 6. Suppose -2*q**2 + 3*q**b + q**3 - 2*q**2 + 0*q**2 - q + 1 = 0. Calculate q.
-1, 1
Let n be -3 + (-16)/(-6) - -1. Let n*z**2 - 1/3 + 1/3*z = 0. What is z?
-1, 1/2
Let m be ((-6)/(-4))/((-3)/(-4)). Factor -2*h - 3*h**m - 2 + 5*h + 2*h**2 + 0*h.
-(h - 2)*(h - 1)
Let t(i) be the first derivative of 7*i**5/2 + 5*i**4/4 + 12. Factor t(z).
5*z**3*(7*z + 2)/2
Let p(c) be the second derivative of c**5/80 - c**4/16 + c**3/8 - c**2/8 + 11*c. Find z such that p(z) = 0.
1
Let k(y) = y**3 - 8*y**2 - 8*y - 9. Let l be k(9). Let b = 332/3 + -108. What is x in -2/3*x**3 + 0*x + 0 - b*x**5 + 10/3*x**4 + l*x**2 = 0?
0, 1/4, 1
Let z be -1*4/(-14) - 2/56. What is n in -1/4*n**2 + 1/2*n - z = 0?
1
Suppose -4 + 1 = 3*w. Let g be 0 - w/((-2)/(-8)). Factor -s**3 - 3*s**g + 3*s**4 + s**4 + 2*s**3.
s**3*(s + 1)
Let j(c) = c**3 - 10*c**2 - 10*c - 11. Suppose -4*t - t + 55 = 0. Let o be j(t). Determine w, given that 2*w**4 + 3*w**3 + w**5 + o*w**5 - w**4 - 5*w**3 = 0.
-2, 0, 1
Let i(j) be the first derivative of -j**6/24 - j**5/10 + j**4/8 + 2*j**3/3 + 7*j**2/8 + j/2 - 5. Factor i(g).
-(g - 2)*(g + 1)**4/4
Let v(f) be the third derivative of -7*f**5/90 - f**4/4 - 2*f**3/9 + 7*f**2. Find m such that v(m) = 0.
-1, -2/7
Factor -2*l + 2*l**2 + 3*l**2 - l**2 - 2*l**2.
2*l*(l - 1)
Let c(v) be the first derivative of -v**4/6 + 2*v**3/9 + 2*v**2/3 + 32. Factor c(t).
-2*t*(t - 2)*(t + 1)/3
Let g be 14/63 - (-68)/18. Find y such that -4 - 1 + 2 - y**2 + g*y**2 = 0.
-1, 1
Let -4/3*v**3 + 0*v**2 + 2/3*v**5 + 0 - 2/3*v**4 + 0*v = 0. What is v?
-1, 0, 2
Let o(h) be the third derivative of h**6/8 + 5*h**5/12 - 55*h**4/24 + 5*h**3/2 + 13*h**2. Factor o(q).
5*(q - 1)*(q + 3)*(3*q - 1)
Factor 4/3 - 1/3*x**3 + 4/3*x - 1/3*x**2.
-(x - 2)*(x + 1)*(x + 2)/3
Factor -1/3 + 0*i**2 + 1/6*i**3 - 1/2*i.
(i - 2)*(i + 1)**2/6
Let x(c) be the second derivative of c**7/280 + c**6/30 + c**5/8 + c**4/4 + 2*c**3/3 - 5*c. Let n(k) be the second derivative of x(k). Solve n(r) = 0 for r.
-2, -1
Let p = 103/327 + 2/109. Let o(r) be the first derivative of 3 - 4/5*r**5 + 0*r**2 + 1/4*r**6 + 0*r - p*r**3 + 7/8*r**4. Let o(n) = 0. Calculate n.
0, 2/3, 1
Let 0 + 3/4*k**3 - 3/2*k + 3/4*k**2 = 0. What is k?
-2, 0, 1
Let c = 121 + -117. Let q(p) be the second derivative of 0 - 1/42*p**c + 0*p**2 - 2*p + 1/21*p**3. Factor q(h).
-2*h*(h - 1)/7
Factor 0 + 0*k - 4/5*k**3 + 1/5*k**4 + 3/5*k**2.
k**2*(k - 3)*(k - 1)/5
Suppose 35 = -18*q + 89. Let m(s) be the first derivative of -5 - s**2 - 4/9*s**q + 4/3*s. Factor m(b).
-2*(b + 2)*(2*b - 1)/3
Let b be (0 - -6)/(27/48). Factor 2/3*z**2 - 16/3*z + b.
2*(z - 4)**2/3
Determine l so that 1/4*l**2 + 0 - 1/4*l**4 - 1/4*l + 1/4*l**3 = 0.
