3
Let l(y) = 6*y**2 + 3*y + 2. Let j be l(-2). Suppose 0*r + 30 = 2*i - 4*r, i - 3*r - j = 0. Suppose z**2 + z**2 - 2*z**4 - z**i + z + 0*z = 0. Calculate z.
-1, 0, 1
Solve 10*b - 7 + 14*b - 3 - 35*b**2 + 21*b = 0 for b.
2/7, 1
Let t(k) be the second derivative of -1/16*k**4 + 3/40*k**5 - 1/40*k**6 + 0*k**2 + 0*k**3 + 0 + 2*k. Factor t(v).
-3*v**2*(v - 1)**2/4
Let a(b) be the first derivative of 2*b**6/3 - 4*b**5/5 - b**4 + 4*b**3/3 + 9. What is t in a(t) = 0?
-1, 0, 1
Let s = -14/3 + 6. Factor 8/3*u**3 - u**4 + 0*u - s*u**2 + 0.
-u**2*(u - 2)*(3*u - 2)/3
Let a(k) = -8*k**5 + 45*k**4 - 61*k**3 + 14*k**2. Let o(h) = -12*h**5 + 68*h**4 - 92*h**3 + 20*h**2. Let r(p) = -8*a(p) + 5*o(p). Suppose r(f) = 0. Calculate f.
0, 1, 3
Determine i so that -10/13*i**2 + 10/13*i**4 + 0 + 2/13*i + 6/13*i**3 - 8/13*i**5 = 0.
-1, 0, 1/4, 1
Factor 2 + b**2 - 9/2*b.
(b - 4)*(2*b - 1)/2
Factor 6 - 6*d + 3*d - 6*d**2 + 3*d**2 + 6*d.
-3*(d - 2)*(d + 1)
Determine x, given that -10*x**2 - 2*x**2 - 2*x**3 - x**3 - 15*x + 3 - 9 = 0.
-2, -1
Let f(b) be the third derivative of 0*b**3 + 1/24*b**4 - 2*b**2 + 0 + 0*b + 1/12*b**5 + 1/120*b**7 + 23/480*b**6. Factor f(l).
l*(l + 1)*(l + 2)*(7*l + 2)/4
Let b = 1245/1039 - 1086265/65457. Let i = b - -114/7. Determine h, given that i*h - 10/9*h**2 + 2/9 = 0.
-1/5, 1
Let 2/7*k**2 - 2/7*k**3 + 4/7*k + 0 = 0. What is k?
-1, 0, 2
Let w(a) be the third derivative of a**7/105 + a**6/150 - 9*a**2. Factor w(c).
2*c**3*(5*c + 2)/5
Let d = 2 - -2. Suppose d*t = 2 + 10. Factor -4*w - w + t*w**3 - 3*w**4 + w + w + 3*w**2.
-3*w*(w - 1)**2*(w + 1)
Let x(h) = 4*h + 34. Let r be x(-8). Find o such that 3/4 - 3/2*o + 3/4*o**r = 0.
1
Let k(i) be the third derivative of 1/8*i**4 - 1/36*i**5 - 1/40*i**6 + 0*i + 0 + i**2 - 1/9*i**3 + 1/90*i**7. Factor k(d).
(d - 1)**2*(d + 1)*(7*d - 2)/3
Suppose 16 = -5*b + 9*b. Let w be ((-96)/(-300))/(b/10). Suppose -4/5*p**3 - 1/5 - 6/5*p**2 - 1/5*p**4 - w*p = 0. Calculate p.
-1
Let j(l) = -l**3 + 6*l**2 - 2*l - 11. Let h be j(5). Suppose h*i - i - 9 = 0. Factor 0*b**2 + 0 + 2/5*b - 2/5*b**i.
-2*b*(b - 1)*(b + 1)/5
Suppose 8 + 0 = 2*m. Let x(b) be the second derivative of -1/20*b**5 + 0*b**2 + b + 0 + 1/6*b**3 + 0*b**m. Find p such that x(p) = 0.
-1, 0, 1
Let q(r) be the first derivative of -1 + 0*r + 7/4*r**4 - 5/3*r**3 + 1/2*r**2 - 3/5*r**5. Factor q(y).
-y*(y - 1)**2*(3*y - 1)
Let t(o) be the second derivative of -o**6/90 + o**5/60 - o. Suppose t(d) = 0. Calculate d.
0, 1
Let r(k) be the second derivative of -5/42*k**4 + 3*k - 1/3*k**3 - 2/7*k**2 + 0. Factor r(b).
-2*(b + 1)*(5*b + 2)/7
Factor -3*w**3 - 12*w**4 + 2*w**2 + 6*w**5 + 2*w**4 + 5*w**3.
