1
Suppose 1 = -j + 4. Factor 2*w**4 + 4*w**3 - 2 + 5*w - w - 8*w**j.
2*(w - 1)**3*(w + 1)
Suppose 0*d + 3*d + 5*b - 6 = 0, 0 = 3*b. Solve -8/11*t - 2/11 - 6/11*t**d = 0 for t.
-1, -1/3
Let a(h) be the third derivative of 3/5*h**5 + 0*h + 13/40*h**6 + 0 + 1/2*h**4 + 1/112*h**8 + 3/35*h**7 - 2*h**2 + 0*h**3. Factor a(p).
3*p*(p + 1)**2*(p + 2)**2
Suppose -n - f - 2 = 0, n - 5*f = 15 + 13. Suppose 5*g**3 + 10*g**2 + 2*g - n*g**3 - g**3 - 4 + 3*g**3 = 0. Calculate g.
-2, -1, 1/2
Let m(d) = 294*d + 8. Let o be m(-4). Let n = o + 8200/7. Suppose n*b + 10/7*b**2 + 8/7 = 0. Calculate b.
-2, -2/5
Let i(c) = -4*c - c - 26*c**2 + 20*c**2. Let j be 52/14 - 2/(-7). Let z(u) = -5*u**2 - 4*u. Let d(g) = j*i(g) - 5*z(g). Factor d(b).
b**2
Let s(o) be the second derivative of 1/10*o**5 - 2*o - 1/2*o**4 + 0 + 4*o**2 + 0*o**3. Factor s(j).
2*(j - 2)**2*(j + 1)
Let y be -9*(-1 + 6/9). Factor -y*r + 2*r + 16*r**3 - 15*r**3 + r**2 - 1 + 0.
(r - 1)*(r + 1)**2
Let i be (2 - 14/6)*9/(-2). Factor -3/2*b**4 + 3/2*b**2 + 0 - 3/2*b + i*b**3.
-3*b*(b - 1)**2*(b + 1)/2
Suppose 7*f - 3*f = 20. Suppose -6 = -0*o - 2*o. What is s in -o*s - 5*s**5 + 4*s - 5*s**4 + f*s**2 + s**5 + 3*s**3 = 0?
-1, -1/4, 0, 1
Let u be (644/105 - 6)*5. Factor -2/3*g**4 - u*g**5 + 2/3*g**2 + 2/3*g**3 + 0*g + 0.
-2*g**2*(g - 1)*(g + 1)**2/3
Let w be ((2 - -4) + -4)/1. Let q be (w - 3) + 1 + 0. What is b in q + 0*b**2 + 3/2*b - 3/2*b**3 = 0?
-1, 0, 1
Factor -7*q**2 + 6*q + 8 - 9*q**2 - 2*q**2 + 16*q**2.
-2*(q - 4)*(q + 1)
Suppose 1350/7 - 180/7*r + 6/7*r**2 = 0. Calculate r.
15
Find b, given that 0 + 2/3*b**2 + 1/3*b + 1/3*b**3 = 0.
-1, 0
Let n(h) be the second derivative of -1/6*h**4 + 2*h**2 + 0 + 1/3*h**3 + 5*h. Factor n(w).
-2*(w - 2)*(w + 1)
Let y(o) be the second derivative of -1/18*o**4 + 0 + 1/9*o**3 + 0*o**2 - 4*o + 1/45*o**6 - 1/30*o**5. Factor y(w).
2*w*(w - 1)**2*(w + 1)/3
Suppose p - 14 = -4*d, 0*p = 4*p + 2*d - 28. Factor -p*b**2 + 2*b**2 + 3*b**2 + 9*b - 3*b**5 - 3 - 5*b**2 - 6*b**3 + 9*b**4.
-3*(b - 1)**4*(b + 1)
Suppose 6*c - 8*c = -10. Let d(u) be the first derivative of -2/15*u**3 + 0*u**2 - 6/25*u**c + 0*u - 3/10*u**4 - 1/15*u**6 + 2. Factor d(q).
-2*q**2*(q + 1)**3/5
Let t be (-5)/((-56)/16 + 1). Let o be 45/84 + (-2)/7. Factor -n + 1 + o*n**t.
(n - 2)**2/4
Let m be (0/2)/((-12)/(-6)). Factor -1/3*g - 1/3*g**5 + 0*g**2 + 2/3*g**3 + m + 0*g**4.
-g*(g - 1)**2*(g + 1)**2/3
Suppose -78 - 22 = 4*k. Let f = k + 25. Factor 1/2*y**3 + 0*y + f + 0*y**2.
y**3/2
Let z(o) be the third derivative of -o**5/15 + o**4/6 + 2*o**2. Factor z(h).
