/7
Let f(x) = -x - 1. Let s be f(-6). Suppose -2*p + 20 = 16. Factor -2/5*d**3 + 0*d**4 + 0*d**p + 1/5*d + 1/5*d**s + 0.
d*(d - 1)**2*(d + 1)**2/5
Factor -135*q + 277*q + 9*q**2 - 3*q**5 - 142*q - 21*q**3 + 15*q**4.
-3*q**2*(q - 3)*(q - 1)**2
Let l = 6 - 3. Factor -v + 2*v**3 + 0*v**l - 2*v**2 - 3*v**3.
-v*(v + 1)**2
Suppose -144 = -3*r + 6*r. Let w be r/80 - 6/(-10). Factor -3/4*f**3 - 3/4*f**4 + w*f + 0 + 0*f**2.
-3*f**3*(f + 1)/4
Let f = 42953 - 8891135/207. Let j = 2/207 + f. Solve -2/3*n**4 + 0 + j*n**2 + 0*n + 0*n**3 = 0.
-1, 0, 1
Let i(c) = 28*c + 36. Let k(h) = h**2 - 28*h - 35. Let s(g) = -5*i(g) - 4*k(g). Factor s(u).
-4*(u + 2)*(u + 5)
Let g(u) be the third derivative of 0*u**3 - 1/180*u**5 + 0 + 0*u - 1/72*u**4 - 3*u**2. Factor g(j).
-j*(j + 1)/3
Let m(i) = -i**2 + 4*i - 6. Let p(r) = -r**2 + 3*r - 5. Let x(o) = 5*m(o) - 6*p(o). Determine s, given that x(s) = 0.
-2, 0
Let l(b) be the third derivative of -2*b**5/15 - 3*b**4/2 - 14*b**3/3 + 47*b**2. Suppose l(s) = 0. Calculate s.
-7/2, -1
Let l(n) be the first derivative of n**2 - 1/120*n**6 + 0*n + 0*n**5 + 1/24*n**4 + 0*n**3 - 2. Let x(f) be the second derivative of l(f). What is u in x(u) = 0?
-1, 0, 1
Let s(m) be the second derivative of -m**4/28 - 3*m**3/7 - 12*m**2/7 + 3*m - 4. Factor s(g).
-3*(g + 2)*(g + 4)/7
Let z = 1211 - 1209. Factor 2/7*u**z + 16/7*u**4 + 0 + 8/7*u**5 + 10/7*u**3