4. Solve d(m) = 0.
-2/9, 1
Let w(t) = -21*t**2 - 1. Let i be (-87)/4 - (-2)/(-8). Let r(x) = 4*x**2. Let z(q) = i*r(q) - 4*w(q). Factor z(d).
-4*(d - 1)*(d + 1)
Let q be 8 + (1 - 4)/1. Suppose q*n - 2 = 13. Determine u, given that -2*u**4 + 0*u**3 + 3*u**3 - 2*u**n - 2*u**3 + 2*u**2 + u = 0.
-1, -1/2, 0, 1
Let p(t) be the first derivative of 8/11*t - 2/11*t**3 + 0*t**2 - 3 - 1/22*t**4. Factor p(j).
-2*(j - 1)*(j + 2)**2/11
Let k(b) = 2*b - 9. Suppose 6 = -2*i + 3*i. Let x be k(i). What is s in 4*s**4 + 3*s**x + 2*s**2 - s**4 + s**5 - s**2 = 0?
-1, 0
Factor -2*n**3 + 159 + 2*n - 159.
-2*n*(n - 1)*(n + 1)
Let z(u) be the first derivative of u**6/180 + u**5/30 + 2*u**3/3 + 3. Let g(r) be the third derivative of z(r). Determine q, given that g(q) = 0.
-2, 0
Let -4 - 4*n**2 + 10*n - 4*n + 28*n**2 + 14*n**3 = 0. What is n?
-1, 2/7
Factor 0 + 2/7*k**4 - 6/7*k**2 + 0*k**3 + 4/7*k.
2*k*(k - 1)**2*(k + 2)/7
Let p(z) be the third derivative of -z**5/140 + 3*z**4/28 + 48*z**2. Solve p(m) = 0.
0, 6
Suppose -4*a + 3*a + q = 2, 2 = -4*a + q. Let b be ((-1)/(-5))/((-3)/(-5)). Factor a*h - b*h**2 + 1/3.
-(h - 1)*(h + 1)/3
Let u(o) be the third derivative of 0*o**4 + 0 + 0*o**3 + 0*o**5 - 1/1680*o**8 + 1/350*o**7 - 1/300*o**6 + 0*o - 4*o**2. What is x in u(x) = 0?
0, 1, 2
Let i be 4 + (-3 - (0 - 2)). Let m be 8/(-10) + 1/5 + 1. Factor -2*t + 8/5*t**i + m*t**5 - 8/5*t**4 + 4/5 + 4/5*t**2.
2*(t - 2)*(t - 1)**3*(t + 1)/5
Let r(p) be the first derivative of 3*p**5/5 - 9*p**4/4 + 3*p**3 - 3*p**2/2 + 59. Determine f so that r(f) = 0.
0, 1
Let w = -78/95 - -97/95. Let s = 17/35 - 2/7. Let 2/5*a - w*a**2 - s = 0. Calculate a.
1
Let f(a) = 5*a**2 + 20*a - 6. Let c(y) = 5*y**2 + 20*y - 5. Let k(l) = -6*c(l) + 5*f(l). Factor k(h).
-5*h*(h + 4)
Let h(b) = 3*b**4 - 7*b**3. Let a(v) = -4*v**4 + 8*v**3. Let f(s) = 5*a(s) + 6*h(s). Find z such that f(z) = 0.
-1, 0
Let x(g) be the second derivative of g**7/56 - 3*g**6/40 + 9*g**5/80 - g**4/16 + 4*g - 5. Factor x(h).
3*h**2*(h - 1)**3/4
Let f(c) be the third derivative of c**8/84 - 6*c**7/35 + 13*c**6/15 - 4*c**5/3 - 4*c**4 + 64*c**3/3 - c**2. What is n in f(n) = 0?
-1, 2, 4
Let d be (312/30)/2 - 5. Find j, given that d + 0*j - 1/5*j**2 = 0.
-1, 1
Let d be (-4 - -4)/(1 + 0). Factor 0 + 0*y**2 - 2/11*y**4 - 2/11*y**3 + d*y.
-2*y**3*(y + 1)/11
Let v(s) be the second derivative of s**6/270 - s**5/90 + s**3/27 - s**2/18 - 30*s. What is f in v(f) = 0?
-1, 1
Factor -2/3*a + 0*a**3 + 4/3*a**4 + 0 + 2/3*a**5 - 4/3*a**2.
2*a*(a - 1)*(a + 1)**3/3
Let z = 227 - 734/3. Let b = 18 + z. Factor 0*v**2 - 1/3*v**4 + 0*v - b*v**3 + 0.
-v**3*(v + 1)/3
Let h(o) = -o - 4. Let f be h(-6). Factor -2*i + 4*i**2 + f*i**2 - i + 0*i**2 - 3*i**3.
