f 1/210*f**6 + 0*f + 0 - l*f**7 - 1/210*f**5 + 0*f**3 - 2*f**2 + 0*f**4. Factor z(t).
-2*t**2*(t - 1)**2/7
Let l be 16/20 - (-32)/10. Let n(b) be the first derivative of -4/33*b**3 + 0*b**2 + 3 + 2/55*b**5 + 0*b**l + 2/11*b. Solve n(h) = 0 for h.
-1, 1
Suppose 2*s - 1 + 9 = 0. Let m = s - -7. Let 0*j**3 + j**4 - j**2 + 5*j - 2*j - j**m - 2*j = 0. What is j?
-1, 0, 1
Suppose 5 = 2*q + 3*h, 0*q - 4*q + h + 31 = 0. Solve 0*j**2 - j**3 - 2*j**4 + q*j**3 + 2*j - 6*j**2 = 0.
0, 1
Let y(m) be the third derivative of 0*m - 1/10*m**5 + 0 + 0*m**3 + 4*m**2 - 1/60*m**6 - 1/6*m**4. Factor y(h).
-2*h*(h + 1)*(h + 2)
Let r(n) be the second derivative of -3*n**5/5 + 5*n**4/3 + 8*n**3/3 - 8*n**2 - 25*n. Factor r(m).
-4*(m - 2)*(m + 1)*(3*m - 2)
Let z be 0/(16/(-4)) + 2. Factor 0 + 1/2*y**3 + 1/2*y + y**z.
y*(y + 1)**2/2
Factor 0*n - 1/4*n**2 + 1/4.
-(n - 1)*(n + 1)/4
Let v(c) be the second derivative of c**7/1680 - c**5/80 + c**4/6 - 2*c. Let m(q) be the third derivative of v(q). Factor m(a).
3*(a - 1)*(a + 1)/2
Let g(i) be the second derivative of i**3/6 + 4*i**2 - 4*i. Let x be g(-6). Factor 2/11*h**4 + 8/11*h + 8/11*h**3 + 2/11 + 12/11*h**x.
2*(h + 1)**4/11
Let u be 6/36 - (-34)/12. Let k be (18/36)/(u/2). Find p, given that 0 + 1/3*p**4 + 1/3*p**3 - 1/3*p**2 - k*p = 0.
-1, 0, 1
Let m(d) be the second derivative of 0 - d + 2/21*d**7 + 0*d**2 - 1/5*d**6 + 1/10*d**5 + 0*d**4 + 0*d**3. Let m(y) = 0. What is y?
0, 1/2, 1
Let p = -2 + -9. Let u(j) = -5*j**4 + 8*j**3 - 5*j**2 + 2*j + 4. Let w(s) = -14*s**4 + 23*s**3 - 15*s**2 + 6*s + 11. Let m(z) = p*u(z) + 4*w(z). Factor m(g).
-g*(g - 2)*(g - 1)**2
Let f(p) = -19*p**4 - 19*p**3 - 11*p**2 - 11. Let u(h) = -5*h**4 - 5*h**3 - 3*h**2 - 3. Let b(t) = -6*f(t) + 22*u(t). Suppose b(z) = 0. Calculate z.
-1, 0
Let k(d) = 4*d + 6. Let z(q) = 5*q + 5. Let m(t) = -3*k(t) + 2*z(t). Let o be m(-7). Factor -3*w**2 - 4 + 1/2*w**3 + o*w.
(w - 2)**3/2
Let n(w) = 2*w**3 + 4*w**2 + 4*w. Let a(j) = -10*j**3 - 19*j**2 - 20*j. Let o(v) = 2*a(v) + 11*n(v). Find m, given that o(m) = 0.
-2, -1, 0
Let n(r) be the third derivative of -r**5/60 + r**4/12 - r**3/6 - r**2. Let n(j) = 0. Calculate j.
1
Let m(y) be the third derivative of -2*y**7/735 + y**6/70 + y**5/105 - y**4/14 + 39*y**2. Factor m(u).
-4*u*(u - 3)*(u - 1)*(u + 1)/7
Let l(p) = -12*p**3 + 56*p**2 - 8*p. Let w(g) = 8*g**3 - 37*g**2 + 5*g. Let c(v) = 5*l(v) + 8*w(v). Factor c(z).
4*z**2*(z - 4)
Let t be (-23)/4 + 9/12. Let d(a) = -2*a**4 + 4*a**3 - 3*a**2. Let c(w) = 4*w**4 - 8*w**3 + 5*w**2. Let n(r) = t*d(r) - 3*c(r). Factor n(o).
-2*o**3*(o - 2)
Let b(h) be the second derivative of h**6/30 + h**5/10 - h**3/3 - h**2/2 + 34*h. Factor b(w).
(w - 1)*(w + 1)**3
Let l(r) = 4*r**2 - r. Let v be l(1). Let w be ((-2)/2)/((-1)/8). Factor 0 + 6*m + w*m**2 + v - 5.
