What is h?
0, 1
Suppose 0 = 3*y - 0*z + 4*z - 17, 0 = -4*y + 2*z + 8. Suppose 0 = 4*b + 2*n - 14, -y*n + n = 2*b - 8. Factor 3/5*v + 2/5 - 1/5*v**b + 0*v**2.
-(v - 2)*(v + 1)**2/5
Suppose -47*n**5 - 40*n**2 - 131*n**3 - 65*n - 158*n**4 + 61*n - 16*n**5 = 0. Calculate n.
-1, -2/7, -2/9, 0
Let i = -48 - -58. Let h = -3 - -5. Factor -h*y + i*y**2 - 13*y**2 + y**3 - 2*y**3.
-y*(y + 1)*(y + 2)
Factor -23*j**2 + 10*j**3 - j**3 + 3*j + 14*j**2 - 3*j**4.
-3*j*(j - 1)**3
Let w = 18 - 16. Let 1 + w + 6*r - 18*r + 3*r**2 + 9 = 0. What is r?
2
Factor 0 + 0*n + 1/3*n**3 - 1/3*n**2.
n**2*(n - 1)/3
Let n = -33 + 34. Let v(y) be the first derivative of -1/27*y**6 + n + 0*y**5 + 4/9*y - 1/3*y**2 - 4/27*y**3 + 2/9*y**4. What is j in v(j) = 0?
-2, -1, 1
Factor 32*t - 5*t**2 + 2*t**2 - 64 - t**2.
-4*(t - 4)**2
Suppose 2 + 16 = 3*x. Let h be (4 - x) + (-10)/(-3). Solve -4/3 - 2/3*k + h*k**2 + 2/3*k**3 = 0 for k.
-2, -1, 1
Let a be (2/(1 - 3))/(-2). Factor -1/2*j**2 + 0 - a*j.
-j*(j + 1)/2
Let v(p) be the second derivative of -p**7/210 + p**6/25 - 2*p**5/25 - 4*p**4/15 + 8*p**3/5 - 16*p**2/5 - 2*p. Factor v(r).
-(r - 2)**4*(r + 2)/5
Suppose 4*v + 5*q - 45 = 0, 4*v - 25 = -0*q - q. What is k in k**v + 0*k + 1/4*k**2 - k**3 - 1/4*k**4 + 0 = 0?
-1, 0, 1/4, 1
Let q(c) = 4*c**4 + 24*c**3 + 8*c**2 - 24*c - 12. Let k(u) = u**2 - 1. Let b(i) = 24*k(i) + q(i). Suppose b(h) = 0. What is h?
-3, -1, 1
Let c be 2/(-6) + 8 + 879/(-117). Factor -4/13*w**2 + 2/13*w + 4/13 - c*w**3.
-2*(w - 1)*(w + 1)*(w + 2)/13
Let 14*l**2 - 5/3*l**4 - 8 - 44/3*l + l**3 = 0. Calculate l.
-3, -2/5, 2
Suppose -j = -6*j + 10. Factor 0*k**2 + 16*k**2 - k**3 + j*k + 10*k + 5*k**3.
4*k*(k + 1)*(k + 3)
Let c(t) be the third derivative of 0*t + 1/735*t**7 + 0 - 1/140*t**6 + 0*t**4 + 8*t**2 + 1/105*t**5 + 0*t**3. Factor c(d).
2*d**2*(d - 2)*(d - 1)/7
Find f, given that -7*f**4 + 3*f**3 + f**4 + 9*f**4 = 0.
-1, 0
Let r(l) be the third derivative of l**9/1008 - l**8/2240 - 2*l**7/525 - l**6/300 - l**4/8 - l**2. Let d(x) be the second derivative of r(x). Factor d(s).
3*s*(s - 1)*(5*s + 2)**2/5
Factor -6*f - 54 - 1/6*f**2.
-(f + 18)**2/6
Suppose -4*b - 5 = j - 23, 5*j = -4*b + 26. Factor -1 - h**b - 2*h**3 + 6*h - 2*h + 3*h**2 - 3 + 0*h**3.
-(h - 1)**2*(h + 2)**2
Let z(v) = -v. Let q(h) = -3*h**2 + 4*h. Let s(b) = -q(b) - 4*z(b). Factor s(o).
3*o**2
Let z = -1616 + 8112/5. Find x such that 82/5*x**3 - 10*x**5 + 2*x**4 - z*x - 8/5 - 2/5*x**2 = 0.
-1, -2/5, 1
Let c(x) be the first derivative of 8 + 4/3*x + 4/9*x**3 + 4/3*x**2. Factor c(d).
4*(d + 1)**2/3
Let r(n) = 4*n**4 + 7*n - 7. Let b(w) = -w**4 - 2*w + 2. Let c(i) = -14*b(i) - 4*r(i). Determine o so that c(o) = 0.