-3*i*(i - 1)**2
Suppose -10*b - 4*b**2 + 4*b + 8*b**2 + 12 + 4*b**3 - 14*b = 0. Calculate b.
-3, 1
Let f = -5 - -8. Factor -2/3*p + 0 - 7*p**2 + 64*p**5 - 20*p**f + 16/3*p**4.
p*(3*p - 2)*(4*p + 1)**3/3
Factor 45*b**3 + 19*b - 21*b**4 + 3*b**5 - 2*b**2 - 37*b**2 - 7*b.
3*b*(b - 4)*(b - 1)**3
Let z be 1 + 0 + 6/(-24). What is a in z*a**4 - 3/2*a**3 + 0*a + 0*a**2 + 0 = 0?
0, 2
Let w(h) be the second derivative of h**7/315 - h**6/54 + 2*h**5/45 - h**4/18 + h**3/27 - 3*h**2/2 + 2*h. Let m(n) be the first derivative of w(n). Factor m(d).
2*(d - 1)**3*(3*d - 1)/9
Factor 14/3*s**3 + 52/3*s**2 + 0 - 16/3*s.
2*s*(s + 4)*(7*s - 2)/3
Let t(b) = 16*b + 290. Let z be t(-18). Factor 7/5*p**z - 16/5*p + 4/5.
(p - 2)*(7*p - 2)/5
Solve -108/7*w**4 + 9*w**3 + 51/7*w**2 - 3/7 - 3/7*w = 0 for w.
-1/3, 1/4, 1
Let a(l) be the second derivative of -1/9*l**4 - 1/27*l**3 + 0 + 2/9*l**2 - 4*l. Factor a(s).
-2*(2*s - 1)*(3*s + 2)/9
Determine d so that -2/9*d + 2/9*d**2 + 0 = 0.
0, 1
Let n(c) be the third derivative of -11*c**8/1512 + 2*c**7/189 + c**6/540 + 35*c**2. Determine m so that n(m) = 0.
-1/11, 0, 1
Suppose -2 - 1 = 3*i - 3*j, 0 = -2*i - 4*j + 16. Factor -2*k**2 - 3 - 7*k**i - 3 - 14*k - 2*k**3 - k**2.
-2*(k + 1)**2*(k + 3)
Let q(p) = -p**2 + 3*p + 3. Let d be q(3). Suppose 4*y + 0*y = 8. Let -4*l + 2*l**3 + 4*l**d - 4*l**3 + y*l = 0. What is l?
-1, 0, 1
Let v(p) be the third derivative of p**6/600 - p**5/300 - 5*p**2. Factor v(j).
j**2*(j - 1)/5
Let m(b) be the first derivative of 3*b**5/5 - 3*b**4/2 - b**3 + 3*b**2 - 2. Factor m(i).
3*i*(i - 2)*(i - 1)*(i + 1)
Let x(g) be the second derivative of -g**7/273 + g**6/195 + g**5/130 - g**4/78 - 13*g. Solve x(c) = 0.
-1, 0, 1
Let x be -4 + 16 + 0 + 2. Suppose 16*q - x - 3*q**2 - 2 - q**2 = 0. Calculate q.
2
Suppose 0 = 4*q, -2*q + q = 2*t. Determine b so that 0*b**3 + 0*b + t*b**4 + 0*b**2 + 0 - 2/7*b**5 = 0.
0
Factor 8/15 + 2/15*y**2 + 8/15*y.
2*(y + 2)**2/15
Let y = 34 - 34. Let p(k) be the third derivative of 0*k**3 - 3*k**2 + 0*k - 1/42*k**7 + y*k**5 - 1/112*k**8 + 0*k**4 - 1/60*k**6 + 0. Solve p(c) = 0 for c.
-1, -2/3, 0
Solve 10/7 - 12/7*i + 2/7*i**2 = 0 for i.
1, 5
Let s(v) be the first derivative of 3*v**3 - 3*v**2/2 - 6*v - 38. Let s(u) = 0. What is u?
-2/3, 1
Let s(t) be the third derivative of t**11/997920 + t**10/453600 - t**5/60 + 3*t**2. Let b(r) be the third derivative of s(r). Let b(w) = 0. What is w?
-1, 0
Let x be 90/12*16/6. Factor -x*c + 5 + 5*c**3 + 12*c**2 - 4*c**4 + 3 + c**3 - 2*c**3.
-4*(c - 1)**3*(c + 2)
Let s(a) be the third derivative of 1/30*a**4 + 0 + 0*a**3 + 1/25*a**5 + 0*a - 10*a**2 - 7/600*a**6. Factor s(z).
-z*(z - 2)*(7*z + 2)/5
Let a(v) be the third derivative of v**8/84 + v**7/30 - v**6/60 - 2*v**5/15 - v**4/12 + v**3/6 + 23*v**2. Find p, given that a(p) = 0.
