. Let y(l) = m*s(l) - n(l). Determine j, given that y(j) = 0.
-1, 0
Suppose -l - 9*x = -4*x, -x - 26 = -5*l. Let f = 95/412 - -2/103. Solve -1/4 - 1/4*q - 1/4*q**l - f*q**4 + 1/2*q**2 + 1/2*q**3 = 0.
-1, 1
Let z(w) be the second derivative of 1/3*w**2 - 2/9*w**3 - 3*w + 0 + 1/18*w**4. Factor z(o).
2*(o - 1)**2/3
Let u = -11/4 + 3. Determine g, given that -u*g**5 + 3/4*g**3 - 1/4*g**4 - 1/2*g + 1/4*g**2 + 0 = 0.
-2, -1, 0, 1
Suppose -4*y = y - 135. Let p be y/12 + (-2)/8. Let 2*m**p - m**2 - m**3 + 0*m**3 = 0. Calculate m.
0, 1
Let n(g) be the third derivative of -1/20*g**6 + 0 - 4*g**2 + 0*g - 1/10*g**5 - 1/112*g**8 + 3/8*g**4 - 1/2*g**3 + 3/70*g**7. Factor n(f).
-3*(f - 1)**4*(f + 1)
Let g(z) be the second derivative of -2/27*z**3 - 3*z + 0 - 1/9*z**2 - 1/54*z**4. What is v in g(v) = 0?
-1
Let d = -1/590 - -1183/1770. Determine f so that d*f**4 - 2/3*f**3 - 2/3 - 8/3*f**2 - 7/3*f + 1/3*f**5 = 0.
-1, 2
Suppose 94 = -2*j + 100. Factor -2/9 - 2/9*k**4 + 4/9*k**2 + 0*k + 0*k**j.
-2*(k - 1)**2*(k + 1)**2/9
Let v(x) be the first derivative of x**3/6 + 2*x**2 + 8*x + 2. Factor v(o).
(o + 4)**2/2
Let p(k) be the second derivative of -k**4/8 - 3*k**3/4 - 3*k**2/2 - 3*k. Find n such that p(n) = 0.
-2, -1
Let n = 638 + -5735/9. Let y(q) be the first derivative of -1/3*q**4 - 1/3*q + n*q**3 - 1/3*q**2 - 3. Factor y(z).
-(z - 1)**2*(4*z + 1)/3
Let r = 8 - 5. Let w = 26 + -26. Solve w*a + 2/3*a**r - 2/3*a**4 + 0*a**2 + 0 = 0.
0, 1
Solve -8/5 + 2*u**3 - 2/5*u**2 - 2/5*u**5 - 16/5*u + 2/5*u**4 = 0.
-1, 2
Let k = 8 - 0. Let t = k - 5. Factor -4/5 + 2*h - 8/5*h**2 + 2/5*h**t.
2*(h - 2)*(h - 1)**2/5
Find h such that 9*h + 10*h**4 - 14*h**2 + 4 - 2*h**3 - 11*h + 4*h**5 + 0*h**3 = 0.
-2, -1, 1/2, 1
Let n(y) be the second derivative of -2*y**7/21 - 4*y**6/15 + 3*y**5/5 + 4*y**4/3 - 8*y**3/3 + 24*y. Factor n(t).
-4*t*(t - 1)**2*(t + 2)**2
Let t(v) = v**4. Let m(r) = r**5 + 8*r**4 + r**3. Suppose -3*a - 42 = -2*x, x + 0*a + a = 11. Suppose 4*j + 9 = -x. Let g(c) = j*t(c) + m(c). Factor g(l).
l**3*(l + 1)**2
Factor -702*t + 705*t + 0*t**2 - 3*t**2.
-3*t*(t - 1)
Let l(y) be the second derivative of 2/9*y**3 + 0*y**2 - 1/18*y**4 + 0 - 1/30*y**5 + 4*y. Factor l(j).
-2*j*(j - 1)*(j + 2)/3
Let 4*a**3 - 16 + 4*a**2 - 16*a + 6*a**3 - 6*a**3 = 0. What is a?
-2, -1, 2
Let a(u) be the first derivative of u**4/8 + u**3/2 + u**2/2 - 1. Factor a(r).
r*(r + 1)*(r + 2)/2
Let u(t) be the third derivative of -13*t**6/120 - 19*t**5/15 - 35*t**4/8 + 3*t**3 - 22*t**2. Suppose u(d) = 0. What is d?
-3, 2/13
Factor -13*t**2 + 20 - 8*t + 28*t + 18*t**2.
5*(t + 2)**2
Suppose 3 = 4*l - 3*l. Suppose 3 = w - 5*h, 5*h + 9 = l*w + h. Factor 5 + 2*g + 4*g**w - 5 + 8*g**4 - 6*g**3 - 8*g**2.