0
Let v(b) = -6*b + 3*b + 4*b. Let z be v(3). Find y such that 0 + 0*y - 1/5*y**z + 1/5*y**2 = 0.
0, 1
Let -f**5 + 602*f**2 + f**4 - 602*f**2 = 0. What is f?
0, 1
Let a(d) be the second derivative of -d**2 + 0 + 1/6*d**4 - 1/20*d**5 + 3*d + 1/6*d**3. Factor a(w).
-(w - 2)*(w - 1)*(w + 1)
Let f(y) be the second derivative of -y**6/135 + y**5/30 - y**4/27 - 6*y. What is b in f(b) = 0?
0, 1, 2
Let i = 7 - 12. Let l be (2/15)/((-1)/i). Solve 4/3*g**3 + 0*g + 0 - l*g**2 - 2/3*g**4 = 0.
0, 1
Suppose 60*z - 104 = 136. Suppose -36*v**2 - 24/5*v + 0 - 75*v**z - 90*v**3 = 0. Calculate v.
-2/5, 0
Let h(v) be the second derivative of 0 + v + 1/60*v**5 + 1/72*v**4 + 0*v**2 + 0*v**3 + 1/180*v**6. Factor h(f).
f**2*(f + 1)**2/6
Let q(t) be the first derivative of 5*t**3/3 - 20*t + 16. Factor q(x).
5*(x - 2)*(x + 2)
Suppose 2*c + 2 = -2*q, 0*c - 5*c - 20 = 0. Solve -n**2 + q*n**5 + n + 3*n**2 - n**2 + 12*n**3 - 10*n**4 - 7*n**2 = 0 for n.
0, 1/3, 1
Let f(u) = 8*u**3 + u**2 + u - 5. Let g be (4/(-3))/(4/(-12)). Let x(a) = 8*a**3 - 4. Let q(h) = g*f(h) - 5*x(h). Find i, given that q(i) = 0.
-1/2, 0, 1
Let w(r) be the first derivative of 2/3*r**3 + 0*r + 0*r**2 + 1/2*r**4 + 1 - 1/3*r**6 - 2/5*r**5. Factor w(j).
-2*j**2*(j - 1)*(j + 1)**2
Solve 2/9*z**3 - 2/9*z**2 + 0*z + 0 = 0.
0, 1
Let k = 9 + -7. Determine m so that 6*m - 3 - 6*m**2 + m**2 + k*m**2 = 0.
1
Suppose 0 = k + w + 1, 4*k - w - 10 - 1 = 0. Factor 2*q**k + 0*q**2 + 1 - q - 3 + q**3.
(q - 1)*(q + 1)*(q + 2)
Suppose 2*s = -2, 2*n - 14 = -3*s - s. Suppose 0 = 4*z - 3*j - n, -5*z + 12 = -2*z - 4*j. Determine g, given that 0*g + z - 2/3*g**3 + 2/3*g**2 = 0.
0, 1
Let q(f) be the third derivative of f**8/16800 - f**7/6300 - f**4/4 + 6*f**2. Let i(n) be the second derivative of q(n). Factor i(k).
2*k**2*(k - 1)/5
Factor 3*g + 5*g + 2*g**2 - 7*g - 2 - g**3.
-(g - 2)*(g - 1)*(g + 1)
Let x(m) = m**2 + 8. Let o be x(0). Let l(j) = -j**3 + 7*j**2 + j - 3. Let k be l(7). Factor 6*b**5 + 2*b - 4*b**2 + 2*b**k + 2*b**4 - o*b**5.
-2*b*(b - 1)**3*(b + 1)
Let p be 261/135 + (-1)/3. Factor 2/5*m**2 - p*m + 6/5.
2*(m - 3)*(m - 1)/5
Let m(f) be the second derivative of 2/3*f**3 + f**2 + 4/15*f**6 + 0 - 1/2*f**4 - 2/5*f**5 + 3*f. Find i, given that m(i) = 0.
-1/2, 1
Suppose -10 = -3*o + 2*p, -5*p = -4*o + 8*o - 21. Let y = -2 + o. Suppose j - 6*j**2 - 2 + 5*j - 3*j**2 + 3*j**2 + y*j**3 = 0. What is j?
1
Let n(y) = -19*y**3 + 29*y**2 - 2*y - 13. Let m(k) = 10*k**3 - 14*k**2 + k + 6. Let v(a) = 13*m(a) + 6*n(a). Factor v(t).
t*(4*t - 1)**2
Suppose -1/3 + 1/3*o**2 + 0*o = 0. Calculate o.
-1, 1
Solve 16*a**2 + 55 - 72 - 4*a**3 - 167 - 72 + 64*a = 0 for a.
-4, 4
Let i = 62/5 - 166/15. Factor 2/3*a**2 + i + 2*a.