2*w**2*(w - 1)**2*(3*w + 1)
Suppose -h = -i - 5, 1 - 11 = h + 4*i. Suppose 5*l + 3*a = 9, -a + 9 = 2*a. Find b, given that 5*b + l*b**2 + 4*b + 6 + 3*b**h = 0.
-2, -1
Let d(c) = 7*c - 1. Let f be d(1). Let -6*r**3 + 3*r**2 - 5*r**2 + 4 + f*r - 2*r**4 + 0*r**3 = 0. What is r?
-2, -1, 1
Let g(o) be the third derivative of o**7/1260 - o**6/360 - o**4/4 + 2*o**2. Let z(f) be the second derivative of g(f). Find c such that z(c) = 0.
0, 1
Let k(t) be the first derivative of t**6/2 + 3*t**5/5 + 7. Determine l, given that k(l) = 0.
-1, 0
Let j be 2/(-8) - 42/(-8). Let h be (2/(-1))/(j - 6). Factor 0*n**4 + 4*n**4 + 2*n**5 + 3*n - 4*n**h - 5*n.
2*n*(n - 1)*(n + 1)**3
Let y = 19/9 + -17/9. Factor -4/9*i - y*i**3 + 0 - 2/3*i**2.
-2*i*(i + 1)*(i + 2)/9
Let r(f) be the first derivative of 0*f**2 - 1 + 2/3*f**3 + 0*f**4 + 1/1080*f**6 + 0*f - 1/360*f**5. Let u(k) be the third derivative of r(k). Factor u(c).
c*(c - 1)/3
Suppose -5*c**5 + 0*c**3 + 0 - 15/2*c**4 + 0*c + 5/2*c**2 = 0. Calculate c.
-1, 0, 1/2
Let v(a) be the third derivative of -a**7/560 - a**6/48 - a**5/10 - a**4/4 + a**3 + 5*a**2. Let b(g) be the first derivative of v(g). Factor b(r).
-3*(r + 1)*(r + 2)**2/2
Let v(a) = -2*a**5 - 2*a**4 + 2*a**3 + 13*a**2 + 11. Let f(g) = 2*g**4 - g**3 + 2*g**4 - 3*g**4 + g**5 - 6 - 7*g**2. Let r(l) = -11*f(l) - 6*v(l). Factor r(k).
k**2*(k - 1)*(k + 1)**2
Let a(i) = -i**2 + 7*i + 2. Let l be a(7). Factor 4 - 1 + 9 + 3*b**l - 12*b + 0*b.
3*(b - 2)**2
Let i be 1*-1 + 5 + -4. Factor -2*f**4 + 2*f + 0 - 2*f**3 + i + 2*f**2.
-2*f*(f - 1)*(f + 1)**2
Find l such that 8/5*l**2 - 16/5*l + 4/5*l**3 + 0 - 2/5*l**4 = 0.
-2, 0, 2
Let o(i) be the first derivative of 3/5*i**5 + 3/2*i**4 + 0*i + 0*i**2 + i**3 + 4. Let o(d) = 0. Calculate d.
-1, 0
Let i(c) = 12*c**3 - 45*c**2 + 36*c - 21. Let q(a) = 4*a - 5 + 3*a**3 - a**2 - a - 10*a**2 + 6*a. Let g(l) = -2*i(l) + 9*q(l). Factor g(w).
3*(w - 1)**3
Solve 12*x - 54 - 2/3*x**2 = 0.
9
Let d(w) be the third derivative of -w**9/20160 + w**8/5040 + w**7/5040 - w**6/360 + w**5/30 - 3*w**2. Let u(v) be the third derivative of d(v). Factor u(o).
-(o - 1)**2*(3*o + 2)
Let l(n) = 4*n**3 - 7*n**2 - 7*n + 7. Let m(a) = 8*a**3 - 13*a**2 - 13*a + 13. Let g(h) = 5*l(h) - 3*m(h). Factor g(f).
-4*(f - 1)**2*(f + 1)
Let 0*x - 4/5 + 1/5*x**3 + 3/5*x**2 = 0. What is x?
-2, 1
Let i(q) be the second derivative of -q**7/42 - q**6/30 + q**5/20 + q**4/12 - q. Determine p, given that i(p) = 0.
-1, 0, 1
What is n in 2/5*n + 4/5*n**2 + 2/5*n**3 + 0 = 0?
-1, 0
Determine m, given that 3/2*m**2 + 3/2*m + 1/2*m**3 + 1/2 = 0.
-1
Suppose -12 + 4 = -4*z. Suppose -16 = -z*b - 2*b. Factor 0*f**b + 0*f + 2/5*f**5 - 2/5*f**3 + 0*f**2 + 0.
2*f**3*(f - 1)*(f + 1)/5
Let f be (6/5)/((-6)/(-15)). Determine h so that h**4 + 2*h**2 - 3*h**4 + 3*h**3 + 2*h**2 - 5*h**f = 0.