-1, 0, 1
Let a(m) be the second derivative of -1/18*m**4 + 1/30*m**5 + 0 + 0*m**2 + 0*m**3 - 1/63*m**7 + 5*m + 1/45*m**6. Determine k so that a(k) = 0.
-1, 0, 1
Suppose 4*s = -4 + 24. Suppose 3*i - 6 = 0, -2*d + d = s*i - 12. Factor 2/5*c**4 - 2/5*c**3 + 4/5 - 6/5*c**d + 2/5*c.
2*(c - 2)*(c - 1)*(c + 1)**2/5
Let o(y) be the second derivative of y**5/30 - y**4/18 - 6*y. Factor o(s).
2*s**2*(s - 1)/3
Let k(p) be the third derivative of -p**10/5040 - p**9/1512 - p**8/1680 + p**4/8 + 4*p**2. Let q(x) be the second derivative of k(x). Factor q(j).
-2*j**3*(j + 1)*(3*j + 2)
Factor -7*r**4 + 5*r**4 + 0*r**4 - 20*r**3 - 2*r**4 - 12*r - 28*r**2.
-4*r*(r + 1)**2*(r + 3)
Let a(s) be the second derivative of -s**5/50 - s**4/6 - 7*s**3/15 - 3*s**2/5 - 28*s. Let a(c) = 0. What is c?
-3, -1
Suppose -d + 3*d - 3 = 3*u, 1 = 2*d - u. Let o be d*(-1)/3*-1. Factor o - 10/3*k**2 + 4/3*k + 2*k**3.
2*k*(k - 1)*(3*k - 2)/3
Let h(j) be the third derivative of -6*j**2 + 1/280*j**7 + 1/80*j**6 + 0*j**3 + 1/80*j**5 + 0*j + 0 + 0*j**4. Let h(q) = 0. Calculate q.
-1, 0
Let y(k) be the third derivative of -4*k**2 + 0*k**3 - 1/60*k**6 + 0 - 1/6*k**4 - 1/10*k**5 + 0*k. Factor y(u).
-2*u*(u + 1)*(u + 2)
Let h(d) be the third derivative of d**6/24 + d**5/4 - 4*d**2. What is a in h(a) = 0?
-3, 0
Let c(p) be the third derivative of p**7/735 - p**5/70 - p**4/42 + 9*p**2. Factor c(q).
2*q*(q - 2)*(q + 1)**2/7
Let v(u) be the second derivative of u**8/560 + u**7/140 - u**5/20 - u**4/8 + u**3/2 + u. Let a(j) be the second derivative of v(j). Let a(p) = 0. Calculate p.
-1, 1
Factor -4/7 - 2/7*i**2 - 6/7*i.
-2*(i + 1)*(i + 2)/7
Suppose -5 = n, 5*s - 5*n = s - 71. Let y be (s/30)/(2/(-5)). Factor -5*z**2 + 2*z**2 + 4*z**y - 2*z + 0*z.
z*(z - 2)
What is p in 3*p**5 + 7*p - 5*p**5 + 10*p**4 + 14*p**2 - 11*p - 18*p**3 = 0?
0, 1, 2
Let k be (-37)/148*(2/4 + -1). Let b(g) be the second derivative of 1/4*g**3 - 2*g + 1/40*g**5 + k*g**4 + 1/4*g**2 + 0. Determine r so that b(r) = 0.
-1
Let o(d) be the first derivative of -14*d**3/3 - 3*d**2 + 43. Find s such that o(s) = 0.
-3/7, 0
Let y(w) = w**3 - 6*w**2 + 8*w - 6. Let d be y(5). Factor 10*o**2 + 4*o**2 + d - 2*o**2 - 39*o.
3*(o - 3)*(4*o - 1)
Let d(s) be the first derivative of s**2 - 2*s + 1. Let l be d(3). Factor 5*u**2 + 7*u**2 + 2*u + 12*u**3 + 6*u**5 + 8*u**4 - 4*u**2 - l*u**5.
2*u*(u + 1)**4
Suppose -2*l = -3*p, 5*p - p = l. Let m be (-1 - l)/((-1)/2). Factor -2*d + 4*d**m + 3*d + d**4 - 5*d**4 + d**3 - 2*d.
-d*(d - 1)*(d + 1)*(4*d - 1)
Let o(k) = k - 4. Let i be o(6). Factor -4*b**5 + b**4 + i*b**5 - 2*b**4 - b**4.
-2*b**4*(b + 1)
Suppose -4*z**2 - 2 - 30*z - 33 + z**2 + 8*z**2 = 0. What is z?
-1, 7
Let y = -80 - -174. Let r = 476/5 - y. Factor r*n**4 + 0 + 4/5*n**3 - 2/5*n**2 + 0*n.
2*n**2*(n + 1)*(3*n - 1)/5
Let q be 1/(-2)*(0 + -4). Factor 6*d**2 - 7*d**4 + 0*d + d**4 + q*d**3 - 2*d.