2*(m + 1)*(4*m - 1)
Let a(l) be the first derivative of l**7/252 - l**6/90 + l**5/120 - 4*l + 5. Let u(r) be the first derivative of a(r). Suppose u(t) = 0. Calculate t.
0, 1
Let g be (4*-1)/(-2 - -4). Let w be 0 - (g - 2)/8. Factor -w*h**2 + 0 + 0*h.
-h**2/2
Let l(q) = 3*q**2 + 19*q + 19*q - 4*q**2 - 46*q + 22. Let m be l(-10). Factor 6/5*a + 3/5*a**3 + 0 - 9/5*a**m.
3*a*(a - 2)*(a - 1)/5
Let f(d) = -d. Let n be f(-2). Suppose -n*q + 24 = 5*x, 3 = -x + 4*q - 1. Find l such that 6*l**x - 2*l**5 + 3*l**2 + 0*l**2 - 6*l**3 - l**2 = 0.
0, 1
Let y be (-17)/(-3) + 8/24. Determine c so that -8*c + y - 18*c**2 + 3*c**2 - c = 0.
-1, 2/5
Let g(i) be the second derivative of -i**7/210 + i**6/75 - i**5/100 - 4*i. Factor g(x).
-x**3*(x - 1)**2/5
Let j(p) be the second derivative of -11*p + 3/20*p**5 - 1/4*p**4 + 0 + 0*p**3 + 0*p**2. Factor j(q).
3*q**2*(q - 1)
Suppose -2*t + 3*o = 3, -o = -t - 23 + 22. Factor 0*j - 10/9*j**4 + t + 0*j**2 - 2/9*j**3.
-2*j**3*(5*j + 1)/9
Factor 17 + 20*d + 19*d - 6*d**2 + 4.
-3*(d - 7)*(2*d + 1)
Let d = -6 - -8. Factor -3*c**d + 4*c - 2*c + 4*c**2 + 2*c**2.
c*(3*c + 2)
Suppose -3*d + 17 - 11 = 0. Solve -2/5 - 4/5*u - 2/5*u**d = 0.
-1
Let i(u) be the third derivative of -u**7/490 + u**6/180 - u**5/210 - u**3/6 + 6*u**2. Let s(a) be the first derivative of i(a). Solve s(h) = 0.
0, 1/2, 2/3
Suppose b - 1 = 1. Suppose 3*o = -4*t + 8, -2*o = -2*t + b*o + 4. Factor -z**3 - t*z - 3*z**3 + 3*z**3 + 3*z + z**2 - 1.
-(z - 1)**2*(z + 1)
Suppose 0*m + 3 = m. Suppose 0 = 2*o + m*o - 10. Factor 8/5*v**o + 6/5*v**3 - 2/5*v - 4/5.
2*(v + 1)**2*(3*v - 2)/5
Let z be ((3 + -2)*-6)/(-2). Let g be (-12)/(-5) + z/5. Factor -3*v - g*v**2 + 0*v - v - v**4 + 4 + 4*v**3.
-(v - 2)**2*(v - 1)*(v + 1)
Suppose -2 = -z - 0*z. Find n, given that n**5 + 4*n**2 + 2*n - 4*n**4 - z*n**5 - n**5 + 0*n = 0.
-1, 0, 1
Let j(m) be the third derivative of 1/35*m**7 - 2/5*m**5 + 1/112*m**8 + 0 + 0*m + 4*m**2 - 7/8*m**4 - m**3 - 1/20*m**6. Suppose j(l) = 0. Calculate l.
-1, 2
Let d(f) be the first derivative of f**6/90 + f**5/30 - f**3/9 - f**2/6 - 2*f + 2. Let b(r) be the first derivative of d(r). Find a such that b(a) = 0.
-1, 1
Let o = 76 + -149/2. Determine c so that 0*c**4 - 3/4*c + o*c**3 + 0 - 3/4*c**5 + 0*c**2 = 0.
-1, 0, 1
What is s in 0 + 0*s**2 - 2/7*s + 2/7*s**3 = 0?
-1, 0, 1
Let m(q) = q + 2. Let k be m(1). Factor s**2 - s**2 - 3 + 3*s**2 - 3*s + 3*s**k + 0*s**3.
3*(s - 1)*(s + 1)**2
Let o(k) = k**3 + 3*k**2 - k. Let l be o(-3). Solve z**5 + 4*z**2 - l*z**2 + z**2 - z - 2*z**4 = 0.
-1, 0, 1
Solve -4/13*d + 10/13*d**4 - 10/13*d**2 + 4/13*d**3 + 0 = 0 for d.
-1, -2/5, 0, 1
Let r(w) = -w**2 - 7*w. Let k be r(-4). Solve -6*z - 7*z**2 - 4*z**2 - k*z**3 - 4*z**4 - 1 - 2*z**2 = 0.