2*g*(g - 1)*(g + 1)*(4*g - 1)
Let s(w) = -w**2 + 1. Let o(y) be the first derivative of -y**3/3 - y**2 + 2*y - 5. Let x(r) = -3*o(r) + 6*s(r). Determine c so that x(c) = 0.
0, 2
Let q(j) = j**2 + 11*j + 3. Let n be q(-10). Let l = -4 - n. Solve -5*d**l + 6*d**2 + d**4 - d + 3*d + 2*d - 8 = 0 for d.
-1, 2
Suppose -4*h + s + 301 = -0*h, 2*h - 2*s = 146. Let b be h/18 + (-8)/36. Factor -15 - 2*x**b - 2*x**3 + 2*x**2 + 15 + 2*x**5.
2*x**2*(x - 1)**2*(x + 1)
Let p = -1416 - -9920/7. Find b such that -18/7*b**4 + 0 + 16/7*b**2 - 6/7*b**3 + p*b = 0.
-2/3, 0, 1
Suppose -2*a + 6 + 0 = 0. Factor -4*v**3 + 3*v**3 - 3*v**3 - v + 3*v**a - 2*v**2.
-v*(v + 1)**2
Let c(o) be the third derivative of o**7/7560 - o**5/360 + o**4/6 + 2*o**2. Let w(n) be the second derivative of c(n). Factor w(h).
(h - 1)*(h + 1)/3
Let r be 2 - (7 + 2)/(-3). Factor -b**3 - 10*b**r + 4*b**5 - b**2 + b**4 + 7*b**5.
b**2*(b - 1)*(b + 1)**2
Let w(y) be the first derivative of -y**4/4 + 2*y**3/3 + y**2/2 - 2*y - 1. Factor w(u).
-(u - 2)*(u - 1)*(u + 1)
Let q(f) = f**4 - f**2 + 1. Let h(p) = -3*p**4 + 39*p**3 - 39*p**2 - 3*p + 18. Let t(a) = -h(a) + 12*q(a). Factor t(m).
3*(m - 1)**3*(5*m + 2)
Let q be ((-4)/7)/(-2) - (-186)/84. Let -9/2*u + 7/2*u**4 - 1 - q*u**2 + 9/2*u**3 = 0. What is u?
-1, -2/7, 1
Suppose -q + 695 = 691. Factor 1/3 + 1/2*y - 1/6*y**2 - 1/2*y**3 - 1/6*y**q.
-(y - 1)*(y + 1)**2*(y + 2)/6
Suppose -5*i + l + 47 + 54 = 0, -4*i + 3*l + 83 = 0. Find b such that -22*b + 8 - 7*b + i*b**2 - 9*b - 6*b = 0.
1/5, 2
Let h be (0 + 4 - (-82)/(-20))*-12. Determine y so that 0 - h*y**2 + 2/5*y**3 + 4/5*y = 0.
0, 1, 2
Let h(p) be the third derivative of -p**7/42 + p**6/12 + p**5/3 - 5*p**4/12 - 5*p**3/2 + 3*p**2 - 4*p. Find y such that h(y) = 0.
-1, 1, 3
Suppose -8 + 4 = -2*p. Suppose -p*y + 6*y = 0. Suppose y + 0*u**2 + 1/4*u**3 + 0*u = 0. Calculate u.
0
Suppose -19/4*w**4 - 1/4*w**3 - 7/4*w**5 + 2*w + 23/4*w**2 - 1 = 0. What is w?
-2, -1, 2/7, 1
Let g(k) be the first derivative of -k**4/20 + k**3/5 - 27. What is w in g(w) = 0?
0, 3
Let s(f) = f**3 + 7*f**2 - f - 5. Let j be s(-7). Factor -2*c**3 - 2*c**2 - 6*c**3 - 6*c**j - 2*c**4.
-2*c**2*(c + 2)**2
Let i(r) be the second derivative of 3*r**7/56 + r**6/20 - 27*r**5/80 + r**3/2 + 28*r. What is b in i(b) = 0?
-2, -2/3, 0, 1
Let m(a) be the first derivative of a**4/10 - 4*a**2/5 - 11. Factor m(d).
2*d*(d - 2)*(d + 2)/5
Suppose -22*o = 2*b - 24*o, -2*b - 5*o + 35 = 0. Find y such that 1/2 - 3/4*y - 5/4*y**2 - 9/4*y**4 + 1/2*y**b + 13/4*y**3 = 0.
-1/2, 1, 2
Suppose 2*q - 2*s + 2 = 0, 0 = 5*s - 7*s + 10. Let r(n) be the first derivative of -1 - 3/4*n**q - 4*n**3 + 0*n - 6*n**2. Solve r(v) = 0 for v.
-2, 0
Let j(g) = -g**2 - 6*g + 4. Let w(u) = 4*u**2 + 17*u - 12. Let k(h) = 7*j(h) + 2*w(h). Let v be k(8). Factor -v*z**2 - z**2 + 3*z**2.
