. Factor a(b).
-2*(7*b + 1)**2
Let r(k) be the third derivative of -k**7/210 + k**6/120 + k**5/20 - 5*k**4/24 + k**3/3 + 2*k**2. Factor r(t).
-(t - 1)**3*(t + 2)
Let t(b) = -2*b**3 - 2*b**2 + 3*b + 2. Let r be t(-2). Factor 1 + r*o**3 + 3*o**4 + 3*o**3 - 4*o**2 - 2*o - o**3 - 4*o**3.
(o - 1)*(o + 1)**2*(3*o - 1)
Let c(m) = 9*m**4 - 15*m**3 - m**2 + 79*m - 72. Let i(s) = 10*s**4 - 14*s**3 - 2*s**2 + 78*s - 72. Let d(l) = 6*c(l) - 5*i(l). Suppose d(w) = 0. What is w?
-2, 1, 3
Let c(v) be the first derivative of -v**3/15 + v/5 + 3. Factor c(i).
-(i - 1)*(i + 1)/5
Let r be 31/(-11 - (-2 + -1)). Let b = 37/8 + r. Factor 1/4 - 1/2*j**3 - b*j**2 + 0*j.
-(j + 1)**2*(2*j - 1)/4
Let x(z) be the second derivative of -1/16*z**4 + 0*z**2 - 4*z + 0 - 1/8*z**3. Let x(d) = 0. What is d?
-1, 0
Let k = 4 - -2. Factor o**2 + 4*o**4 - o**4 + k*o**5 + 3*o**3 - 5*o**5.
o**2*(o + 1)**3
Let t(h) be the third derivative of 2*h**7/735 - 15*h**2. Let t(i) = 0. What is i?
0
Let t(b) be the first derivative of b**6/27 - 2*b**5/9 + b**4/9 + 16*b**3/27 + 53. Let t(a) = 0. Calculate a.
-1, 0, 2, 4
Let s(q) be the second derivative of -q**7/1890 + q**6/1080 + q**5/60 - q**4/3 - 2*q. Let t(z) be the third derivative of s(z). Find l, given that t(l) = 0.
-1, 3/2
Let l(y) = 2*y + 0 + 1 + y**2 + 3. Let m(k) = -k**2 - 2*k - 5. Let n(d) = -4*l(d) - 3*m(d). Find x, given that n(x) = 0.
-1
Let q be (-3 - 585/6)/(-3). Let j = q - 33. Solve -1/4*m**4 + 1/4 + 0*m**2 + j*m - 1/2*m**3 = 0 for m.
-1, 1
Let g(y) be the second derivative of -y**5/40 - y**4/24 + y**3/6 - 4*y. Factor g(z).
-z*(z - 1)*(z + 2)/2
Let v(r) be the third derivative of -1/100*r**5 - 6*r**2 + 1/600*r**6 + 1/40*r**4 + 0 + 0*r - 1/30*r**3. Let v(h) = 0. Calculate h.
1
Let g(x) be the first derivative of 2/21*x**3 + 7 + 0*x**2 + 0*x. Factor g(c).
2*c**2/7
Suppose 5*q - 7 = -2. Let n(r) = r**4 - r**2 + r. Let y(x) = x**5 - 9*x**4 + x**3 + 9*x**2 - 8*x. Let k(i) = q*y(i) + 6*n(i). Determine s, given that k(s) = 0.
-1, 0, 1, 2
Let -1 - 1/2*i**2 - 3/2*i = 0. Calculate i.
-2, -1
Determine m, given that 16/7*m - 10/7*m**5 + 36/7*m**3 - 2*m**4 + 0 + 8*m**2 = 0.
-2, -1, -2/5, 0, 2
Let d(u) be the second derivative of -u**5/80 - u**4/16 - u**3/12 + 3*u - 4. Factor d(g).
-g*(g + 1)*(g + 2)/4
Let l = 93 - 93. Let n(q) be the third derivative of 0*q - 1/210*q**7 + 2*q**2 + 1/6*q**3 - 1/60*q**6 + l + 1/12*q**4 + 0*q**5. Suppose n(f) = 0. What is f?
-1, 1
Let l be (-16)/(-30) + (-3)/18. Let m = 5/6 + l. Factor -2/5*f**2 - m*f - 4/5.
-2*(f + 1)*(f + 2)/5
Let i(w) = -w**3 + 6*w**2 + 1. Let r be i(6). Let p be (0 - r)/(7/(-2)). Determine o so that 2/7*o - p*o**3 + 0*o**2 + 0 = 0.
-1, 0, 1
Let -1/3*w**3 + 11/3*w - 2 - 4/3*w**2 = 0. What is w?
-6, 1
Let f(x) be the second derivative of -3*x**5/110 - x**4/6 - 2*x**3/11 + x. Solve f(q) = 0.