2*(a + 1)*(a + 2)/3
Let t be -8 - ((-196)/16 + 4). Factor 0*s**2 - 5/4*s**4 + s**5 + 0*s + t*s**3 + 0.
s**3*(s - 1)*(4*s - 1)/4
Let d(l) be the third derivative of -l**7/4200 + l**6/1800 - l**3 - 4*l**2. Let h(o) be the first derivative of d(o). Factor h(i).
-i**2*(i - 1)/5
Let w = 13 - 10. Suppose -w*l = 2*l. Factor 4/3*f + l - 2/3*f**2.
-2*f*(f - 2)/3
Let d(t) = t**2 - 13*t + 15. Let z be d(13). Let v be (-10)/z - 13/(-6). Factor -2 + 0*q + v*q**2 + 1/2*q**3.
(q - 1)*(q + 2)**2/2
Let b(x) be the second derivative of -x**7/14 + x**6/10 + 9*x**5/10 - 7*x**4/2 + 11*x**3/2 - 9*x**2/2 - 76*x. Factor b(j).
-3*(j - 1)**4*(j + 3)
Let m(q) be the second derivative of q**5/150 + q**4/20 + 2*q**3/15 + q**2/2 + q. Let b(x) be the first derivative of m(x). Factor b(s).
2*(s + 1)*(s + 2)/5
Let f = -14 + 10. Let g = f - -7. Find k, given that 0 - 2/5*k**4 + 2/5*k**g + 2/5*k**2 - 2/5*k = 0.
-1, 0, 1
Let t be 4 - 0 - (-1 - -1). Let j = 5 + -3. What is m in -1/3 - 27*m**t - 30*m**3 - 11/3*m - 9*m**5 - 46/3*m**j = 0?
-1, -1/3
Let q(u) be the first derivative of -u**3 - 15*u**2 - 75*u + 18. Let q(a) = 0. What is a?
-5
Suppose 2*h - 9 = -1. Factor -9*y**3 - 3*y + 3*y**4 + 2*y**2 - h*y**2 + 10*y**2 + y**2.
3*y*(y - 1)**3
Let g be 0 - (3 + -1) - (-17 + 15). Let t(k) be the first derivative of 1 - 1/2*k**4 - k + k**3 + g*k**2. Solve t(h) = 0.
-1/2, 1
Let c(g) = g**3 - 3*g**2 + 2*g - 3. Let n be c(3). Find j such that j**3 + 2*j**3 - 2*j**n = 0.
0
Solve -h**2 - 13*h**3 + 8*h + 5*h**3 - 4*h**4 + 5*h**2 = 0 for h.
-2, -1, 0, 1
Let i(p) = -p + 15. Let y be i(-11). Solve s**2 - 24 + 59 + 6*s - y = 0 for s.
-3
Determine y, given that -26/3*y + 2*y**3 + 4/9*y**4 - 4/9*y**2 - 4 = 0.
-3, -1/2, 2
Let c = -601 + 604. Let n = 21/2 + -9. Solve -n*u - 1 + 3/2*u**c + 1/2*u**4 + 1/2*u**2 = 0.
-2, -1, 1
Suppose 0 = l + 3*j + 4, 3*l + j + 2 = -3*j. Suppose l*n = 14 - 6. Factor 0*o**4 - 2*o**n + o**5 + 2*o**3 - o**3.
o**3*(o - 1)**2
Let j(p) = 4*p**2 - 20. Let b(l) = l - 1. Let n = -12 - -13. Let m(q) = n*j(q) - 8*b(q). Let m(g) = 0. Calculate g.
-1, 3
Let a(b) be the first derivative of b**4/26 + 60. Factor a(v).
2*v**3/13
Let g(b) be the second derivative of b**7/105 - b**6/20 + b**5/15 - b**2 + 4*b. Let u(c) be the first derivative of g(c). What is q in u(q) = 0?
0, 1, 2
Factor 0*y + 0 + 2/15*y**2.
2*y**2/15
Let i(o) be the first derivative of 27/4*o**4 - 2 + 18*o**3 + 8*o + 18*o**2. Suppose i(b) = 0. What is b?
-2/3
Let d(h) = 3*h + 5*h - h**2 - 10*h + 7*h**2. Let k(l) = -5*l**2 + 2*l. Let g(w) = 3*d(w) + 4*k(w). Factor g(a).
-2*a*(a - 1)
Let d be (-3 + 0)*((-85)/(-25) - 4). Solve -d*a**2 + 0 - 6/5*a = 0 for a.
-2/3, 0
Let t(o) be the third derivative of -o**9/18900 - o**8/4200 + o**7/3150 + o**6/450 + o**4/8 + 9*o**2. Let q(x) be the second derivative of t(x). Factor q(v).
-4*v*(v - 1)*(v + 1)*(v + 2)/5
Let u(m) = -m**4 - 3*m**3 - 3*m**2 - 3*m - 4. Let z(q