-2*z**2
Let r(i) = i**2 - 7*i + 3. Let v be r(7). Factor 0*n**v - n**3 - n + 2*n**3.
n*(n - 1)*(n + 1)
Let k(u) be the third derivative of 0*u**5 + 7/30*u**6 + 0 + 0*u - 1/3*u**4 + 1/3*u**3 - 17/105*u**7 + 1/28*u**8 - u**2. Determine b so that k(b) = 0.
-1/2, 1/3, 1
Let u(h) = 5*h**5 + 9*h**4 + 2*h**2 + 6*h + 6. Let b(r) = 4*r**5 + 8*r**4 + r**2 + 5*r + 5. Let j(c) = -6*b(c) + 5*u(c). Let j(o) = 0. Calculate o.
-1, 0, 2
Let f(r) be the first derivative of 4*r**5/15 - 2*r**4/3 + 4*r**3/9 + 6. Factor f(c).
4*c**2*(c - 1)**2/3
Let c(x) be the third derivative of x**8/33600 - x**7/2100 + x**6/300 - x**5/15 - 2*x**2. Let b(n) be the third derivative of c(n). Factor b(f).
3*(f - 2)**2/5
Let d(s) = -5*s**3 + 6*s**2 - 5. Let p(h) = -h**3 + 1. Let c(z) = d(z) - 3*p(z). Determine x so that c(x) = 0.
-1, 2
Let z(o) = -3*o**3 - 5*o**2 + 2*o - 2. Let i(p) = -7*p**3 - 11*p**2 + 5*p - 5. Let a(q) = 2*i(q) - 5*z(q). Solve a(b) = 0.
-3, 0
Let z(k) be the second derivative of -2/15*k**3 - 19/75*k**6 + 3/10*k**5 - 1/30*k**4 + 0*k**2 + 3*k + 1/15*k**7 + 0. Suppose z(o) = 0. What is o?
-2/7, 0, 1
Let v be 2/(-14)*(-16 + 6 + 8). Factor 8/7*c + 6/7 + v*c**2.
2*(c + 1)*(c + 3)/7
Let b be 2*(30/(-8) - -4). Let n(g) be the first derivative of 0*g + 0*g**5 - b*g**4 + 1 + 0*g**3 + 1/2*g**2 + 1/6*g**6. What is a in n(a) = 0?
-1, 0, 1
Let y be (-2)/3 - 17/(-3). Determine v so that 0*v + 9*v**y + v - 8*v**5 - 2*v**3 = 0.
-1, 0, 1
Let s(j) = 6*j**4 + 5*j**3 + j - 4. Let d(b) = 13*b**4 + 9*b**3 - b**2 + 3*b - 10. Let r(h) = 2*d(h) - 5*s(h). Factor r(u).
-u*(u + 1)**2*(4*u - 1)
Let l(x) = -3 - 1 - x - x. Let i be l(-3). What is m in -i*m**2 + 0*m**2 + 0*m - 2*m = 0?
-1, 0
Factor -2/3*h + 1/3*h**4 - h**3 + 1/3*h**5 - 5/3*h**2 + 0.
h*(h - 2)*(h + 1)**3/3
Let n = -5 + 5. Suppose 3*o + c = 3, -5*o - c + n*c + 7 = 0. Suppose o*h**3 + 2*h**3 - 10*h**2 + 6 + 2*h - 2 = 0. What is h?
-1/2, 1, 2
Let g(i) be the second derivative of -3/4*i**2 + 3/40*i**5 - 10*i + 1/8*i**4 + 0 - 1/4*i**3. Let g(j) = 0. Calculate j.
-1, 1
Let a = -1 - -5. Let v(u) be the second derivative of 0 + 2/3*u**3 - 2*u + 1/6*u**a + 0*u**2. Factor v(i).
2*i*(i + 2)
Factor -21*d**2 - 6*d - 3/7.
-3*(7*d + 1)**2/7
Let q(b) be the third derivative of 0*b**4 - 1/120*b**5 + 0 + 6*b**2 + 0*b + 0*b**3 + 3/160*b**6 + 5/1344*b**8 - 1/70*b**7. Find d such that q(d) = 0.
0, 2/5, 1
Let m be 5/(-5) - 4/(-1). Let l(k) = k**3 + 5*k**2 + 3*k + 5. Let v be l(-4). Factor 2*r**3 - 2*r + 4*r - v*r**2 + r**m + 4*r**4.
r*(r - 1)*(r + 2)*(4*r - 1)
Let p = -1/134 - -673/402. Suppose -p*h**5 + h**3 + 0 + 7/3*h**2 - 7/3*h**4 + 2/3*h = 0. What is h?
-1, -2/5, 0, 1
Let q(f) be the second derivative of f**4/3 - 2*f**3 + 4*f**2 + 5*f. Factor q(j).
4*(j - 2)*(j - 1)
Solve 