-1, 1/4, 1
Let o = -25 + 27. Let h(q) be the third derivative of 1/180*q**5 + 0 + 0*q + 3*q**o + 0*q**4 + 0*q**3 - 1/630*q**7 + 0*q**6. Solve h(g) = 0 for g.
-1, 0, 1
Let z(p) be the second derivative of 0*p**4 + 0*p**2 + 0 - 1/9*p**3 - p + 1/30*p**5. Solve z(c) = 0 for c.
-1, 0, 1
Let p(h) be the second derivative of h**4/18 - h**3/9 - 6*h. Factor p(r).
2*r*(r - 1)/3
Let v(o) = -11*o**2 - 19*o - 19. Let k(f) = -6*f**2 - 9*f - 9. Let d(q) = 5*k(q) - 3*v(q). Factor d(w).
3*(w + 2)**2
Suppose 0 = -503*j + 480*j + 115. Find r such that 1/2*r**2 + 1/4*r + 3/4*r**j + 0 - r**3 - 1/2*r**4 = 0.
-1, -1/3, 0, 1
Let p(q) be the third derivative of 0*q - 1/30*q**4 - 1/15*q**3 + 0 - 1/150*q**5 - 2*q**2. Suppose p(j) = 0. What is j?
-1
Let j(o) = -7*o**3 - 9*o**2 + 7*o + 9. Let s(v) = v + 3. Let n be s(-9). Let q(r) = -6*r**3 - 10*r**2 + 6*r + 10. Let i(w) = n*j(w) + 5*q(w). Factor i(b).
4*(b - 1)*(b + 1)*(3*b + 1)
Suppose -7/2*w**4 - 5/2*w**2 + 8*w + 6 - 1/2*w**5 - 15/2*w**3 = 0. What is w?
-3, -2, -1, 1
Let m(x) be the first derivative of -1/8*x**4 + 0*x + 1 + 1/4*x**2 - 1/20*x**5 + 1/12*x**3. Factor m(a).
-a*(a - 1)*(a + 1)*(a + 2)/4
Suppose 9*s + 2*p = 5*s - 2, -1 = p. Find h, given that -1/3*h**2 + s + 2/3*h - 1/3*h**3 = 0.
-2, 0, 1
Suppose 5*r + 4*m = 45, -r - 4*m + 6 = -19. Suppose -16 = -r*u + u. Factor 0*i**4 + u*i**3 - i**4 + 2*i**2 - 3*i**3.
-i**2*(i - 2)*(i + 1)
Let r(o) be the third derivative of 2/15*o**5 + 1/12*o**4 + o**2 + 0 + 0*o**3 + 1/168*o**8 + 1/10*o**6 + 4/105*o**7 + 0*o. Suppose r(m) = 0. Calculate m.
-1, 0
Let a be -5 + (-2 - -4) - -7. Determine g, given that 4*g**3 - 4/3 - 4/3*g**a - 2*g**5 + 8/3*g**2 - 2*g = 0.
-1, -2/3, 1
Let b(y) = -y**3 - 4*y**2 - 4*y - 2. Let q be b(-3). Let s be (4/(-14))/(-1*2/14). Factor 1/4*w**s + q + w.
(w + 2)**2/4
Let d = 1 + 1. Suppose d*p - 8 = -0*p. What is t in 3*t**5 + 5*t**4 + 0 - 6*t**2 - 3 - 9*t + 6*t**4 - 2*t**p + 6*t**3 = 0?
-1, 1
Let f(k) be the third derivative of 1/2*k**3 + 4*k**2 + 1/135*k**5 - 1/405*k**6 + 0*k + 0 - 1/108*k**4. Let i(m) be the first derivative of f(m). Factor i(d).
-2*(2*d - 1)**2/9
Let c(j) be the third derivative of -j**5/120 + j**4/24 - j**3/12 - 7*j**2. Factor c(m).
-(m - 1)**2/2
Let b = -1 + 4. What is p in 4 + 0*p**2 - 6*p + b*p**2 - p**2 = 0?
1, 2
Suppose 0*t + 3 = t. Let a be (t/(-12))/(1/(-12)). Solve -6*n**4 + 0*n**a - 3*n**5 - 3*n**3 + 0*n**3 = 0.
-1, 0
Let z(t) be the second derivative of -t**7/399 + 2*t**6/285 - t**4/57 + t**3/57 + 24*t. Factor z(r).
-2*r*(r - 1)**3*(r + 1)/19
Let i(s) be the second derivative of s**8/840 + s**7/588 - s**6/630 - s**3/6 - 2*s. Let c(g) be the second derivative of i(g). Find q such that c(q) = 0.
-1, 0, 2/7
Let b(u) be the first derivative of -2*u**3/33 + 4*u**2/11 - 6*u/11