-3, -2/3, 0
Factor 0*c**2 + 0 + 2/3*c**3 - 2/3*c.
2*c*(c - 1)*(c + 1)/3
Factor -32/7*x**4 + 2/7*x + 16/7*x**3 + 0 + 2*x**2.
-2*x*(x - 1)*(4*x + 1)**2/7
Let m be (3*-11)/(5/(-5)). Let n = -65/2 + m. What is d in n*d**3 + 4*d - 2 - 5/2*d**2 = 0?
1, 2
Determine q so that -1/3*q**3 + 0*q + 0 + 2/3*q**4 - 1/3*q**5 + 0*q**2 = 0.
0, 1
Let c(g) = -8*g**4 + 6*g**3 + 2*g**2 - 6*g - 6. Let k = 4 - -1. Let w(j) = 7*j**4 - 5*j**3 - 2*j**2 + 5*j + 5. Let i(y) = k*c(y) + 6*w(y). Factor i(m).
2*m**2*(m - 1)*(m + 1)
Suppose x = n, -2*x - 24 = -7*x - n. Suppose -2*v**4 - v**2 - 2*v**5 + 0*v**3 + v**2 + x*v**3 = 0. What is v?
-2, 0, 1
Suppose -2*n + 4*n = 6. Solve -2*h**2 - 8*h**n - 2*h + 7*h**2 + 3*h**2 = 0.
0, 1/2
Let w be ((-14)/(-12))/(210/90). Let w*t**3 - 1 - 2*t**2 + 5/2*t = 0. Calculate t.
1, 2
Factor -2/3*a + 1/2*a**2 - 2/3.
(a - 2)*(3*a + 2)/6
Let v(l) = 2*l**3 + 2*l**2 - l. Let n(q) = -q**3 - q**2 + q. Let r(d) = -3*n(d) - v(d). Factor r(z).
z*(z - 1)*(z + 2)
Suppose 5*o - 2*d = -8, -5*d + 20 = -5*o + 7*o. Let z(j) be the first derivative of -1/2*j + 1/3*j**3 + o*j**4 + 0*j**2 - 1/10*j**5 + 2. Factor z(s).
-(s - 1)**2*(s + 1)**2/2
Solve -2/3*p - 4/3 + 1/6*p**3 + 1/3*p**2 = 0 for p.
-2, 2
Let w = 1 - 1. Suppose 0 = -2*f + k - 1 + 9, -5*f = -k - 17. Factor -1 + 0*q - 2*q**f + 6*q**2 + w*q + 3 - 6*q.
-2*(q - 1)**3
Let r(n) be the first derivative of 2*n**5/25 + n**4/6 + n**3/15 + 2*n - 2. Let z(b) be the first derivative of r(b). Solve z(l) = 0 for l.
-1, -1/4, 0
Suppose -14*f + 19*f = 0. Let w(o) be the third derivative of f*o + 7/30*o**5 + o**2 + 0 + 0*o**3 + 1/6*o**4. Factor w(d).
2*d*(7*d + 2)
Let b(r) be the first derivative of -r**6/21 + 2*r**5/35 + r**4/7 - 4*r**3/21 - r**2/7 + 2*r/7 - 10. Let b(g) = 0. What is g?
-1, 1
Factor -4/3 - 2*d - 2/3*d**2.
-2*(d + 1)*(d + 2)/3
Let u = -160 + 484/3. Let p(w) be the first derivative of 0*w - u*w**3 - w**2 - 1/2*w**4 + 2. Determine o, given that p(o) = 0.
-1, 0
Let y(i) be the second derivative of i**4/12 - 7*i**3/6 - 3*i**2/2 + 2*i. Let w be y(8). Factor w*t - 7*t**2 - 13*t**2 - t + 25*t**3.
t*(5*t - 2)**2
Suppose 0 = -2*r + u - 12, 5*r - u - 5 + 32 = 0. Let w(g) = -g**2 + 13*g. Let h(n) = 20*n - 2 - 2*n**2 + 2. Let x(o) = r*h(o) + 8*w(o). Solve x(p) = 0 for p.
-2, 0
Let z(g) be the first derivative of g**4/30 - 8*g**3/45 + 24. Let z(n) = 0. Calculate n.
0, 4
Let d = -17 + 5. Let q be ((-52)/d - 2) + 3. Factor 2/3*p - 2*p**5 - 4*p**3 - q*p**4 + 0 + 0*p**2.
-2*p*(p + 1)**3*(3*p - 1)/3
Factor 1/4*z**4 - 1/4*z**2 - 1/2*z + 1/2*z**3 + 0.
z*(z - 1)*(z + 1)*(z + 2)/4
Let h(r) be the second derivative of -4*r**7/147 - r**6/15 - r**5/35 + r**4/42 + 13*r. Solve h(v) = 0 for v.
