13*a.
-2*(a - 2)*(a - 1)/13
Let i(d) = d**2 + 6*d + 5. Let u be i(-5). Factor f - f**5 - 2*f**2 + 4*f**2 + u*f**4 + f**4 - 3*f**4.
-f*(f - 1)*(f + 1)**3
Suppose -4*l + 31 = d + 4*d, 0 = -d + l - 1. Solve 13*n**d - 7*n**3 + 2*n**2 - 2*n**3 = 0 for n.
-1/2, 0
Let z(v) be the second derivative of -v**4/4 + 3*v**3/2 - 34*v. Find r such that z(r) = 0.
0, 3
Let h be (-11)/33 + 14/6. Let m(x) be the third derivative of 0 + 1/240*x**5 + 0*x - h*x**2 + 0*x**6 - 1/840*x**7 + 0*x**3 + 0*x**4. Find u such that m(u) = 0.
-1, 0, 1
Let w = -10 - -15. Suppose -l**2 - 2*l**3 - l**2 - l + w*l = 0. Calculate l.
-2, 0, 1
Let u(l) = 256*l**5 - 64*l**4 - 144*l**3 - 43*l**2 - 3*l + 1. Let j(d) = d**2 + d + 1. Let q(x) = -j(x) + u(x). Factor q(m).
4*m*(m - 1)*(4*m + 1)**3
Let j(b) = 3*b**2 + b - 2. Let m(f) = -16*f**2 - 6*f + 11. Let g(x) = 22*j(x) + 4*m(x). Factor g(k).
2*k*(k - 1)
Factor 0 + 4/3*a**2 + 2/3*a**3 + 2/3*a.
2*a*(a + 1)**2/3
Let v(y) be the third derivative of y**5/240 + y**4/96 + 4*y**2. Factor v(w).
w*(w + 1)/4
Let z(x) = -x**3 + 2*x**2 + 14*x. Let i(l) = l. Let f(o) = -22*i(o) + 2*z(o). Let f(c) = 0. What is c?
-1, 0, 3
Factor 4/11*i**2 - 2/11 - 2/11*i**4 + 0*i**3 + 0*i.
-2*(i - 1)**2*(i + 1)**2/11
Let p = 381/4 - 2643/28. Suppose -3 = -u + 10*m - 11*m, 5*m - 11 = -4*u. Factor -2/7*k**u - p*k**2 - 6/7*k**3 - 2/7*k + 0.
-2*k*(k + 1)**3/7
Let v(a) be the first derivative of -a**6/6 - 6*a**5/5 - 7*a**4/2 - 16*a**3/3 - 9*a**2/2 - 2*a - 8. Factor v(g).
-(g + 1)**4*(g + 2)
Let p be ((-12)/(-75))/((-21)/(-15) + -1). Find a, given that -24/5*a + 16/5 - p*a**3 + 12/5*a**2 = 0.
2
Factor 16/9*w + 14/9*w**4 + 2/9*w**5 + 40/9*w**2 + 0 + 4*w**3.
2*w*(w + 1)*(w + 2)**3/9
Let c(j) be the third derivative of j**5/15 - 16*j**2. Factor c(f).
4*f**2
Let u(v) be the first derivative of 3/2*v**2 + 1 + 0*v - v**3. Factor u(t).
-3*t*(t - 1)
Let j = 168 - 166. Find d, given that 4/3*d - 2/9*d**j - 2 = 0.
3
Let j(d) = -4*d**5 - 2*d**4 + 5*d**2 + 4*d. Let k(o) be the first derivative of -o**6/6 + o**3/3 + o**2/2 - 3. Let r(y) = -j(y) + 3*k(y). Factor r(u).
u*(u - 1)*(u + 1)**3
Suppose -4*c - i + 5*i = 0, 3*c - 35 = -4*i. Factor c*h + 2*h - 5*h + 3*h**2 + h.
3*h*(h + 1)
Let m = 99/2 - 49. Suppose m*v**5 + 0*v**4 - v**3 + 1/2*v + 0 + 0*v**2 = 0. Calculate v.
-1, 0, 1
Let z(t) be the third derivative of -1/180*t**5 + 0 + 0*t + 1/9*t**3 + 4*t**2 - 1/72*t**4. Determine a, given that z(a) = 0.
-2, 1
Let d(u) be the second derivative of -u**7/3360 + u**6/720 - 5*u**3/6 - u. Let n(a) be the second derivative of d(a). Factor n(l).
-l**2*(l - 2)/4
Let y(j) = j + 1. Let o be y(7). Determine r, given that 3*r**2 - r**4 - 2 + 19*r - o*r - r**3 - 10*r = 0.
