6 - f. Factor 2*d + 1/2 + d**3 + r*d**2.
(d + 1)**2*(2*d + 1)/2
Let j = -7 - -8. Let n be -2*2*j/(-14). Determine f, given that -2/7*f - n*f**2 + 4/7 = 0.
-2, 1
Let f(h) be the first derivative of 2/3*h - 1/6*h**4 + 2/3*h**3 + 1 - h**2. Determine t, given that f(t) = 0.
1
Let m be 4/30 + (-240)/(-1575). Factor -2/7*b - 4/7 + m*b**2.
2*(b - 2)*(b + 1)/7
Let f be (-4)/10 - 22/(-5). Suppose 4*m - f = 3*m. Factor 2*i**2 - 2*i**4 + i**5 + m*i - i - 4*i.
i*(i - 1)**3*(i + 1)
Let s be 6*((-1)/(-5))/(-59 + 61). Factor s*t + 3/5*t**2 + 0.
3*t*(t + 1)/5
Let j be (-4 - 147/(-36))/(3/9). What is z in -3/4*z - 1/4 - 3/4*z**2 - j*z**3 = 0?
-1
Let q be (8/(-6))/(10/(-15)). Solve -5*u**2 + 2*u**q + 26*u + 13*u**2 - 12 = 0.
-3, 2/5
Let j(g) = -2*g**2 - 19*g - 7. Let f be j(-9). Let 4/7*a**f - 2/7*a**3 - 2/7*a + 0 = 0. What is a?
0, 1
Factor 60*a + 42 + 3 + 3*a**4 - 20*a**3 - 10*a**2 + 2*a**4.
5*(a - 3)**2*(a + 1)**2
Factor -2/9*q**2 - 2/9*q**3 + 1/3*q**4 - 1/9*q**5 - 1/9 + 1/3*q.
-(q - 1)**4*(q + 1)/9
Factor -24*n**2 - 64/3*n - 20/3 - 4/3*n**4 - 32/3*n**3.
-4*(n + 1)**3*(n + 5)/3
Let r(h) = -11*h**3 + 9*h**2 + 6*h + 5. Let b(d) = -d**3 + d**2 + 1. Let k(p) = -18*b(p) + 2*r(p). Factor k(z).
-4*(z - 1)**2*(z + 2)
Let z(c) = -c**3 + 10*c**2 + c - 10. Let y be z(10). Let m(u) be the first derivative of 1/5*u**2 + y*u - 2/15*u**3 + 3. Factor m(v).
-2*v*(v - 1)/5
Suppose -15 = -z - 4*z. Solve -3/2*v**z - 1/2*v**4 - v**2 + 0*v + 0 = 0.
-2, -1, 0
Let b = -115 + 121. Let l(c) be the second derivative of 0*c**2 + c + 1/168*c**7 + 0*c**4 + 1/120*c**b + 0 + 0*c**5 + 0*c**3. Factor l(x).
x**4*(x + 1)/4
Let m be (-2)/6*(-17 + 11). Factor -7*n**m + 2*n**2 + n**2 + 16.
-4*(n - 2)*(n + 2)
Suppose 2*h - 5*h - 4*o = 0, -4*h = -5*o. Factor -2/9 + h*k + 2/9*k**2.
2*(k - 1)*(k + 1)/9
Suppose -2/3*a**2 + a**5 - a**3 + 0 + 2/3*a**4 + 0*a = 0. What is a?
-1, -2/3, 0, 1
Let z(x) be the second derivative of x**6/15 + x**5/10 - x**4/6 - x**3/3 + 3*x. Solve z(u) = 0.
-1, 0, 1
Let d(n) be the second derivative of 7/30*n**6 + 0 - 23/20*n**5 + 14/3*n**3 - 4*n**2 + 2*n + 1/2*n**4. Let d(z) = 0. What is z?
-1, 2/7, 2
Let x(g) be the third derivative of 0*g**6 + 1/27*g**3 + 0*g**4 - 1/135*g**5 + 0*g + 0 + 1/945*g**7 - 5*g**2. Factor x(a).
2*(a - 1)**2*(a + 1)**2/9
Suppose -4/15*g**2 - 2/5*g**5 + 2/15 + 2/15*g**4 - 2/5*g + 4/5*g**3 = 0. What is g?
-1, 1/3, 1
Let r(u) = u**2 - 2*u - 3. Let c be r(4). Let n = 4 - 2. Find h such that -c*h**2 + h**2 + 3*h**n - h + h**4 + h**3 = 0.
-1, 0, 1
Let q(m) = 7*m**3 + 4*m**2 + 7*m + 5. Let l = 2 + -1. Let o = -4 + l. Let r(k) = 4*k**3 + 2*k**2 + 4*k + 3. Let n(x) = o*q(x) + 5*r(x). Let n(b) = 0. What is b?
-1, 0
Factor -2/3*q**2 - 2/3 - 4/3*q.