-2*d*(d - 1)*(d + 1)*(3*d - 1)
Let z(x) = -3*x**4 + 9*x**3 - 3*x. Let a(r) = r**3 + r**2 - r. Let o(n) = -3*a(n) + z(n). Factor o(h).
-3*h**2*(h - 1)**2
Let v = -2/271 - -277/813. Factor -v*z**3 - 1/3 + 1/3*z + 1/3*z**2.
-(z - 1)**2*(z + 1)/3
Let n(i) = -8*i**3 + i**2 + 2*i. Let s(c) = -39*c**3 + 6*c**2 + 9*c. Let f(v) = 24*n(v) - 5*s(v). Let f(m) = 0. Calculate m.
0, 1
Let t(o) = 0*o**3 + 3*o - o**3 - o - 6 + 5*o**2. Let s be t(5). Determine j, given that 3*j**s - j**4 - j**2 - j**2 = 0.
-1, 0, 1
Let c be (22/8)/(27/12). Let y(k) be the first derivative of 4/3*k**4 + 0*k - 2 + 7/15*k**5 + 1/3*k**2 + c*k**3. Factor y(j).
j*(j + 1)**2*(7*j + 2)/3
Let p(x) be the first derivative of x**6/900 - x**5/300 - 5*x**3/3 + 7. Let b(t) be the third derivative of p(t). Determine z so that b(z) = 0.
0, 1
Let v(a) be the second derivative of -2/5*a**2 + 1/5*a**3 - 1/50*a**5 + 0*a**4 - 4*a + 0. Factor v(z).
-2*(z - 1)**2*(z + 2)/5
Let o(l) be the first derivative of l**5/45 - l**4/12 + l**3/9 - l**2/18 + 6. Factor o(d).
d*(d - 1)**3/9
Suppose 0 = -0*k + 4*k. Let s(z) be the third derivative of 0*z + k*z**4 + 0*z**3 - 2*z**2 + 0 + 1/60*z**5. Factor s(o).
o**2
Let g(p) = p**2 + p - 2. Let a be g(2). Factor 0*j - 4*j - 60*j**a + 10*j**2 + 117*j**3 - 8*j + 2*j**2 - 300*j**5.
-3*j*(2*j + 1)**2*(5*j - 2)**2
Let g(n) be the first derivative of -2/27*n**3 - 2 - 8/9*n - 4/9*n**2. Suppose g(i) = 0. What is i?
-2
Let r(z) = -z**3 - 7*z**2 - 8*z - 4. Let u be r(-6). Let c be (-1 - 11)*(-2)/u. Solve 2/3*p**2 + 2/9 - 2/3*p - 2/9*p**c = 0.
1
Let b be ((-3)/(-24) + 0)/(4/24). Solve -b*h - 3/4*h**2 - 1/4*h**3 - 1/4 = 0.
-1
Factor 12*w + 37*w**2 - 29*w**2 - 2*w**3 - w**3 - w**3.
-4*w*(w - 3)*(w + 1)
Let b = 3607/7 + -515. Find m, given that 2/7*m**3 - b - 6/7*m**2 + 6/7*m = 0.
1
Factor 8/7 + 2/7*f**2 - 8/7*f.
2*(f - 2)**2/7
Let f(v) be the second derivative of -v**4/96 - v**3/24 - v**2/16 - 11*v. Factor f(y).
-(y + 1)**2/8
Let k(w) = -w**2 - 25*w - 1. Let n(f) = -f**2 - 3*f - 1. Let a be n(-5). Let p(r) = r + 6*r - 2*r. Let g(d) = a*p(d) - 2*k(d). Determine q so that g(q) = 0.
1/2, 2
Let i(s) be the second derivative of 0*s**2 + 1/10*s**5 + s + 0*s**3 + 0 - 1/6*s**4. What is n in i(n) = 0?
0, 1
Let a = -9 + 15. Factor -1 - y**2 + y**2 - 8*y + a*y - y**2.
-(y + 1)**2
Let t(k) = -18*k**4 - 39*k**3 - 6*k**2 + 9*k - 3. Let x(f) = 17*f**4 + 40*f**3 + 5*f**2 - 10*f + 4. Let g(s) = -4*t(s) - 3*x(s). Find o, given that g(o) = 0.
-1, 0, 2/7
Let l be 4/6 + (-546)/1224. Let n = l + 1/34. Suppose 1/2*h**4 - h**3 + 3/4*h**5 + n*h - 1/2*h**2 + 0 = 0. Calculate h.
-1, 0, 1/3, 1
Let t(y) = y + 1. Let d be t(3). Factor 36*r**3 - 3*r - d*r**2 + 5*r**2 - 4*r**2.
3*r*(3*r - 1)*(4*r + 1)
Let q(r) = r*