2 - 7*u + 7. Let j(r) = 7*n(r) + 3*v(r). Factor j(k).
-3*k**4*(k + 1)
Let j = 1419 + -1419. Determine i so that -15*i**2 - 5*i + j - 45/4*i**3 = 0.
-2/3, 0
Let h(q) = 3*q**2 + 3*q - 4. Let g be h(-3). Let n = g + -41/3. Let -1/3*o**2 - n - 2/3*o = 0. What is o?
-1
Suppose 3*h + 2*h - 4*z + 10 = 0, -5*h + 2*z - 20 = 0. Let x(a) = 7*a**2 - 11*a + 15. Let i(t) = 2*t**2 - 3*t + 4. Let s(y) = h*x(y) + 22*i(y). Factor s(r).
2*(r - 1)*(r + 1)
Let i(u) be the third derivative of u**5/60 + 7*u**4/24 - 4*u**3/3 + 19*u**2. Let r = 9 + -15. Let a(c) = -c + 1. Let d(x) = r*a(x) - i(x). Factor d(g).
-(g - 1)*(g + 2)
Determine t so that 3*t**3 + 3*t**2 + 9*t**2 + 3*t + 3*t**2 - 9*t**2 = 0.
-1, 0
Suppose -10*z = z. Let l(n) be the first derivative of z*n + 1/2*n**2 - 1/4*n**4 + 0*n**3 + 3. Factor l(o).
-o*(o - 1)*(o + 1)
Determine g, given that -6/7*g**3 + 0 - 2/7*g**4 + 2/7*g**5 + 4/7*g + 2/7*g**2 = 0.
-1, 0, 1, 2
Let w(s) be the first derivative of 9/2*s**2 + 6*s - 2*s**3 - 4. Factor w(i).
-3*(i - 2)*(2*i + 1)
Let c(x) be the second derivative of 1/5*x**3 + 2*x + 0*x**2 - 1/20*x**4 + 0. Let c(u) = 0. Calculate u.
0, 2
Let t(i) = -3*i - 2. Let w be t(-2). Factor 0*b - 1/4*b**3 + 0 + 0*b**2 + 1/4*b**w.
b**3*(b - 1)/4
Let n(w) be the second derivative of w**7/126 + w**6/90 - w**5/30 - w**4/18 + w**3/18 + w**2/6 + 10*w. Factor n(p).
(p - 1)**2*(p + 1)**3/3
Let y(c) be the second derivative of c**7/315 + c**6/225 - c**5/150 - c**4/90 - 31*c. Let y(v) = 0. What is v?
-1, 0, 1
Let m(h) be the third derivative of h**6/10 + 16*h**5/15 + 5*h**4/6 + 2*h**2 - 22*h. Find b, given that m(b) = 0.
-5, -1/3, 0
Let f(z) be the first derivative of z**4/2 + 8*z**3/3 + 4*z**2 - 4. Suppose f(c) = 0. What is c?
-2, 0
Suppose 2*y + 2 - 4 = 0. Let f = y + -2. Let o(j) = -j**4 + j**3 + j**2 + j. Let i(g) = -2*g**4 + 8*g**3 - 10*g**2. Let z(k) = f*i(k) - 2*o(k). Factor z(m).
2*m*(m - 1)**2*(2*m - 1)
Let t be 6/8 + 1650/40. Let b = t - 42. Determine d, given that b + 4/3*d**2 + 8*d**4 - 6*d**3 - 10/3*d**5 + 0*d = 0.
0, 2/5, 1
Let a(w) be the third derivative of 0*w + 1/300*w**5 + w**2 + 0 + 0*w**3 - 1/120*w**4. Factor a(j).
j*(j - 1)/5
Let w(m) be the first derivative of -m**3/15 + m**2/10 + 1. Factor w(q).
-q*(q - 1)/5
Let v(r) = -r**3 - 5*r**2 - r - 3. Let b be v(-5). Suppose -2*l - 13 = -p, -p - 4 = b*l + 3. Factor -o**p + 5*o**3 - 2*o**3.
2*o**3
Let r(z) be the first derivative of 2/33*z**3 + 2 - 1/11*z**2 + 0*z. Factor r(s).
2*s*(s - 1)/11
Let h(q) be the third derivative of -q**9/15120 + q**8/4032 - q**7/7560 - q**6/2160 + q**4/12 - 3*q**2. Let k(u) be the second derivative of h(u). Factor k(y).
-y*(y - 1)**2*(3*y + 1)/3
Factor 1/9*o**3 + 0 + 0*o + 1/9*o**2.
o**2*(o + 1)/9
Suppose 2*y = 6 - 0. Find c, given that -4*c**3 + 3*c**4 + 0*c**y - 5*c**4 + 5 + 4*c - 3 = 0.