-2, -1, 1
Factor -2*h**2 + 428*h**3 + 13*h - 427*h**3 - 12*h**2.
h*(h - 13)*(h - 1)
Suppose 5 - 1 = 2*p. Factor -4 + 4 + f + p*f**2 - f**5 - 2*f**4 + 0.
-f*(f - 1)*(f + 1)**3
Let s(b) be the first derivative of -2*b**6/3 - 12*b**5/5 - 3*b**4 - 4*b**3/3 - 5. Find v, given that s(v) = 0.
-1, 0
Let s(f) = f**2 - 3*f + 2. Suppose 55 = -0*j + 5*j. Let g(o) = 5*o**2 - 15*o + 10. Let h(d) = j*s(d) - 2*g(d). Factor h(x).
(x - 2)*(x - 1)
Let v(m) be the first derivative of -2*m**3/9 - 2*m**2/3 + 4. Factor v(r).
-2*r*(r + 2)/3
Let r(x) be the first derivative of 3 + 0*x + 4/3*x**3 + 0*x**2 - 1/2*x**4. Determine w, given that r(w) = 0.
0, 2
Let w(t) be the third derivative of t**5/30 - t**3/3 - 2*t**2. Factor w(g).
2*(g - 1)*(g + 1)
Let 0 + 2/3*y**4 - 2/3*y**2 + 2*y**3 - 4/3*y - 2/3*y**5 = 0. What is y?
-1, 0, 1, 2
Let o be (20/120)/((-2)/(-24)). What is c in 2/9*c**3 + 0*c + 4/9*c**o + 0 = 0?
-2, 0
Factor 0 - 4/3*l**3 + 2/3*l**2 + 2/3*l.
-2*l*(l - 1)*(2*l + 1)/3
Let y = 6541/60 - 109. Let z(h) be the third derivative of 0*h + 2*h**2 + 1/12*h**4 - 1/6*h**3 + 0 - y*h**5. Factor z(r).
-(r - 1)**2
Let n(j) be the third derivative of j**8/756 - j**6/90 - 2*j**5/135 - 10*j**2. Let n(w) = 0. Calculate w.
-1, 0, 2
Let s(q) be the first derivative of q**6/180 + q**5/30 + q**4/12 + q**3/9 - q**2 - 4. Let j(g) be the second derivative of s(g). Factor j(n).
2*(n + 1)**3/3
What is v in 0 + 25/2*v**2 + 5/2*v**4 - 10*v**3 - 5*v = 0?
0, 1, 2
Suppose r + 1 = y, 4*y - 8 = -0*r + 3*r. Factor -z + 0*z**2 + y*z + 10*z**3 - 14*z**2.
2*z*(z - 1)*(5*z - 2)
Let f = -489814/35 + 13996. Let i(u) be the first derivative of 26/21*u**3 + 1/3*u**6 + 2/7*u**2 + 27/14*u**4 + 0*u + f*u**5 - 2. Let i(m) = 0. Calculate m.
-1, -2/7, 0
Let l(g) = 5*g**3 + 16*g**2 + 13*g + 2. Let q = -10 - -19. Let m = 7 - q. Let p(y) = y**3 - y. Let u(v) = m*p(v) - l(v). Solve u(a) = 0 for a.
-1, -2/7
Let q(k) = 6*k + 8 + 5*k - 9*k. Let l be q(-3). Find d such that -3 + 3*d - 3/4*d**l = 0.
2
Let w(p) be the first derivative of 2*p - 1/18*p**3 - 1/36*p**4 + 1/3*p**2 - 1. Let b(u) be the first derivative of w(u). Suppose b(x) = 0. What is x?
-2, 1
Let o be 4/((-12)/(-9)) + 2. What is f in -2*f**3 + 0 + o*f**2 - 5*f**2 + 3*f**2 - 1 = 0?
-1/2, 1
Factor 0 + 15/2*b**3 - 14*b**2 - 2*b.
b*(b - 2)*(15*b + 2)/2
Let v(i) = i**2 + 17*i + 4. Let q be v(-17). Factor 2/3*f**5 + 0 - 2/3*f**3 + 0*f + 0*f**q + 0*f**2.
2*f**3*(f - 1)*(f + 1)/3
Let i(x) = -x - 7*x**2 + 5*x**5 + 44*x**3 - 45*x**3 + 5 + 8*x**4 + 0*x**5. Let r(a) = a**3 + a**2 + 1. Let m(p) = -i(p) + 3*r(p). Solve m(w) = 0.
-1, 2/5, 1
Let b(f) be the third derivative of 0*f**5 + 0*f**3 - 1/60*f**4 - f**2 + 0 + 1/300*f**6 + 0*f. What is i in b(i) = 0?
-1, 0, 1
Let w(s) = -s**3 - 6*s**2 + s + 2. Let y(z) = z**2. Let q(g) = -3*w(g) - 12*y(g). Factor q(v).