-4*h*(h - 1)
Let u(a) be the third derivative of a**7/1470 - a**6/840 - a**5/420 + a**4/168 + 4*a**2 + 8*a. Factor u(s).
s*(s - 1)**2*(s + 1)/7
Let t(k) = 10*k**2 - 26*k - 4. Let m(p) = 2*p**2 - 5*p - 1. Let y(x) = 2*x + 6. Let u be y(5). Let b(s) = u*m(s) - 3*t(s). Factor b(h).
2*(h - 2)*(h + 1)
Factor 2/9*o**3 - 10/9 + 22/9*o - 14/9*o**2.
2*(o - 5)*(o - 1)**2/9
Let j(m) be the first derivative of 2*m**3/27 - 2*m/9 - 17. Factor j(d).
2*(d - 1)*(d + 1)/9
Let m(i) be the first derivative of -i - 2/3*i**3 + 5/12*i**4 + 1 + 1/2*i**2 - 1/10*i**5. Let j(v) be the first derivative of m(v). Factor j(k).
-(k - 1)**2*(2*k - 1)
Let h be (-5)/240*-8 - 1/(-2). Factor h*n**3 + 0*n**2 - 4/3 - 2*n.
2*(n - 2)*(n + 1)**2/3
Factor 10*i**2 - 13*i**2 - 4*i**4 + 7*i**2.
-4*i**2*(i - 1)*(i + 1)
Factor -5*t**5 - 11*t**3 + 5*t**4 + 6*t**3 + 5*t**3.
-5*t**4*(t - 1)
Let k(h) be the first derivative of 1/3*h**3 + 2/15*h**5 + 5/12*h**4 - h**2 + 1 + 0*h. Let q(d) be the second derivative of k(d). Let q(r) = 0. Calculate r.
-1, -1/4
Let p = 9 - 3. Suppose 0 = 2*s + 8, 2*v - p = 3*s + 12. Factor 0*t**3 - 4*t**2 + 3*t - t + 2*t**v.
2*t*(t - 1)**2
Let k(r) = -2*r**2 + 3*r - 1. Let v(n) = -2*n**2 + 4*n - 2. Suppose -3*m + f + 10 = -m, -m = -2*f - 8. Let j(o) = m*k(o) - 3*v(o). Factor j(g).
-2*(g - 1)*(g + 1)
Find u, given that -4 + 2*u - 1/4*u**2 = 0.
4
Let s(m) be the second derivative of 4*m + 0*m**6 + 1/294*m**7 - 1/70*m**5 + 0 + 1/42*m**3 + 0*m**4 + 0*m**2. Factor s(g).
g*(g - 1)**2*(g + 1)**2/7
Let f = 6 + -8. Let c be (0 - -9) + f/(-2). Let -c*k + 4 + k**5 + 8*k**3 - 6*k**4 - k**2 + 5*k**2 - 2*k**4 + k**5 = 0. What is k?
-1, 1, 2
Let d(z) be the third derivative of z**6/600 + z**5/150 + 6*z**2. Solve d(j) = 0 for j.
-2, 0
Let g(m) = -46*m**3 + 144*m**2 + 66*m - 198. Let k(b) = 4*b**3 - 13*b**2 - 6*b + 18. Let f(o) = -6*g(o) - 68*k(o). Factor f(j).
4*(j - 1)*(j + 3)**2
Factor 0*l**2 + 0*l - 4/5*l**3 + 2*l**4 + 0.
2*l**3*(5*l - 2)/5
Let d = 100 + -96. Let w(m) be the first derivative of 0*m + 1/6*m**2 + 2/9*m**3 + 1 + 1/12*m**d. Let w(a) = 0. What is a?
-1, 0
Let f(q) = 3*q**2 + 8*q + 5. Let m(j) = -5*j**2 - 12*j - 7. Let d(g) = -7*f(g) - 5*m(g). Factor d(w).
4*w*(w + 1)
Let r be 2/(-12) - 844/(-24). Let l be 2/4*28/r. Solve 2/5 + 0*m - l*m**2 = 0.
-1, 1
Suppose -140 = -4*d - 132. Factor 4/5*m + 2/5 + 2/5*m**d.
2*(m + 1)**2/5
Factor 2/13 - 18/13*q + 48/13*q**2 - 32/13*q**3.
-2*(q - 1)*(4*q - 1)**2/13
Suppose 7*o + 12 - 26 = 0. Let p(r) = -r**2 - 8*r. Let g be p(-8). Determine i so that -1/3*i + g + 1/3*i**o = 0.
0, 1
Let g(m) be the second derivative of 6*m + 0*m**2 + 0*m**3 - 3/20*m**5 - 1/2*m**4 + 0. Let g(b) = 0. Calculate b.
-2, 0
Let k(g) = 3*g**2 + 2. Let w be (-9)/(-3) + -2 - -4. Let m(d) = 2*d**2 + 2. Let i(p) = w*m(p) - 4*k(p). Factor i(b).
