*3 + 176*q**2 + 148*q - 20. Let j(x) = -20*i(x) + 3*s(x). Let j(n) = 0. Calculate n.
-6, -1, 0
Suppose -5*u + 3*t + 4 = -9, 0 = -2*u + 2*t + 6. Let a(h) be the first derivative of -2 - 1/18*h**4 - 1/9*h**u - 4/27*h**3 + 0*h. Factor a(w).
-2*w*(w + 1)**2/9
Let u(l) be the first derivative of -1/7*l**2 + 0*l - 2/7*l**3 - 3/14*l**4 - 1 - 2/35*l**5. Suppose u(f) = 0. What is f?
-1, 0
Let l(w) = 14*w**3 - 2*w**2 + 2*w - 1. Let a be l(1). Suppose -j - a = -5*g, j - 8 - 3 = -3*g. Find r such that 1 - r**j - r**3 + 4*r**2 - 3*r + 0*r**3 = 0.
1
Suppose 4*k = 2*j - 6, 2*j = 2*k + 5 + 1. Let u(f) be the first derivative of k*f + 4 - 3*f**3 + f**2 + 7/4*f**4. Determine t so that u(t) = 0.
0, 2/7, 1
Let t(a) = a**2 - 5*a + 6. Let w be t(4). Let z(g) = g**2 - g + 3. Let f be z(0). Factor w*i**3 - f*i + i + 2*i**2 - i**4 - i**4.
-2*i*(i - 1)**2*(i + 1)
Let t be 1085/(-4923) - 18/(-81). Let d = t - -3275/3829. Determine k so that 0 + 6/7*k**2 + 2/7*k**4 + d*k**3 + 2/7*k = 0.
-1, 0
Let p(d) be the first derivative of -d**5/20 - 3*d**4/8 - d**3 - 3*d**2 - 3. Let n(r) be the second derivative of p(r). Let n(j) = 0. What is j?
-2, -1
Let q(m) be the second derivative of m**5/150 + m**4/18 + 7*m**3/45 + m**2/5 - 9*m. Determine o so that q(o) = 0.
-3, -1
Suppose -u = 2*u - 12. Let j(z) be the second derivative of 1/12*z**u + 0 + 1/2*z**2 + z + 1/3*z**3. Factor j(c).
(c + 1)**2
Let y(o) be the second derivative of -o**5/4 - 5*o**4/3 - 25*o**3/6 - 5*o**2 - 24*o. Let y(d) = 0. Calculate d.
-2, -1
Let u(i) be the first derivative of 0*i - i**3 + 3 - 3/4*i**4 - 1/5*i**5 - 1/2*i**2. Factor u(z).
-z*(z + 1)**3
Let p(o) be the third derivative of o**8/16800 + o**7/3150 + o**6/1800 - o**4/8 - 3*o**2. Let r(a) be the second derivative of p(a). Solve r(z) = 0.
-1, 0
Let g(o) = o**2 + 4*o + 4. Let b be g(-3). Factor 4*a + a**2 - b + a**3 + a - 3*a - 3*a.
(a - 1)*(a + 1)**2
Let p(i) be the second derivative of 7*i**6/75 - 6*i**5/25 + i**4/10 + 2*i**3/15 - 2*i. Find c, given that p(c) = 0.
-2/7, 0, 1
Factor -2/9*s**3 + 0 + 0*s + 0*s**2 - 2/9*s**4.
-2*s**3*(s + 1)/9
Let m(d) = d + 6. Let n be m(-4). Suppose -j + s + s + 5 = 0, 0 = -3*j - n*s + 7. Solve -r + 2*r**j + 2*r**2 + 4 - 1 - r**4 - 4 - r**5 = 0 for r.
-1, 1
Let m(y) = 6*y**2 + y + 26. Let p = 27 + -5. Let r(l) = l**2 + 5. Let s(w) = p*r(w) - 4*m(w). Factor s(a).
-2*(a - 1)*(a + 3)
What is s in -5/3*s + 1 + 1/3*s**3 + 1/3*s**2 = 0?
-3, 1
Let q(f) = -f**2 + 6*f + 6. Let p be q(6). Suppose s + 5*t + 13 = 0, -p*s + 9 = -3*s - t. Suppose 3*o**4 - 7*o**4 + 0*o**4 + s*o**3 = 0. Calculate o.
0, 1/2
Suppose z + 8 = -2*x + 4, -x = -z + 5. Solve 2*b**5 + 0*b**2 + 4*b**4 - 6*b**2 + z*b**2 - 3*b + b = 0 for b.
-1, 0, 1
Let n be (-135)/(-18) - 1/(-2). Let d = -6 + n. Factor -2/5*u**3 - 4/5*u**4 + 2/5*u**d + 0 + 0*u.
