.
6
Solve 3/4*x - 1/2*x**2 - 1/4 - 1/4*x**5 + 3/4*x**4 - 1/2*x**3 = 0.
-1, 1
Let j be 0 + 0 - 2/(-8). Factor 0 - t + 0*t**2 + j*t**3.
t*(t - 2)*(t + 2)/4
Let d(y) = y**3 - y**2 - 1. Let g(b) = -13*b**3 - 35*b**2 - 240*b + 299. Let j(t) = 22*d(t) + 2*g(t). Find q such that j(q) = 0.
-12, 1
Let a be (0 + (-3)/3)*-2. Let 7*i**3 + 0*i**5 + 2*i**5 + 10*i - 2 - 7*i**2 - 10*i**4 + 13*i**3 - 13*i**a = 0. Calculate i.
1
Let c be -1*5*2/(-25). Let s = 11/5 + -2. Solve -c*x**2 + s*x + 1/5*x**3 + 0 = 0.
0, 1
Suppose 4*p + m = -2, 0 = -6*m + 4*m + 4. Let k(d) = -2*d**2 - 6*d. Let a(o) = -o**2 - o + 1. Let l(u) = p*k(u) + 4*a(u). Factor l(t).
-2*(t - 2)*(t + 1)
Let w(p) be the first derivative of -p**5/15 - p**4/12 - 4. Factor w(m).
-m**3*(m + 1)/3
Let w(g) = -g - 4. Let h be w(-7). Factor 10*r**2 - 8*r**4 - 6*r**h + 6*r**4 - 4*r**4 - 12*r**4 - 2*r.
-2*r*(r + 1)*(3*r - 1)**2
Suppose 0 = -m + 2*p + 20, 0 = -5*m - 2*p + 63 - 23. Let z be -1 - (26/m - 4). Factor -z*g - 4/5*g**2 + 6/5*g**3 + 0.
2*g*(g - 1)*(3*g + 1)/5
Let x(d) = 6*d**2 - 5*d**2 + 2 - 3 + 3*d**2. Let k(y) = 5*y**2 - 1. Let p(a) = -3*k(a) + 4*x(a). Suppose p(c) = 0. What is c?
-1, 1
Let r(f) be the second derivative of f**4/4 + f**3/2 - 3*f**2 + 3*f. Determine j so that r(j) = 0.
-2, 1
Let b be ((-2)/4)/((-25)/20). Factor 0*s + 2/5*s**2 - b.
2*(s - 1)*(s + 1)/5
Factor 3*r**2 + 6*r**2 + 8*r - 12 - 5*r**2 + 0*r**2.
4*(r - 1)*(r + 3)
Let m(c) be the third derivative of -c**6/240 + c**5/12 + 23*c**4/48 + c**3 - 20*c**2. Suppose m(d) = 0. What is d?
-1, 12
Let r(b) = -2*b**2 - 32*b + 36. Let p be r(-17). Solve 0*f - 1/4*f**p + 0 = 0 for f.
0
Suppose -2*n + 12 = -0*n. Let w(q) be the first derivative of -11*q**5 + 2 + 23/3*q**3 + 4*q**2 - 25/6*q**n - 19/4*q**4 - 4*q. Factor w(f).
-(f + 1)**3*(5*f - 2)**2
Let p(j) = -j + 1. Let i(z) = 5*z**2 + 59*z + 46. Let n(y) = -i(y) - 4*p(y). Factor n(t).
-5*(t + 1)*(t + 10)
Let i = 57/145 - -1/145. Factor 2/5*a**2 - i*a + 0.
2*a*(a - 1)/5
Let n = 60 - 60. Factor -1/5*q**2 + n*q + 0.
-q**2/5
Factor 119*j**4 + 6*j**5 - 23*j**2 + 32*j**3 + 9*j**5 + 34*j**5 + 35*j**3 - 16*j + 4.
(j + 1)**3*(7*j - 2)**2
Let j(g) be the second derivative of 25*g**4 + 10*g**3 + 3*g**2/2 - 26*g. Find i such that j(i) = 0.
-1/10
Let v(b) = b**3 - 3*b**2 + 3. Let y(k) = -k - 2. Let p be y(-5). Let l be v(p). Solve -5*a + 4*a + 3*a**2 + 2*a + 2*a**l = 0.
-1, -1/2, 0
Suppose -2*u = x - 2*x - 6, 5 = u. Let r(a) be the first derivative of a**3 + 1/2*a + 1/2*a**x + 1/10*a**5 + a**2 + 2. Factor r(y).
(y + 1)**4/2
Let u = -151/102 + 28/17. Suppose 0*x - 1/3*x**3 + u*x**4 + 0 + 1/6*x**2 = 0. Calculate x.
0, 1
Let n(a) = -a**2 - a + 4. Let g be n(0). Factor b**2 + 0*b + 2*b - g*b**2 + 2*b**2.
