*2 + 10*o + 18. Let f(k) = -3*k**2 + 9*k + 18. Let a(v) = 6*d(v) - 5*f(v). Factor a(n).
3*(n + 2)*(n + 3)
Let v(q) = 2*q**2 + q. Let s(b) = -b**2. Let t(g) = 3*s(g) + 3*v(g). Factor t(f).
3*f*(f + 1)
Let y(b) = -2*b**4 + 18*b**2 - 13*b + 3. Let z(w) = 3*w**4 - 17*w**2 + 12*w - 2. Let l(r) = -2*y(r) - 3*z(r). Let l(d) = 0. What is d?
-2, 0, 1
Let i(q) be the third derivative of 1/60*q**5 + 1/24*q**6 + 1/3*q**3 + 0 - 5/24*q**4 - 10*q**2 + 0*q - 1/70*q**7. Factor i(a).
-(a - 1)**2*(a + 1)*(3*a - 2)
Let q(v) be the second derivative of v**7/735 - v**5/210 - v**2/2 - v. Let s(a) be the first derivative of q(a). Solve s(w) = 0.
-1, 0, 1
Let o(n) be the first derivative of 2*n**3/45 + n**2/15 - 4*n/15 + 8. Factor o(a).
2*(a - 1)*(a + 2)/15
Let z(h) be the third derivative of 0 + 0*h - 5*h**2 + 1/15*h**5 + 2*h**3 - 2/3*h**4. Factor z(v).
4*(v - 3)*(v - 1)
Let r(k) = k**5 - k**4 + k**3 - 3*k**2 - 2. Let i = 27 - 16. Let m(v) = -6*v**5 + 6*v**4 - 5*v**3 + 16*v**2 + 11. Let d(t) = i*r(t) + 2*m(t). Factor d(b).
-b**2*(b - 1)**2*(b + 1)
Suppose -3*j - 54 = 3*l, 2*l + 4*j = l - 12. Let f be (-4)/(-6)*(-15)/l. Determine o, given that 0*o - 1/2*o**2 + f = 0.
-1, 1
Let z = 682 + -682. Factor 0 - 6/11*v**3 + 0*v + 4/11*v**2 + 2/11*v**5 + z*v**4.
2*v**2*(v - 1)**2*(v + 2)/11
Let p(d) = 25*d**4 + 80*d**3 + 60*d**2 - 15. Let i(c) = -37*c**4 - 120*c**3 - 90*c**2 + 23. Let x(z) = 5*i(z) + 8*p(z). Determine j so that x(j) = 0.
-1, 1/3
Let -1/9 + 0*z + 1/9*z**2 = 0. Calculate z.
-1, 1
Let c(k) be the first derivative of 2*k**3/21 + 11*k**2/7 - 34. Suppose c(r) = 0. What is r?
-11, 0
What is i in -42*i**3 + 0 + 132/5*i**2 - 24/5*i + 15*i**4 = 0?
0, 2/5, 2
Suppose -2/7*n**2 - 2/7*n + 4/7 = 0. What is n?
-2, 1
Let c be -1*(-3)/(-21) - -1. Solve 32/7*k + c*k**2 - 32/7*k**3 + 8/7 - 2*k**4 = 0.
-2, -1, -2/7, 1
Let q = -2/353 + -12351/706. Let n = -17 - q. Suppose -1/2*x**2 + x - n = 0. Calculate x.
1
Let r(w) be the third derivative of w**8/112 - w**7/70 - w**6/8 - 3*w**5/20 - 19*w**2. Factor r(m).
3*m**2*(m - 3)*(m + 1)**2
Let h(n) = -3*n + 17. Let j be h(5). Let c(f) be the first derivative of -1/4*f**4 + 3/2*f**j - 2*f + 4 + 0*f**3. Factor c(q).
-(q - 1)**2*(q + 2)
Let d be (-2)/(-11) + 27/33. Let h(c) = 3*c**3 - 1. Let m be h(d). Factor 0*p + p**m - 2*p + p.
p*(p - 1)
Suppose 3*h = 3*f - 6, 0 = -4*f - 0*h - 2*h + 8. Let a be f*(2 + (-68)/40). Factor 0 + a*z**2 + 6/5*z.
3*z*(z + 2)/5
Let s be 3 + 0 - 2 - -2. Determine a, given that -3*a**2 + 5*a - 2*a - 3*a**s + 3*a**2 = 0.
-1, 0, 1
Let f(q) be the first derivative of 5*q**5/2 - 5*q**4/4 - 4*q**3 + 5*q**2/2 - q/2 + 5. Factor f(u).
(u - 1)*(u + 1)*(5*u - 1)**2/2
Suppose 4*g = 2*r + 16, -2*r = 2*g - r. Factor 2/7 - 2/7*x**g + 0*x.