-2*u**2*(u + 1)*(2*u - 1)/5
Let z be 0 - (-2*9/6 + 3). Factor z + 2/5*p + 8/5*p**2.
2*p*(4*p + 1)/5
Let v be (-4)/(-6)*1*3. Let a be (-2)/3 + 11/3. Factor -2*d**v + 5*d**a + d**4 - 5*d**3 + 1.
(d - 1)**2*(d + 1)**2
Let g(u) be the third derivative of 0*u**3 - 5*u**2 + 0*u + 0 - 1/60*u**5 + 1/12*u**4. Factor g(k).
-k*(k - 2)
Let z(b) be the first derivative of -b**4/24 - b**3/12 - 3*b + 2. Let q(o) be the first derivative of z(o). Find x such that q(x) = 0.
-1, 0
Let s be (60/210)/(0 - 16/(-14)). Suppose s*g**2 - 1/2 + 1/4*g = 0. Calculate g.
-2, 1
Let v(f) = f. Suppose 3*j = 10 + 32. Let h(x) = 7*x**2 + 2*x + 2. Let d(t) = j*v(t) + 2*h(t). Factor d(p).
2*(p + 1)*(7*p + 2)
Let t(v) be the third derivative of -v**8/42 + v**7/35 + 13*v**6/60 - 17*v**5/30 + v**4/4 + 2*v**3/3 + 3*v**2. Suppose t(d) = 0. What is d?
-2, -1/4, 1
Let k = 68 + -66. Suppose -1 = 2*q - 5. Solve 3*g + g**k - 4*g**3 - g - g**2 + q*g**5 = 0.
-1, 0, 1
Suppose 3*h = 5*u - 19, 2*h = -u + 3*u - 6. Solve 1/2*i**2 + 1/4*i - 1/4*i**u - 1/2*i**4 + 0*i**3 + 0 = 0.
-1, 0, 1
Suppose 5*j + 0 - 20 = 0. Suppose -7*k - j = -9*k. Factor -26/7*m**k - 8/7*m + 8/7 - 10/7*m**3.
-2*(m + 1)*(m + 2)*(5*m - 2)/7
Let -3/4 - 9*t**2 - 9/2*t - 15/2*t**3 - 9/4*t**4 = 0. Calculate t.
-1, -1/3
Let o = -25 - -44. Suppose -24 - 49*u**2 - 36*u**2 + 108*u + o*u**2 - 63*u**3 = 0. Calculate u.
-2, 2/7, 2/3
Suppose -4*r - 4 = -2*r. Let w be (-22)/(-4)*(-4)/r. Suppose -w*q**2 + 4 + 28*q + 56*q**2 - 20*q**3 - 8*q**3 - 49*q**4 = 0. What is q?
-1, -2/7, 1
Suppose -4*a + 2 = 2*u, 5*a + u = 6*u + 25. Let l(f) = -a*f + 3*f + 6*f**2 - 5*f**2. Let k(y) = -y**2 - y. Let w(m) = -3*k(m) - 4*l(m). Let w(n) = 0. What is n?
-1, 0
Let f(w) be the first derivative of w**7/840 - w**5/40 + w**4/12 - w**3 - 3. Let d(q) be the third derivative of f(q). Determine n, given that d(n) = 0.
-2, 1
Let i = 6693/9590 - -2/959. Let y(n) be the second derivative of -3*n + 0 - 3/2*n**3 - 4/3*n**4 - i*n**5 - n**2 - 1/42*n**7 - 1/5*n**6. Factor y(u).
-(u + 1)**4*(u + 2)
Let p(b) be the third derivative of -b**8/168 + 2*b**7/105 - b**6/60 + 7*b**2. Factor p(d).
-2*d**3*(d - 1)**2
Suppose 13/8*p**2 + 9/8*p**4 + 1/2 + 5/2*p - 15/4*p**3 = 0. Calculate p.
-1/3, 2
Find x such that 3/2*x**3 + 0 - 9/4*x**4 + 2*x + 5*x**2 = 0.
-2/3, 0, 2
Suppose s + 0*s - 23 = 2*z, -27 = 3*z + s. Let b be 41/13 + z/65. Factor 2 - 3*x**2 + x**4 - 8*x**3 + 0*x**4 + x + 7*x**b.
(x - 2)*(x - 1)*(x + 1)**2
Factor 20/13*q + 2/13*q**2 + 50/13.
2*(q + 5)**2/13
Let o(z) be the first derivative of 0*z**2 + 1/9*z**3 - 2 - 1/12*z**4 + 0*z. Factor o(a).
-a**2*(a - 1)/3
Let q(z) be the third derivative of -z**5/60 + 5*z**4/12 - 25*z**3/6 - 12*z**2. Factor q(x).