-1, 1
Let a(k) be the second derivative of -k**6/285 + k**4/114 - 2*k. Suppose a(y) = 0. What is y?
-1, 0, 1
Let b = 2/13 - -7/39. Let q(c) be the first derivative of -4/3*c**3 + 1 + b*c**6 + 2*c + 2/5*c**5 + c**2 - c**4. Determine y, given that q(y) = 0.
-1, 1
Find f, given that 0 + 8*f + 4/3*f**2 = 0.
-6, 0
Let o(u) be the second derivative of 2*u - 1/36*u**4 + 1/2*u**2 + 1/9*u**3 + 0. Suppose o(x) = 0. Calculate x.
-1, 3
Let p be (-6)/(-3) - 2/(-1). Factor 2*d - 3*d**2 - 3*d - 4*d**p + 5*d**4 + 2 + d**3.
(d - 1)**2*(d + 1)*(d + 2)
Determine p so that -3*p**4 + 125*p - 11*p**3 - 113*p + 2*p**3 = 0.
-2, 0, 1
Let m be ((-2)/3 + (-2)/(-3))/2. Find j such that m + 1/2*j**2 - j = 0.
0, 2
Let s(u) = 7*u**2 - 78*u + 503. Let d(w) = -13*w**2 + 156*w - 1007. Let h(j) = 4*d(j) + 7*s(j). Factor h(v).
-3*(v - 13)**2
Let -11*i**2 - i**3 - 4*i**2 + 12*i + 4*i**3 = 0. What is i?
0, 1, 4
Let w(h) = 9*h - 7. Let b be w(1). Solve -1/6 - 1/3*z - 1/6*z**b = 0 for z.
-1
Let h be (-2)/8 - ((-335)/(-100) - 4). Let k(g) be the first derivative of -h*g**5 - 32*g**2 - 4*g**4 - 2 - 16*g**3 - 32*g. Factor k(w).
-2*(w + 2)**4
Let j(f) be the first derivative of f**4/10 + 4*f**3/15 + f**2/5 + 14. Solve j(s) = 0 for s.
-1, 0
Suppose -3*s = 3*p - 21, -6*s + s = 2*p - 26. Let j be 3/10*s/3. Determine d so that -2/5 + 2/5*d**2 + j*d - 2/5*d**3 = 0.
-1, 1
Let n(l) = -12*l**4 - 13*l**3 - 8*l**2 + 27*l + 27. Let b(a) = 11*a**4 + 14*a**3 + 9*a**2 - 26*a - 26. Let z(u) = 7*b(u) + 6*n(u). Solve z(q) = 0.
-2, -1, 1
Let a(p) = p**3 + p**2 + 2*p + 2. Let n be a(0). Factor -10/7*l**3 + 8/7 + 16/7*l - n*l**2.
-2*(l - 1)*(l + 2)*(5*l + 2)/7
Suppose -1 = 2*t + 2*c - 3, 4*c = -2*t - 2. Factor -9/4 - 3/2*i + 3/2*i**t + 2*i**2 + 1/4*i**4.
(i - 1)*(i + 1)*(i + 3)**2/4
Let n(t) = 2*t**3 - 8*t - 6. Let a(g) = 4*g**3 - g**2 - 16*g - 11. Let o(f) = -2*a(f) + 5*n(f). Determine l so that o(l) = 0.
-2, -1, 2
Let u(w) be the second derivative of -w**4/6 + 2*w**3/3 - w**2 + 21*w. Suppose u(y) = 0. What is y?
1
Let q(x) = 5*x**2 + 2*x. Let m(t) = 6*t**2 + 3*t. Let w(z) = -4*m(z) + 5*q(z). Factor w(d).
d*(d - 2)
Let f(r) be the first derivative of -r**5/35 + r**4/14 + r**3/7 - 2*r**2/7 - 4*r/7 + 26. Factor f(j).
-(j - 2)**2*(j + 1)**2/7
Let k = -277/24 - -95/8. Factor -i**2 - 5/3*i + k*i**3 + 1/3*i**4 - 2/3.
(i - 2)*(i + 1)**3/3
Let m(z) be the third derivative of -z**2 + 2/735*z**7 + 0*z**3 + 0*z**4 + 1/140*z**6 + 0 + 1/210*z**5 + 0*z. Factor m(p).
2*p**2*(p + 1)*(2*p + 1)/7
Let c(u) be the first derivative of 2*u**3/15 + 2*u**2/5 + 2*u/5 + 12. What is q in c(q) = 0?
-1
Factor 0*b + 3/2*b**2 - 3/2*b**4 + 0 + 3/2*b**5 - 3/2*b**3.
3*b**2*(b - 1)**2*(b + 1)/2
Let m(n) = 2*n**2 - 6. Let f be m(-2). Solve -2/9*q**4 - 8/9*q**f + 0*q + 8/9*q**3 + 0 = 0 for q.