-1, -1/2
Let s be (69/(-12) + 6)*8/6. Factor 0 - s*j**3 - 1/3*j**4 + 1/3*j + 1/3*j**2.
-j*(j - 1)*(j + 1)**2/3
Let k(l) = l. Let c be k(-4). Let a be 4/(-42) + c/(-6). Factor a*d + 2/7 + 2/7*d**2.
2*(d + 1)**2/7
Let q = 965 - 962. What is o in 0*o**2 + 0 - 2/5*o**5 + 4/5*o**q - 2/5*o + 0*o**4 = 0?
-1, 0, 1
Let q = 888 + -885. Factor 0*k**2 + 1/5*k**4 - 2/5*k**q + 0 + 0*k.
k**3*(k - 2)/5
Let j(u) = -u**4 - u**3 + u + 1. Let b = 9 - 10. Let o(d) = d**3 - d - 1. Let h(t) = b*o(t) - j(t). Factor h(m).
m**4
Determine d, given that -3/2*d**2 - 15/2 - 9*d = 0.
-5, -1
Let l(y) be the first derivative of -y**4 + 4*y**3 - 4*y**2 - 4. Let l(s) = 0. Calculate s.
0, 1, 2
Let s(m) be the first derivative of m**6/48 - m**5/4 + 3*m**4/4 - 11*m**3/12 + 7*m**2/16 - 51. Factor s(z).
z*(z - 7)*(z - 1)**3/8
Suppose 0*p - 2*p**2 + 20/3*p**3 - 8/3*p**5 + 6*p**4 + 0 = 0. What is p?
-1, 0, 1/4, 3
Factor -7*n**2 - 13*n**2 + 17*n**2 - 24 + 18*n.
-3*(n - 4)*(n - 2)
Solve -3/2*d**4 + 0*d**3 + 0*d + 0 + 3/2*d**2 = 0 for d.
-1, 0, 1
Let c(v) be the third derivative of -v**5/20 + v**4/2 - 3*v**3/2 - 3*v**2. Factor c(m).
-3*(m - 3)*(m - 1)
Let v(l) be the first derivative of -3 + l**3 - 3*l**3 + 3*l**2 + 2*l**3 + 9*l - l**3. Factor v(r).
-3*(r - 3)*(r + 1)
Let k be -3 - -2 - (-9 + 5). Factor -k*i + 3*i**3 - 3*i**5 + 3*i + 0*i**5.
-3*i**3*(i - 1)*(i + 1)
Factor 1/2*s**2 + 7/2*s - 4.
(s - 1)*(s + 8)/2
Let r = 47 - 13. Let w = -168/5 + r. Factor 3/5*f - 1/5*f**2 - w.
-(f - 2)*(f - 1)/5
Suppose -3*w + 65 = 17. Let x be (2*w/(-2))/(-7). Factor 8/7*f**5 - 8*f**4 - x - 172/7*f**2 + 146/7*f**3 + 88/7*f.
2*(f - 2)**3*(2*f - 1)**2/7
Let a(l) be the third derivative of 0 + 0*l - 5/12*l**4 - 1/6*l**6 + 1/21*l**7 - 1/168*l**8 + 1/3*l**5 + 1/3*l**3 - l**2. Factor a(z).
-2*(z - 1)**5
Let z(x) be the first derivative of x**6/14 - 3*x**4/4 + 2*x**3/7 + 18*x**2/7 - 24*x/7 + 28. Find f, given that z(f) = 0.
-2, 1, 2
Suppose 4*a = 4*m - 4, 2*m - 26 = -6*a + 2*a. Let p = -3 - -3. Suppose p*b + 2/3*b**3 + 0*b**2 + 0*b**4 + 0 - 2/3*b**m = 0. Calculate b.
-1, 0, 1
Let c(r) be the second derivative of -r**6/120 + r**5/80 + r**4/48 - r**3/24 + 11*r. Factor c(f).
-f*(f - 1)**2*(f + 1)/4
Factor -6*a**4 + 3*a**2 + 0*a**4 + 3*a**4.
-3*a**2*(a - 1)*(a + 1)
Suppose -10*o - 2*o**2 - 28 - 12 + 7*o**2 = 0. Calculate o.
-2, 4
Let i(s) be the third derivative of -s**8/20160 + s**7/1260 - s**6/180 - s**5/12 + 5*s**2. Let b(v) be the third derivative of i(v). Solve b(q) = 0.
2
Suppose 29*w = -110 + 110. Suppose 0*h**2 + 0*h**4 - 2/19*h**3 + 2/19*h**5 + w*h + 0 = 0. What is h?
-1, 0, 1
Let l(z) be the second derivative of z**5/20 - z**4/8 + 3*z**2/2 - 9*z. Let q(k) be the first derivative of l(k). Factor q(a).
3*a*(a - 1)
Solve 6/7*l**2