-(x - 5)**2
Suppose 0 = -4*g + 5*g + 1. Let l(h) = h**3 - h - 1. Let m(o) = o**4 - 3*o**3 - 3*o**2 + o + 3. Let i(v) = g*m(v) - 3*l(v). Solve i(x) = 0 for x.
-1, 0, 2
Let m = 1 + -1. Suppose 18 = 2*y - m. Factor -2*w**2 + 2*w**3 - y + 9.
2*w**2*(w - 1)
Let g(t) be the second derivative of 0*t**2 + 0 + 0*t**3 + 1/21*t**4 + 2*t - 1/70*t**5. Factor g(h).
-2*h**2*(h - 2)/7
Suppose -f - 4*f - 17 = l, 0 = 4*l + 4*f + 4. Let w be (60/(-16) + 3)/(-3). Factor 0*j**2 - 1/4*j + w*j**l + 0.
j*(j - 1)*(j + 1)/4
Suppose 13 + 44 = -3*d. Let g = -7 - d. Factor 4*s**3 - s**3 - 4*s**3 - 15*s**4 + g*s**2 + 4*s.
-s*(s - 1)*(3*s + 2)*(5*s + 2)
Let v(z) = -2*z**2 - 23*z - 15. Let d(w) = w**2 - w. Let q(x) = 3*d(x) - v(x). Factor q(j).
5*(j + 1)*(j + 3)
Let a(y) be the first derivative of -1/9*y**2 - 2 + 0*y - 2/27*y**3. Suppose a(r) = 0. Calculate r.
-1, 0
Let h(j) be the first derivative of -j**6/39 + 2*j**5/65 + j**4/26 - 2*j**3/39 - 12. Solve h(v) = 0 for v.
-1, 0, 1
Let g = -120 - -120. Let n(w) be the third derivative of 0*w + 3/8*w**4 - 3*w**2 + g - 1/15*w**5 - 1/3*w**3. Find j such that n(j) = 0.
1/4, 2
Factor -1/4*r**3 + 0*r**2 + 0 + 0*r.
-r**3/4
Let c = -5 + 5. Suppose c = g - 4*g. Factor 0 + g + 2*f**2.
2*f**2
Let v be ((-16)/(-5) - 3)*1. Let n(d) be the first derivative of 2/15*d**3 - v*d**2 - 2 - 4/5*d. Solve n(q) = 0 for q.
-1, 2
Let r = 986 - 986. What is y in 1/2*y + r - 1/4*y**2 = 0?
0, 2
Let o be (-5)/(-4) + 6/8. Factor 0*u**2 + u**4 + 0*u**2 - u**o.
u**2*(u - 1)*(u + 1)
Suppose -3*q = 6*q - 18. Factor 2/9*c + 0 - 4/9*c**3 + 2/9*c**q.
-2*c*(c - 1)*(2*c + 1)/9
Let b(n) be the third derivative of 11*n**6/120 - 2*n**5/15 + 5*n**4/24 - 5*n**2. Let j(a) = 7*a**3 - 5*a**2 + 3*a. Let r(m) = -5*b(m) + 8*j(m). Factor r(z).
z*(z - 1)*(z + 1)
Suppose 5*g - 4*v - 10 = 0, g = 5*v + 5 - 3. Factor -1/2 - 7/2*c**3 - 5/2*c - c**4 - 9/2*c**g.
-(c + 1)**3*(2*c + 1)/2
What is y in 2*y - 7/2*y**3 - 25/4*y**2 + 1 = 0?
-2, -2/7, 1/2
Let g(s) = s**3 + 9*s**2. Let n be g(-9). Let o(v) be the second derivative of 1/7*v**2 - v - 1/105*v**6 + 0 + 1/35*v**5 + n*v**4 - 2/21*v**3. Factor o(a).
-2*(a - 1)**3*(a + 1)/7
Let 0*p + 3/2*p**2 - 3/4*p**3 + 0 = 0. Calculate p.
0, 2
Let g = -6 - -10. Suppose -2*d + d + g = 2*c, 5*c - 4*d - 36 = 0. Factor -2*z + 2*z**2 - 6*z**2 + 2*z**3 + c*z.
2*z*(z - 1)**2
Let h(y) be the first derivative of -y**7/210 - y**6/90 - 4*y**3/3 + 4. Let j(r) be the third derivative of h(r). Factor j(a).
-4*a**2*(a + 1)
Let p(d) be the second derivative of -d**5/190 - d**4/38 + d**3/57 + 3*d**2/19 + 9*d. Factor p(j).
-2*(j - 1)*(j + 1)*(j + 3)/19
Suppose 4/3*w - 2*w**2 + w**3 - 1/6*w**4 + 0 = 0. Calculate w.
0, 2
Let u be 10/15 - 30/72. Find y such that 1/4*y**2 + 1/2*y + u = 0.
-1
Let q be 49/(-21) + 1*3. Solve 0*c + 0 