0, 2
Let z be ((-3)/9)/((-3)/27). Solve 6*l**2 - 3*l - 5*l**2 - l**z - l**4 + 4*l**2 = 0 for l.
-3, 0, 1
Factor 0 + 0*g - 2/3*g**4 - 2/3*g**5 + 0*g**2 + 0*g**3.
-2*g**4*(g + 1)/3
Suppose 5*t + 3 = 6*t. Factor -1 - 9*l - 109/4*l**2 - 49/4*l**4 - 63/2*l**t.
-(l + 1)**2*(7*l + 2)**2/4
Let x(b) = -1. Let t(q) = -10*q**2 + 24*q - 2. Let v(k) = t(k) + 6*x(k). Factor v(w).
-2*(w - 2)*(5*w - 2)
Let b be 468/(-20) + (-8)/(-20). Let y = -20 - b. What is i in -i**4 + 0*i + 2/3*i**y + 0*i**2 + 0 = 0?
0, 2/3
Factor 0 + 2/3*i + 2/3*i**2.
2*i*(i + 1)/3
Let j(q) be the second derivative of 4*q - 1/15*q**4 + 0 + 1/15*q**3 - 1/50*q**5 + 2/5*q**2. Determine c, given that j(c) = 0.
-2, -1, 1
Factor -81/7*r - 3/7*r**3 + 27/7*r**2 + 81/7.
-3*(r - 3)**3/7
Let g(k) be the second derivative of k**9/168 - k**8/70 - 11*k**7/420 - k**6/90 + k**3/6 + 2*k. Let o(s) be the second derivative of g(s). Factor o(x).
2*x**2*(x - 2)*(3*x + 1)**2
Suppose 12*n - 48 = 8*n. Suppose z - n = -4*b, -2*z + 24 = 2*b + 3*z. Solve 0 - 6*k**5 - 4/7*k**b - 30/7*k**3 - 68/7*k**4 + 0*k = 0 for k.
-1, -1/3, -2/7, 0
Factor 0 + 0*r**2 - 1/4*r + 1/4*r**3.
r*(r - 1)*(r + 1)/4
Let k = 3 - -2. Let -5 + s + s**2 + 0*s**2 + k = 0. What is s?
-1, 0
Let i = -3 - -7. Suppose -12 + i = 2*g + 3*b, 0 = g + 3*b + 10. Let 2/3*k**g + 0 + 2/3*k**4 + 0*k + 4/3*k**3 = 0. Calculate k.
-1, 0
Let i(b) = -13*b + 169. Let f be i(13). Factor 4/5*z**3 - 6/5*z**4 + 0*z + f + 2/5*z**2.
-2*z**2*(z - 1)*(3*z + 1)/5
Factor 10/11*w**2 + 0 - 4/11*w - 2/11*w**4 - 6/11*w**3 + 2/11*w**5.
2*w*(w - 1)**3*(w + 2)/11
Let s(x) be the third derivative of -x**8/168 + x**7/105 + x**6/30 - x**5/15 - x**4/12 + x**3/3 + 4*x**2. Solve s(d) = 0.
-1, 1
Let f = -773 - -3869/5. Let -1/5*z**2 + 4/5*z - f = 0. Calculate z.
2
Let r(m) be the first derivative of -m**7/3 - 4*m**6/5 + 2*m**5/5 + 2*m + 1. Let s(k) be the first derivative of r(k). Factor s(w).
-2*w**3*(w + 2)*(7*w - 2)
Let i(h) be the first derivative of -h**3/15 + h**2/10 + 2*h/5 + 11. Find z, given that i(z) = 0.
-1, 2
Let 4*v**2 + 3*v**2 + 2*v**2 - 4*v - 8 - 5*v**2 = 0. Calculate v.
-1, 2
Let i(x) be the third derivative of -x**9/15120 + x**8/2520 + x**5/30 - 2*x**2. Let n(m) be the third derivative of i(m). Factor n(q).
-4*q**2*(q - 2)
Let n(h) be the second derivative of -h**5/270 + h**3/27 + 3*h**2 - 3*h. Let d(k) be the first derivative of n(k). Factor d(j).
-2*(j - 1)*(j + 1)/9
Let d be 5/(-15)*3/12*-4. Solve -1/3*j**3 + d*j**5 + 0*j + 0 - 1/3*j**4 + 1/3*j**2 = 0.
-1, 0, 1
Let t = 27 + -185/7. Factor 2/7*n + t*n**4 - 4/7*n**2 + 0*n**3 + 0 - 2/7*n**5.
-2*n*(n - 1)**3*(n + 1)/7
Let s(q) be the third derivative of q**6/120 - q**5/20 - q**4/6 + 3*q**2. Factor s(k)