-2*(q + 1)**2/3
Find t such that 8/7*t + 6/7*t**2 - 8/7*t**3 + 2/7*t**4 - 8/7 = 0.
-1, 1, 2
Let x = 3159/5 + -631. Factor 1/5*n**5 + 2/5 - x*n**3 - 2/5*n**2 + 0*n**4 + 3/5*n.
(n - 2)*(n - 1)*(n + 1)**3/5
Suppose 3*f + 22 = -5*h + 5*f, -h - 26 = 5*f. Let o = 8 + h. Factor 9*g - 2*g + 9*g**2 + 3 + 3*g**3 + o*g.
3*(g + 1)**3
Let t(w) be the first derivative of 2/3*w**3 - 4*w - w**2 + 2. Solve t(g) = 0.
-1, 2
Let z(i) be the second derivative of -i**4/24 + i**3/3 - i**2 + 2*i. Factor z(y).
-(y - 2)**2/2
Let l = -236 + 237. Factor -1/2*w**3 - 5/2*w + l + 2*w**2.
-(w - 2)*(w - 1)**2/2
Let f = 1/6 + 1/3. Let w(i) be the second derivative of 1/4*i**4 + 0 - f*i**3 - 3*i**2 + i. Solve w(n) = 0 for n.
-1, 2
Suppose 5*k = -4*p + 2, 2*k - 2*p - 6 = 2. Factor -5*l**3 - 2*l + 2*l**3 - l**4 - l**3 - 5*l**k.
-l*(l + 1)**2*(l + 2)
Let n(j) be the second derivative of -j**4/6 + j**3 - 2*j**2 - 4*j. Factor n(p).
-2*(p - 2)*(p - 1)
Let c(y) be the third derivative of -y**8/224 + y**7/70 - y**5/20 + y**4/16 + 2*y**2 - 37. Suppose c(v) = 0. Calculate v.
-1, 0, 1
Let t(k) be the third derivative of -k**6/120 - k**5/30 - k**4/24 + 6*k**2. Let n be t(-1). Factor n + 0*u + 3/2*u**2.
3*u**2/2
Let l(x) be the first derivative of -x**4/42 + 2*x**3/63 + x**2/21 - 2*x/21 - 5. What is j in l(j) = 0?
-1, 1
Let z(r) be the first derivative of 2/3*r**3 + 0*r + 0*r**2 - 6 - 1/2*r**4. Factor z(b).
-2*b**2*(b - 1)
Factor 8/17*b + 6/17 + 2/17*b**2.
2*(b + 1)*(b + 3)/17
Let l(d) be the first derivative of 0*d - 2/11*d**3 + 0*d**2 - 1/22*d**4 - 10. Solve l(i) = 0.
-3, 0
Let k(j) be the third derivative of j**7/420 - j**5/120 + 10*j**2. Determine h so that k(h) = 0.
-1, 0, 1
Factor -8 - 6*x**4 + 7 + x**4 - 4 + 10*x**2.
-5*(x - 1)**2*(x + 1)**2
Let p(y) be the second derivative of 4*y + 0 - 1/12*y**4 - 2/5*y**2 + 4/15*y**3 + 1/100*y**5. Factor p(h).
(h - 2)**2*(h - 1)/5
Factor 2/17*o**3 + 0 + 0*o + 2/17*o**2.
2*o**2*(o + 1)/17
Let v(w) be the first derivative of -w**3 + 8. Let a(r) = r**2. Let q(o) = 14*a(o) + 6*v(o). Factor q(g).
-4*g**2
Suppose -2*l + 5*l - 12 = 0. What is n in -1 + 1 + 0*n**2 + l*n - 2*n**2 = 0?
0, 2
Let y = -2049/14 - -293/2. Factor -y*m**3 + 0*m**2 + 2/7*m**4 + 0*m + 0 - 1/7*m**5.
-m**3*(m - 1)**2/7
Let k = -40 + 43. Find w such that 0 - 1/3*w + 3*w**5 - 2*w**4 + 2*w**2 - 8/3*w**k = 0.
-1, 0, 1/3, 1
Factor 2/15*a**5 + 14/15*a**4 + 32/15*a + 38/15*a**3 + 8/15 + 10/3*a**2.
2*(a + 1)**3*(a + 2)**2/15
Let c(g) be the second derivative of 0 + 0*g**2 + 6*g + 2/21*g**3 + 1/84*g**4. Solve c(m) = 0 for m.
-4, 0
Let c = -26 + 29. Let z(x) be the second derivative of 0*x**4 + 0 + 1/147*x**7 - x + 0*x**c + 0*x**2 + 0*x**5 - 1/105*x**6. Determine l, given that z(l) = 0.
0, 1
Factor -2/9*p**2 + 2/9 + 2/9*p - 2/9*p**3.
-2*(p - 1)*(p + 1)**2/9
Let s(w) be the first derivative of -w**6/24 - 3*w**5/20 + 9*w**4/16 + 23*w**3/12 + 3*w**2/2 - 2. Let s(n) = 0. What is n?