3*(v - 1)*(v + 1)*(v + 2)
Let j be ((-2)/8)/(7/28*-3). Factor 0*h**4 + 2/3*h**3 - 1/3*h**5 + 0 + 0*h**2 - j*h.
-h*(h - 1)**2*(h + 1)**2/3
Suppose 8*p - 3*p + 625 = 0. Let k be p/(-180) + 2/(-8). Find f such that -56/3*f**2 - k - 46/9*f - 160/9*f**3 + 128/9*f**4 = 0.
-1/4, 2
Let f(b) be the first derivative of -b**7/1050 + b**6/600 + b**5/300 - b**4/120 - b**2 + 1. Let r(a) be the second derivative of f(a). Factor r(u).
-u*(u - 1)**2*(u + 1)/5
What is z in 22*z**3 - 2*z**3 + 12*z**2 - 4*z**2 + 4*z**5 + 16*z**4 = 0?
-2, -1, 0
Let b = 2767/6 - 460. Suppose 3*t - 4*t = 0. Factor t - b*j**2 - 1/3*j.
-j*(7*j + 2)/6
Determine j so that -14/13*j**3 - 30/13*j**2 - 2*j - 8/13 - 2/13*j**4 = 0.
-4, -1
Let u(a) be the first derivative of -a**4/8 + a**3/6 + a**2/4 - a/2 + 1. Find t, given that u(t) = 0.
-1, 1
Let q = 7 + -1. Let -z**3 - 4*z - z**3 - 2*z**3 + 2*z**3 + q*z**2 = 0. What is z?
0, 1, 2
Let d be 26/40*-4 - -5. Let -9/5*g**2 + 12/5 + d*g = 0. What is g?
-2/3, 2
Let p(x) be the first derivative of -x**6/6 - x**5 - 7*x**4/4 + x**3/3 + 4*x**2 + 4*x - 1. Let p(f) = 0. What is f?
-2, -1, 1
Let a(k) be the third derivative of k**7/2520 - k**5/120 + k**4/24 - 2*k**2. Let v(n) be the second derivative of a(n). What is z in v(z) = 0?
-1, 1
Let y(o) = -3*o - 3. Let v be y(-2). Suppose v*x**2 + 9*x**3 + 0*x**2 + 0*x**5 + 0*x**2 + 9*x**4 + 3*x**5 = 0. What is x?
-1, 0
Let s(r) be the third derivative of 64*r**7/525 - 4*r**6/5 + 26*r**5/25 - 37*r**4/60 + r**3/5 - 6*r**2. Solve s(t) = 0.
1/4, 3
Suppose 2*d - 5*d + 6 = 0. Let p = -15 - -19. Suppose a + p + a**d - 4 = 0. Calculate a.
-1, 0
Let l(c) be the third derivative of c**8/560 - c**7/350 - 3*c**6/200 + c**5/20 - c**4/20 - 8*c**2. Suppose l(m) = 0. What is m?
-2, 0, 1
Let c(r) be the first derivative of 5*r**6/9 - 16*r**5/15 - 13*r**4/2 - 68*r**3/9 - 8*r**2/3 + 36. Find k such that c(k) = 0.
-1, -2/5, 0, 4
Let k be (-56)/(-21)*9/6. Let b(c) be the second derivative of c**2 + 1/20*c**5 + 2*c + 5/6*c**3 + 0 + 1/3*c**k. Let b(x) = 0. Calculate x.
-2, -1
Let r(g) be the third derivative of -2*g**7/147 - 2*g**6/105 + 2*g**5/35 + 2*g**4/21 - 2*g**3/21 - 5*g**2. Determine v, given that r(v) = 0.
-1, 1/5, 1
Let p be -1 - (1 + (-1 - 2)). Suppose 0 = a - p - 1. Factor w**3 + 2*w**2 - 3*w**3 + 0*w**a.
-2*w**2*(w - 1)
Let s(a) = a**5 - 5*a**3 + a - 3. Let z(q) = -6*q**5 + 29*q**3 - 6*q + 17. Suppose 94 = h - 42. Suppose 2*j = -2*j + h. Let x(y) = j*s(y) + 6*z(y). Factor x(f).
-2*f*(f - 1)**2*(f + 1)**2
Suppose 3*a = -2*a. Let q(m) = a*m - m**4 + m**3 + 0*m. Let z(f) = 7*f**4 - 3*f**3 + 3*f**2 + f. Let o(w) = -6*q(w) - z(w). Solve o(b) = 0.
-1, 0
Let h(m) be the second derivative of m**6/90 + m**5/10 + m**4/3 + 5*m**3/9 + m**2/2 + 5*m. Factor h(q).
(q + 1)**3*(q + 3)/3
Let m = 4 - 