-2, 0, 1
Let x(n) be the third derivative of -7*n**2 - 1/420*n**6 + 0*n**4 - 1/210*n**5 + 0*n**3 + 0*n + 0. Factor x(c).
-2*c**2*(c + 1)/7
Let h(f) be the third derivative of -f**7/210 + f**6/30 - f**5/20 - 7*f**2. Factor h(p).
-p**2*(p - 3)*(p - 1)
Let b(d) = -7*d**4 - 5*d**3 + 4*d**2 + 4*d + 4. Let a(u) = 8*u**4 + 4*u**3 - 5*u**2 - 5*u - 5. Let k(z) = -4*a(z) - 5*b(z). Factor k(i).
3*i**3*(i + 3)
Let r be (-8)/(-24) - 16/(-6). Find n such that -24*n**2 - 13*n**4 - 3 + 18*n + 7*n**4 - 18*n**r + 33*n**4 = 0.
-1, 1/3, 1
Let i be 2/(-14) - (-171)/266. Find s such that -1/2 + s - i*s**2 = 0.
1
Let u(a) = -2*a**4 - 4*a**3 + 5*a**2 + 9*a + 2. Let j(r) = 3*r**2 - r - r**2 - 4*r**2 + r**2. Let q(m) = 5*j(m) + u(m). Let q(s) = 0. What is s?
-1, 1
Let z(d) be the second derivative of d**7/630 - d**4/12 - 4*d. Let g(q) be the third derivative of z(q). Factor g(u).
4*u**2
Let y(l) be the third derivative of 1/2016*l**8 + 0*l**3 + 1/630*l**7 - 4*l**2 + 0*l**5 + 1/720*l**6 + 0*l**4 + 0 + 0*l. Find h such that y(h) = 0.
-1, 0
Let c(g) = g**2 - 4*g + 7. Let i be c(7). Suppose -8 = 5*s - i. Determine w so that w**3 - 2*w + s*w - 3*w = 0.
-1, 0, 1
Factor -440*y**2 - 10 - 80*y**3 + 2 - 12 - 5 - 205*y.
-5*(y + 5)*(4*y + 1)**2
Let o(w) = w**3 + 8*w**2 + 7*w + 3. Let y be o(-7). Let 2/13*u**4 + 0*u + 0 - 2/13*u**2 + 0*u**y = 0. Calculate u.
-1, 0, 1
Let y(u) be the third derivative of -u**5/12 + 5*u**4/24 + 5*u**3/3 + 19*u**2. Solve y(r) = 0.
-1, 2
Suppose -2*g = 2*m - 14 + 2, -2*m = -4*g + 12. Let c(y) be the first derivative of -y**2 + 0*y + 0*y**3 - 1/3*y**6 - 1 + y**g + 0*y**5. Factor c(o).
-2*o*(o - 1)**2*(o + 1)**2
Let n(u) be the first derivative of u**7/70 + u**6/20 - u**4/4 - u**3/2 + u**2/2 - 4. Let d(v) be the second derivative of n(v). Find s such that d(s) = 0.
-1, 1
Let d(m) be the third derivative of m**7/105 - m**6/30 - 2*m**5/15 + m**4/6 + m**3 + 5*m**2. Let d(q) = 0. What is q?
-1, 1, 3
Let l(x) = x**4 + x**3 - 3*x**2 - x + 4. Let v(f) = -f**3 + f - 1. Let i(c) = l(c) + 2*v(c). Factor i(g).
(g - 2)*(g - 1)*(g + 1)**2
Let h be (-1)/1 + 4/((-12)/(-3)). Let x(g) be the second derivative of -1/48*g**4 + g - 1/40*g**6 + h*g**2 + 0*g**3 + 0 + 1/168*g**7 + 3/80*g**5. Factor x(m).
m**2*(m - 1)**3/4
Let b(a) be the second derivative of -3*a**5/20 + a**4/4 + 4*a. Suppose b(i) = 0. Calculate i.
0, 1
Let m = -10 + 15. Let i(a) be the first derivative of -3 + 0*a**2 + 0*a**3 + 0*a + 1/8*a**4 + 1/10*a**m. Suppose i(k) = 0. What is k?
-1, 0
Factor 2/11*n**4 + 0*n**3 + 0 + 0*n - 2/11*n**2.
2*n**2*(n - 1)*(n + 1)/11
Suppose 20 = -y + 6*y. Solve -y - 4*n + 4*n - n**2 + 4*n = 0.
2
Let g(q) = -q**3 + q**2 - q - 1. Let m(b) = 7*b**3 - 6*b**2 + 15*b + 12. Let a(w) = 24*g(w) + 3*m(w). Suppose a(p) = 0. What is p?
-1, 4
Let c = -9 - -11. What is o in 7*o*