-4, -1, 0, 3
Let z(o) = 3*o**3 + 10*o**2 - 7*o - 2. Let b(w) = -6*w**3 - 19*w**2 + 13*w + 5. Let v(m) = 4*b(m) + 7*z(m). Suppose v(c) = 0. What is c?
-2, -1, 1
Let s(p) = p**3 + 4*p**2 + 5*p + 24. Let v be s(-4). Factor 0 + 2/7*k**v + 6/7*k**3 + 4/7*k**2 + 0*k.
2*k**2*(k + 1)*(k + 2)/7
Let l = -7 - -12. Factor -l*w**5 + 8*w**5 + 4*w**3 - 22*w**4 + 2*w**3 + 13*w**4.
3*w**3*(w - 2)*(w - 1)
Factor 8/11*r**3 + 0*r + 2/11*r**5 + 8/11*r**4 + 0*r**2 + 0.
2*r**3*(r + 2)**2/11
Let m(b) = 12*b**2 - 3*b - 12. Let x(k) = k**3 + 11*k**2 - 2*k - 12. Let a(g) = 2*m(g) - 3*x(g). Factor a(w).
-3*(w - 1)*(w + 2)**2
What is q in 12/5*q + 8/5*q**3 + 18/5*q**2 + 2/5 = 0?
-1, -1/4
Let u(o) = 7*o - 11. Let j be u(2). Find c such that 4/9*c**j + 0 - 2/9*c + 2/9*c**2 = 0.
-1, 0, 1/2
Let r = 22/115 + 71/230. Find p, given that 0 + 1/2*p**2 + p - r*p**3 = 0.
-1, 0, 2
Let -1/4*b**4 + 0*b**2 - 1/4*b**3 + 0 + 0*b = 0. Calculate b.
-1, 0
Let o(x) be the second derivative of 2*x**7/21 - 6*x**6/5 + 6*x**5 - 46*x**4/3 + 22*x**3 - 18*x**2 + 23*x. Suppose o(l) = 0. Calculate l.
1, 3
Solve 0 + 0*y + 1/2*y**2 - 1/2*y**3 + 1/2*y**5 - 1/2*y**4 = 0 for y.
-1, 0, 1
Let j(u) = -10*u**5 + u**4 + 10*u**3 - 7*u**2 + 3. Let p(r) = 10*r**5 - 2*r**4 - 10*r**3 + 6*r**2 - 2. Let i(g) = -4*j(g) - 6*p(g). Find c such that i(c) = 0.
-1, 0, 2/5, 1
Let v = 4 + -3. Let g be v - (-3)/(-6)*2. Factor -2*a**3 - 2*a**2 + g*a**2 + 3*a**4 + a**3.
a**2*(a - 1)*(3*a + 2)
Let z(x) be the first derivative of -x**4/2 + 3*x**2 - 4*x + 1. Factor z(r).
-2*(r - 1)**2*(r + 2)
Let w(a) be the first derivative of a**3/5 + 6*a**2/5 - 4. Factor w(s).
3*s*(s + 4)/5
Let r = 12 + -16. Let c(q) = 4*q**2 + 3*q - 7. Let f(b) = 3*b**2 + 3*b - 6. Let v(u) = r*c(u) + 5*f(u). Suppose v(k) = 0. What is k?
1, 2
Let p(q) be the third derivative of q**5/420 + 3*q**4/56 + 4*q**3/21 - 18*q**2 + q. Solve p(r) = 0.
-8, -1
Suppose -7*u = -2*u + 15. Let c(p) = -3*p**2 - 4*p - 4. Let w(z) = -4*z**2 - 4*z - 4. Let t(d) = u*c(d) + 2*w(d). Factor t(q).
(q + 2)**2
Let c = -7 + 11. Let b be 2/(-8) - (-13)/c. Determine d so that -d**2 + 3*d**4 + 2*d**b + 2*d**2 - 2*d**4 = 0.
-1, 0
Let t = -558 + 561. Find z such that -1/3*z**2 + 2/3*z - 1/3*z**t + 0 = 0.
-2, 0, 1
Let f(d) be the third derivative of -d**8/20160 + d**6/2160 - 5*d**4/24 - 3*d**2. Let y(t) be the second derivative of f(t). Solve y(b) = 0.
-1, 0, 1
Factor -10/11*t**2 + 0 + 4/11*t + 6/11*t**3.
2*t*(t - 1)*(3*t - 2)/11
Let v(f) be the third derivative of -7*f**6/40 + f**5/4 + 2*f**4 + 2*f**3 + 3*f**2. Determine u, given that v(u) = 0.
-1, -2/7, 2
Let s(m) = -8*m**2 - 14*m - 4. Let x(o) = -7*o**2 - 14*o - 4. Let f(t) = 6*s(t) - 4*x(t).