-2*(b - 1)*(b + 1)
Let k(n) be the first derivative of -n**3/5 - 3*n**2/10 - 2. Find g, given that k(g) = 0.
-1, 0
Let p(h) be the first derivative of h**9/6048 + h**8/3360 + 2*h**3/3 - 4. Let k(f) be the third derivative of p(f). Factor k(v).
v**4*(v + 1)/2
Let y(w) be the second derivative of w**7/105 + w**6/25 + w**5/25 - w**4/15 - w**3/5 - w**2/5 + 12*w. Factor y(v).
2*(v - 1)*(v + 1)**4/5
Let a = 4 - 1. Suppose 4*n - 5 - a = 0. Factor 5*k - k - n*k - 2*k**2.
-2*k*(k - 1)
Determine w so that 1/4*w**4 + 0 + 3/4*w**3 - 3/4*w**5 - 1/4*w**2 + 0*w = 0.
-1, 0, 1/3, 1
Let z be 3 - ((-18)/12 - 2) - 6. Let g(n) = n**2 - 4*n - 1. Let b be g(5). Factor 0 - 1/2*k - z*k**b - 3/2*k**2 - 3/2*k**3.
-k*(k + 1)**3/2
Suppose -5*f + 8 = 2*r + 4, -5*f + 5*r = 10. Factor 0*o + 3/4*o**5 + 3/2*o**4 + 3/4*o**3 + f*o**2 + 0.
3*o**3*(o + 1)**2/4
Factor 3*n**5 - 8*n**4 - 3*n**3 + 9*n**3 - n**4.
3*n**3*(n - 2)*(n - 1)
Let j = -7 + 17. Suppose -4*y + 21 = q - 16, j = 2*y. Factor 4 - 4*h + 22*h**2 - h**3 - q*h**2 - 4*h.
-(h - 2)**2*(h - 1)
Let w be -8*(4 + (-105)/24). Let f(n) be the second derivative of -1/12*n**4 + 0*n**5 + 0*n**w + 1/30*n**6 + 0*n**2 + 2*n + 0. Factor f(d).
d**2*(d - 1)*(d + 1)
Let g(l) = l**3 + 4*l**2 - 3*l - 6. Let k(v) = -3*v**2 + 3*v + 6. Let r(u) = 3*g(u) + 2*k(u). Factor r(w).
3*(w - 1)*(w + 1)*(w + 2)
Let v(b) be the first derivative of -b**7/3360 + b**6/720 - b**5/480 + b**3/3 - 1. Let h(a) be the third derivative of v(a). Factor h(g).
-g*(g - 1)**2/4
Let n(s) be the first derivative of -2*s**5/35 - 3*s**4/14 - 2*s**3/21 + 3*s**2/7 + 4*s/7 + 5. Suppose n(t) = 0. Calculate t.
-2, -1, 1
Factor 9/4*r - 3/2 - 3/4*r**2.
-3*(r - 2)*(r - 1)/4
Let t(y) be the first derivative of y**5/25 - y**4/4 + 4*y**3/15 - 34. What is b in t(b) = 0?
0, 1, 4
Let l(v) be the first derivative of 1/540*v**6 + 1/36*v**4 + 2/3*v**3 + 1 + 0*v**2 + 0*v + 1/90*v**5. Let m(f) be the third derivative of l(f). Factor m(d).
2*(d + 1)**2/3
Let x(z) be the third derivative of z**9/120960 + z**5/30 - 3*z**2. Let m(r) be the third derivative of x(r). Factor m(t).
t**3/2
Let z(m) be the first derivative of 18*m**2 - 64/3*m**3 + 2 - 8*m + 14*m**4 - 24/5*m**5 + 2/3*m**6. Determine a, given that z(a) = 0.
1, 2
Let y be 11 + 2 - (-4 + 5). Suppose -4*k + 12 = -y. Find l, given that k*l**2 + 19*l - 19*l + 2*l**3 - 2*l**2 = 0.
-2, 0
Let o(h) be the first derivative of h**6/9 - 2*h**5/15 - h**4/3 - 7. Determine b so that o(b) = 0.
-1, 0, 2
Let d be (-2)/2 - 1 - -4. Suppose 0 = d*b - 3 - 1. Factor -5*f**3 + 3*f**2 + f**2 - 2*f**b.
-f**2*(5*f - 2)
Let v(p) be the first derivative of p**6/6 - p**5/5 - p**4/4 + p**3/3 + 13. Factor v(r).
r**2*(r - 1)**2*(r + 1)
Suppose 2/5 + 0*q - 2/5*q**2 = 0. Calculate q.
-1, 1
Let h(z) = z**2 - 11*z + 2. Let k = 1 - -10. Let f be h(k). Factor -1/4*y**f - 1/2*y - 1/4.
-(y + 1)**2/4
Let i = -66 + 70. Let z(p) be the second derivative of -5/6*p**i + 0 - 4