-2*(x - 1)*(x + 1)/7
Let d(f) = f**3 + 8*f**2 + 2. Let p be d(-8). Factor y**5 - 5*y**4 + 5*y**4 - p*y**3 + y**5.
2*y**3*(y - 1)*(y + 1)
Suppose 2*c = 12 - 2. Suppose c*w - w - 20 = 0. Factor -u**w + 3*u**4 + 0*u**4 + 2*u**4 - 10*u**3 + 7*u**2 - 2*u + u**3.
-u*(u - 2)*(u - 1)**3
Let k be 2 + (24/(-10))/3. Factor -9/5*i**5 + 0*i**2 + 0 + 0*i + k*i**4 - 1/5*i**3.
-i**3*(3*i - 1)**2/5
Let c(u) = -4 + 0*u + u - 3*u. Let o be c(-6). Suppose o*t**3 + 0*t**4 + 4*t**2 - 10*t**4 - 2*t**3 = 0. Calculate t.
-2/5, 0, 1
Let p(f) be the second derivative of -1/11*f**2 - 2*f - 1/66*f**4 + 0 - 2/33*f**3. Solve p(t) = 0.
-1
Let p(r) be the first derivative of -2*r**3/27 - 2*r**2/9 - 2*r/9 + 16. Determine z, given that p(z) = 0.
-1
Let r(v) be the third derivative of v**7/1260 - v**6/180 - 7*v**4/24 + 2*v**2. Let z(u) be the second derivative of r(u). Find c such that z(c) = 0.
0, 2
Let a(m) be the third derivative of -m**6/40 + m**5/20 + m**4/4 - 19*m**2. Solve a(x) = 0.
-1, 0, 2
Let q(c) be the second derivative of -c**4/21 - 2*c**3/7 + 20*c**2/7 - 2*c + 14. Determine r so that q(r) = 0.
-5, 2
Suppose -2*d + 6*d = -3*n + 72, 3*d - 109 = -5*n. Let i be (1/2)/(6/n). Find u such that -i*u - 2/3 - u**2 = 0.
-1, -2/3
Let r(x) = 3*x**2 - 2*x. Let j(b) = -b**2 + b. Let v(d) = d**2 + 2*d - 1. Let t be v(-3). Let l(n) = t*j(n) + r(n). Let l(i) = 0. What is i?
0
Let g(u) be the second derivative of -1/5*u**4 + 9/50*u**5 + 1/10*u**6 - 4/5*u**3 + 1/70*u**7 + 4*u + 0*u**2 + 0. Solve g(l) = 0 for l.
-2, 0, 1
Solve -12/13 - 2/13*h + 2/13*h**2 = 0.
-2, 3
Let f(l) be the first derivative of 9/25*l**5 + 3/20*l**4 + 0*l**2 - 1 - 2/5*l**3 + 0*l. Factor f(w).
3*w**2*(w + 1)*(3*w - 2)/5
Let i(h) be the third derivative of h**8/60480 + h**7/15120 - h**6/1080 - h**5/30 - 2*h**2. Let j(p) be the third derivative of i(p). Let j(g) = 0. What is g?
-2, 1
Let g(l) be the first derivative of l**2 + 1/2*l**4 + 0*l - 4/3*l**3 - 4. Find b such that g(b) = 0.
0, 1
Factor 10*q**3 + q**4 + 20*q**2 + q**4 + 8*q - 4*q**2.
2*q*(q + 1)*(q + 2)**2
Let s = 2/691 - -8270/7601. Factor 0*j - s*j**3 + 18/11*j**4 + 2/11*j**2 + 0.
2*j**2*(3*j - 1)**2/11
Suppose 0 = 5*z - 6 - 4. Determine t so that 8*t**2 - 1 + 4 - 9*t**z - 2 = 0.
-1, 1
Let h(j) be the second derivative of -j**6/15 + j**5/5 - j**4/6 + 38*j. Factor h(m).
-2*m**2*(m - 1)**2
Let c(v) = -3*v**2 + 16*v - 11. Let x(b) = 5*b**2 - 24*b + 16. Let p(r) = -7*c(r) - 5*x(r). Let z(l) = l**2 - l + 1. Let a(m) = p(m) + 5*z(m). Factor a(t).
(t + 1)*(t + 2)
Let j(s) be the first derivative of -3*s**4/4 + s**3/2 - 13. Find h such that j(h) = 0.
0, 1/2
Let g(h) be the third derivative of h**5/60 - 5*h**4/12 + 3*h**3/2 + 60*h**2. Determine z, given that g(z) = 0.
1, 9
Let n(k) be the second derivative of k**5/10 + k**4/2 - k. Factor n(y).
2*y**2*(y + 3)
Let t = -2 - -5. Let m(w) be the first derivative of 2*w**2 - 2*w - 1 - 2/3*w**t. Solve m(j) = 0.