-1, 0, 1/4
Let k(o) be the third derivative of -o**6/200 - o**5/50 + o**4/40 + o**3/5 + o**2. Find p, given that k(p) = 0.
-2, -1, 1
Let m(c) be the second derivative of c**5/16 + 5*c**4/48 - 5*c**3/6 - 5*c**2/2 + 2*c - 8. Factor m(r).
5*(r - 2)*(r + 1)*(r + 2)/4
Let o be (-165)/(-3) - (-2 + 2). Suppose o = 4*p + i, -4*p + 2*i = -2*i - 60. Factor 44*d**2 - 1 + 4*d**4 - 16*d + p*d**4 + 3 - 48*d**3.
2*(d - 1)**2*(3*d - 1)**2
Let r be (18/(-12))/(2/5). Let i = 49/12 + r. Factor 0 - i*b**2 + 1/3*b.
-b*(b - 1)/3
Let j(t) = 3*t**2 - 3*t + 12. Let g(d) = -d. Let b(y) = 18*g(y) - j(y). Let b(w) = 0. Calculate w.
-4, -1
Let d(f) be the second derivative of -f**6/300 + 2*f**5/75 - f**4/15 + 3*f**2/2 - 2*f. Let j(h) be the first derivative of d(h). Factor j(p).
-2*p*(p - 2)**2/5
Factor 24*z**4 + 2*z**3 - 2*z**3 + 8*z**2 - 8*z**3 + 2*z**5 - 26*z**4.
2*z**2*(z - 2)*(z - 1)*(z + 2)
Let s(r) be the third derivative of 7*r**5/60 + r**4/4 - 69*r**2. Solve s(i) = 0.
-6/7, 0
Let c = -13 + 17. Suppose 2*y + 3*y - w + 1 = 0, -2*w + 2 = -c*y. Determine t, given that -1/4*t**5 + 0*t + y + 1/4*t**4 - 1/4*t**2 + 1/4*t**3 = 0.
-1, 0, 1
Factor -4*m + 4 - 2*m**2 + 16*m - 9*m - 5*m.
-2*(m - 1)*(m + 2)
Let q(g) be the second derivative of -3*g**5/20 + g**3/2 - 3*g. Solve q(v) = 0.
-1, 0, 1
Let x be -10*1/(-2) - -3. Let y = 11 - x. Suppose 0*a - 2/5*a**2 + 0 + 2/5*a**y = 0. Calculate a.
0, 1
Let c(f) be the third derivative of f**8/90720 - f**6/3240 - f**5/30 - 5*f**2. Let n(y) be the third derivative of c(y). Factor n(z).
2*(z - 1)*(z + 1)/9
Let 0*n**2 + 9/2*n**4 - 3/2*n**5 + 0*n**3 + 0*n + 0 = 0. Calculate n.
0, 3
Let q(h) = h**2 - 7*h - 3. Let t be q(7). Let u be t/((-3)/2) + 2. Factor -4 + u - c**5 - c**5 + 4*c**4 - 2*c**3.
-2*c**3*(c - 1)**2
Let g be 35/(-2) - -2 - -3. Let h = -12 - g. Solve 0*b + 1/2*b**4 - h*b**2 + 1/2*b**5 - 1/2*b**3 + 0 = 0 for b.
-1, 0, 1
Let w(m) be the second derivative of 4*m - 1/20*m**5 - 2*m**2 + 1/40*m**6 + 0*m**4 + 0*m**3 + 0. Let v(q) be the first derivative of w(q). Factor v(j).
3*j**2*(j - 1)
Let x(o) be the second derivative of -o**6/15 + 3*o**5/10 - o**4/6 - o**3 + 2*o**2 + 5*o. Let x(p) = 0. Calculate p.
-1, 1, 2
Suppose 0 = -34*d + 29*d + 5. Let w be d - (-4 + 5/2). Factor -1/2*a**5 - 5*a**3 + 5*a**2 + 1/2 - w*a + 5/2*a**4.
-(a - 1)**5/2
Let -18/5 + 3/5*z**2 - 3/5*z = 0. Calculate z.
-2, 3
Let o be 2/(9/(-12) - -1). Let c = o + -15/2. Let 1/2*m + 0 + c*m**3 + m**2 = 0. Calculate m.
-1, 0
Suppose 3*q - 3 - 15 = 0. Let s = q - 5. Factor 2*m**2 - 2*m**4 + m**4 - 2 + s.
-(m - 1)**2*(m + 1)**2
Suppose -7 = -2*k - 3. Solve -2*v**3 - 4*v**2 + 4*v**k + 2 - 2*v**2 - v + 3*v**3 = 0.
-1, 1, 2
Let g(j) = j**5 + j**4 - 2*j**2 - 2. Let i(x) = x**4 - x**2 - 1. Let k(u) = g(u) - 2*i(u). Factor k(f).
f**4*