-b*(b - 2)
Let k be 7 + ((-5)/5)/1. Factor -k*h + 3/2*h**2 + 6.
3*(h - 2)**2/2
Let a(x) be the second derivative of x**6/120 + x**5/20 + x**4/8 + x**3/6 + x**2/8 - 5*x. Factor a(q).
(q + 1)**4/4
Let n(y) be the third derivative of 0*y + 1/84*y**4 - 1/210*y**5 + 0*y**3 - 6*y**2 + 0. Determine d, given that n(d) = 0.
0, 1
Let c be ((-2)/5)/((-2)/10). Let d(o) = -3*o**2 - 3 + 2*o**c + 4*o**2. Let h(v) = -4*v**2 + 4. Let f(y) = 3*d(y) + 2*h(y). Let f(r) = 0. What is r?
-1, 1
Let w(o) be the second derivative of -o**5/20 + o**4/12 + o**3/3 - 5*o. Factor w(s).
-s*(s - 2)*(s + 1)
Let t(s) be the first derivative of -s**5/20 - 5*s**4/16 - 3*s**3/4 - 7*s**2/8 - s/2 + 19. Factor t(n).
-(n + 1)**3*(n + 2)/4
Factor 4*o**3 - 13*o**2 - o**2 - 11*o**2 + 64 - 3*o**2 + 32*o.
4*(o - 4)**2*(o + 1)
Let x(j) be the second derivative of -3/20*j**5 + 1/6*j**4 - 1/12*j**3 + 0 + 1/15*j**6 - 1/84*j**7 + 0*j**2 + 4*j. Suppose x(p) = 0. What is p?
0, 1
Let x(n) = -2*n + 2. Let l be x(-3). Suppose g - 5*g = -l. Factor 2 + 2 + k + 2*k**3 - 2*k - k - 4*k**g.
2*(k - 2)*(k - 1)*(k + 1)
Suppose -q - 2*y = 0, -q = 4*y - 0 + 2. Let k = 16/15 + 4/15. Let -14/3*d**q - 6*d - k = 0. Calculate d.
-1, -2/7
Let b(r) be the first derivative of -r**5/20 - 5*r**2/2 - 8. Let x(u) be the second derivative of b(u). Factor x(t).
-3*t**2
Suppose 0*r + 7*r - 21 = 0. Factor -8*w**r - 7*w**2 + 7*w**4 - 3*w**4 + 11*w**2.
4*w**2*(w - 1)**2
Let v be -4 + (1 - (-3 - -1)). Let z be (0 + 0)*v/(-2). Solve z + 2/3*a + 2/3*a**2 = 0.
-1, 0
Let v(n) be the first derivative of 4*n**3/3 - 4*n**2 - 9. What is z in v(z) = 0?
0, 2
Let m(f) be the first derivative of f**4/9 - 7*f**3/9 + f**2 + 5*f - 5. Let k(a) be the first derivative of m(a). Factor k(g).
2*(g - 3)*(2*g - 1)/3
Suppose -4 + 12 = 4*m. Suppose -2*r = -m*w + 10, 2 = 5*w + 4*r + 4. What is p in 3*p**w + 5*p - 3*p**2 + p**2 - 2*p + 2 = 0?
-2, -1
Let w(g) be the second derivative of 0*g**3 + 1/2*g**2 - 2/105*g**5 + 1/84*g**4 - 3*g + 0. Let u(m) be the first derivative of w(m). Solve u(v) = 0 for v.
0, 1/4
Let i be 1/((-3)/21*-1). Suppose -2*n - 10 = -i*n. Solve 14*c**2 - 2*c - n*c + c - c = 0.
0, 2/7
Factor 1/3*g**5 + 0 + 0*g**2 + 0*g - 2/3*g**4 + 1/3*g**3.
g**3*(g - 1)**2/3
Let j = 2 + 2. Determine h so that j*h + 3*h + 4*h**2 - 6*h = 0.
-1/4, 0
Let g(r) = r**4 - r**3 - 7*r**2 + 3*r + 3. Let j(h) = -h**4 + h**3 - h**2 + h - 1. Let q(b) = -g(b) + j(b). Find n such that q(n) = 0.
-1, 1, 2
Let g be 32/(-210) - 2/(-5). Let x = -1/21 + g. Factor 0 + 0*n - 1/5*n**2 + x*n**3.
n**2*(n - 1)/5
Suppose 3/5*c**4 + 9/5*c - 3*c**2 + 3/5*c**3 + 0 = 0. Calculate c.
-3, 0, 1
Let l(r) be the second derivative of -r**5/120 - r**4/8 - 3*r**3/4 - 9*r**2/4 + 18*r. Let l(g) = 0. What is g?
-3
Let m(d) be the first derivative of d**6/420 + d**5/70 + d**4/28 + d**3/21 + 3*d**2/2 + 3. Let o(w) be the second derivative of m(w). Factor o(t).