1
Let a be 6/(-33) - (-46)/11. Suppose 6 - h + 3*h**a - 2*h**4 - h**2 - 6 + h**3 = 0. Calculate h.
-1, 0, 1
Suppose 5*j - 32 = 4*c, j + 1 = -c + 2. Let p(l) be the second derivative of -l + 0*l**2 - 2/3*l**3 + 7/10*l**5 - 5/6*l**j + 0. Solve p(q) = 0.
-2/7, 0, 1
Suppose -5*l = 2*l - 252. Let n = -34 + l. Let -2/3*g + 0*g**n - 4/9 + 2/9*g**3 = 0. What is g?
-1, 2
Solve 4/3*h**3 + 2/3*h**2 + 2/3*h**4 + 0*h + 0 = 0.
-1, 0
Let r(n) be the first derivative of 2*n**3/9 + 2*n**2/3 - 2*n - 17. Factor r(c).
2*(c - 1)*(c + 3)/3
Let t(i) = -13*i**2 + 3*i - 5. Let q(r) = 19*r**2 - 5*r + 7. Let v(x) = -5*q(x) - 7*t(x). Let v(g) = 0. What is g?
0, 1
Let a(t) be the first derivative of -2*t**5/5 + 5*t**4/2 - 6*t**3 + 7*t**2 - 4*t + 31. Solve a(d) = 0 for d.
1, 2
Factor -5*b**4 - 20*b**3 - 7*b**4 - 5*b**5 - 2*b**4 - 6*b**4.
-5*b**3*(b + 2)**2
What is v in 1/5*v**2 + 0 + 1/5*v = 0?
-1, 0
Suppose 10*v = 6*v - 120. Let l = 32 + v. Factor -4/7*q**l + 2/7*q**3 + 4/7 - 2/7*q.
2*(q - 2)*(q - 1)*(q + 1)/7
Let u(l) = -l**2 + 6*l + 2. Suppose 22 = 5*h + 4*o - 2*o, h = -2*o - 2. Let g be u(h). Suppose 0*b**g + 0 + 1/4*b**3 - 1/4*b = 0. What is b?
-1, 0, 1
Determine c so that -2*c**3 - 20*c**4 - 19*c**4 - 4*c**3 + 37*c**4 = 0.
-3, 0
Let 0 + 2/11*q**2 + 0*q + 2/11*q**4 - 4/11*q**3 = 0. What is q?
0, 1
Let o be ((35/(-63))/(-5))/(3/18). Factor -j**2 - 1/3*j**3 - o*j + 0.
-j*(j + 1)*(j + 2)/3
Find k, given that 2/3*k**3 + 3*k**4 - 2/3*k - 3*k**2 + 0 = 0.
-1, -2/9, 0, 1
Let k(a) be the first derivative of -a**6 + 2*a**5/5 + 7*a**4/3 - 4*a**3/9 - 5*a**2/3 - 2*a/3 - 8. Solve k(c) = 0.
-1, -1/3, 1
Let w(j) = 6*j**2 + 1. Let o be w(-1). What is h in -2*h**3 - o*h**2 + 3*h**2 + 0*h**2 + h - 3*h = 0?
-1, 0
Let w(r) be the first derivative of -2401*r**6/6 + 343*r**5/5 + 392*r**4 - 952*r**3/3 + 104*r**2 - 16*r - 2. Factor w(j).
-(j + 1)*(7*j - 2)**4
Let i(p) be the third derivative of 0*p**3 + 0*p**4 - 2*p**2 + 0*p - 1/105*p**7 + 0 - 1/168*p**8 + 1/30*p**5 + 1/60*p**6. Determine y, given that i(y) = 0.
-1, 0, 1
Let c(r) be the third derivative of r**7/525 - r**6/75 + r**5/30 - r**4/30 - 8*r**2. Solve c(i) = 0 for i.
0, 1, 2
Let n(h) be the second derivative of -2*h**7/7 - h**6/2 - 3*h**5/20 - 6*h. Solve n(y) = 0.
-1, -1/4, 0
Let d = -1 - -4. Suppose 0*j = -d*j. Factor 0 + 0*o + j*o**2 + 8/5*o**4 - 2/5*o**5 - 8/5*o**3.
-2*o**3*(o - 2)**2/5
Let k(f) be the third derivative of 1/90*f**5 - 1/270*f**6 - 1/27*f**3 + 0*f**4 + 0*f - 2*f**2 + 0. Determine y so that k(y) = 0.
-1/2, 1
Suppose v - 3*v + 14 = -5*l, 4*v - 4*l - 16 = 0. Determine s, given that 1 - 1 + v*s**3 + 6*s + 1 - 3 - 6*s**2 = 0.
1
Let x(g) = -