2*(t + 1)**3/7
Suppose 4*t + 17 = b, -3*b - t + 131 = 3*t. Let 48 + b*r**2 - 229*r**2 + 81*r**5 + 129*r**4 - 36*r**3 - 104*r**4 + 164*r**4 = 0. What is r?
-2, -1, -2/3, 2/3
Let l(q) = -6*q**4 - 12*q**3 - 28*q**2 - 24*q - 6. Let j(a) = -7*a**4 - 12*a**3 - 29*a**2 - 25*a - 6. Let g(o) = -4*j(o) + 5*l(o). Factor g(x).
-2*(x + 1)**3*(x + 3)
Let j(r) be the third derivative of r**6/60 + r**5/30 - 5*r**4/12 + r**3 - 4*r**2. Suppose j(o) = 0. Calculate o.
-3, 1
Suppose -25*o + 31*o = 0. Solve -1/2*a**2 + 1/6*a**3 + o + 1/3*a = 0.
0, 1, 2
Let g be (0 + 1)/((-2)/(-6)). Suppose 0 = 5*d - g*d + 2*l, -5*d = -2*l - 14. Find m such that -4*m + d*m**2 - 3*m**2 + 3*m = 0.
-1, 0
Suppose 3*b + 3 = 12. Solve -2*f**3 - 2*f**5 + f**5 + 4*f**3 + b*f - 4*f = 0 for f.
-1, 0, 1
Let y = 5 + -3. Factor 2*q**3 - 2*q**2 + 0*q**2 + 2*q - 2*q**y + 0*q**3.
2*q*(q - 1)**2
Let v(d) be the first derivative of -4 - d + 1/36*d**4 + 0*d**5 + 0*d**3 + 0*d**2 - 1/90*d**6. Let b(h) be the first derivative of v(h). Factor b(n).
-n**2*(n - 1)*(n + 1)/3
Let i(f) = -f**3 + 3*f**2 + 5*f - 2. Let v be i(4). Let c + 4 + 8*c + 3*c + 4*c**2 + c**v = 0. What is c?
-2, -2/5
Suppose -22 = -7*y + 6. Suppose f - y*f = 3*o + 6, 0 = -2*o + 5*f + 31. Factor 4/7*a**4 + 0*a**2 - 2/7*a**o + 0*a + 0 - 2/7*a**5.
-2*a**3*(a - 1)**2/7
What is c in 11*c - 6*c**2 + 18*c**2 - 2*c + 3*c**3 = 0?
-3, -1, 0
Factor -2/3*m**4 + 2/3*m**3 + 0*m + 4/3*m**2 + 0.
-2*m**2*(m - 2)*(m + 1)/3
Let w be (-2)/(-3) - 133/240. Let l(d) be the second derivative of w*d**5 + 0 - 7/8*d**3 - 1/8*d**4 + 4*d - 3/4*d**2. Find f such that l(f) = 0.
-1, -1/3, 2
Let p(k) be the second derivative of k**4/42 - 4*k**2/7 - 3*k. Factor p(h).
2*(h - 2)*(h + 2)/7
Suppose x - 18 = 4*x. Let r be (-5)/15*(x + 0). Find k such that 3*k**2 - 6*k**2 + k**4 + 2*k**r = 0.
-1, 0, 1
Suppose -6/5*i**2 - 2*i + 2/5*i**3 + 2/5*i**4 - 4/5 = 0. Calculate i.
-1, 2
Let h(c) = -c**2 + 9*c + 1. Let q be h(7). Let x = -15 + q. Factor 6/7*f**3 + 4/7*f**2 + 0*f + x - 10/7*f**4.
-2*f**2*(f - 1)*(5*f + 2)/7
Factor -2*t**3 - 7*t**4 - 14*t**3 + 2*t**2 - 6*t**2.
-t**2*(t + 2)*(7*t + 2)
Suppose 0 = -5*d + 2*l, 0 = 6*l - l + 25. Let s be d + 5 + (-6)/2. Factor -2/3*v**2 - 2/3*v + s.
-2*v*(v + 1)/3
Suppose 7*g = 5*g + 6. Let f(h) be the third derivative of 0*h + h**2 - 5/96*h**4 - 1/480*h**6 + 0 - 1/60*h**5 - 1/12*h**g. Factor f(y).
-(y + 1)**2*(y + 2)/4
Factor 18/7*w + 10/7*w**3 + 24/7*w**2 + 4/7.
2*(w + 1)**2*(5*w + 2)/7
Let x(w) be the third derivative of 1/40*w**5 + 1/3*w**3 + w**2 + 0 + 1/8*w**4 + 0*w + 1/480*w**6. Determine m so that x(m) = 0.
-2
Let t = 6 - 5. Suppose i - 3 = t. Factor -i + g**2 - 11*g + 12*g + 2.
(g - 1)*(g + 2)
Le