p.
2/7, 6
Factor -2/17*i**2 - 8/17*i - 6/17.
-2*(i + 1)*(i + 3)/17
Find i such that 4/7*i**5 + 48/7*i**3 + 8/7*i**2 - 32/7*i**4 + 24/7 - 52/7*i = 0.
-1, 1, 6
Let k be 12/7 - 8/(-28). Factor -j**2 - j**2 + 0*j**2 + k.
-2*(j - 1)*(j + 1)
Factor -9*k**2 + 12*k + 3/2*k**3 + 0.
3*k*(k - 4)*(k - 2)/2
Let h = -2 + -2. Let g = h - -6. Factor 2/7*y**g + 4/7*y + 0.
2*y*(y + 2)/7
Let t = -15 - -17. Let v(j) be the first derivative of 0*j - 2 + 1/7*j**t + 1/21*j**6 - 1/7*j**4 + 0*j**5 + 0*j**3. Factor v(s).
2*s*(s - 1)**2*(s + 1)**2/7
Let r be (-2)/5 + (-231)/(-15). Solve -147*q**3 + 5*q**2 - 8*q - 53*q**2 - r*q**3 - 75*q**5 - 12*q**2 - 185*q**4 = 0 for q.
-1, -2/3, -2/5, 0
Let b(j) = 3*j**3 - 21*j**2 - 55*j. Let k(w) = -w**3 + 11*w**2 + 27*w. Let h(i) = -3*b(i) - 7*k(i). Factor h(z).
-2*z*(z + 3)*(z + 4)
Let c be 3 - (-188)/6 - 3. Let f = c + -31. Factor 1/3 - 1/3*z**5 + 2/3*z**3 - 2/3*z**2 - 1/3*z + f*z**4.
-(z - 1)**3*(z + 1)**2/3
Let b = 41 + -39. Let s(z) be the second derivative of -1/3*z**4 + 0 - 1/45*z**6 - z + 4/9*z**3 - 1/3*z**b + 2/15*z**5. Factor s(n).
-2*(n - 1)**4/3
Suppose 5*s - 38 = s - t, 5*s - 4*t = 37. Solve -s + 39/2*o - 9*o**2 = 0.
2/3, 3/2
Let g be (-7)/2*18/(-21). Let c(f) be the third derivative of 0*f - 4*f**2 - 1/420*f**7 + 0*f**4 + 0 + 1/120*f**6 - 1/120*f**5 + 0*f**g. Factor c(i).
-i**2*(i - 1)**2/2
Let h be (-8)/(-36) + (-4)/18. Factor h + 0*r - 2/3*r**2.
-2*r**2/3
Let l be (-32)/216*(-2)/(8/6). What is f in -l*f**2 - 4/9 - 2/3*f = 0?
-2, -1
Let z be 4/10 + 14/(-35) + 3. Let d(i) be the second derivative of 0*i**z + 1/12*i**4 + 0 + 1/20*i**5 + 3*i + 0*i**2. Solve d(t) = 0 for t.
-1, 0
Let p(b) be the second derivative of -b**4/36 + b**3/6 - b**2/3 - 5*b. Factor p(y).
-(y - 2)*(y - 1)/3
Let m be (-3)/12 + 13/4. Let p = 0 + m. Solve -2/3*b + 2/3*b**p - 2/3*b**2 + 2/3 = 0 for b.
-1, 1
Let l(y) = y**5 - y**4 - y**3 + y + 1. Let h(w) = 3*w**5 + 5*w**2 + 9*w**4 + 3 - 7*w**3 + 0 - 5 - 7*w**5 - 3*w. Let g(z) = -h(z) - 2*l(z). Factor g(f).
f*(f - 1)**3*(2*f - 1)
Factor -8/7*w**3 - 8/7*w - 2/7 - 12/7*w**2 - 2/7*w**4.
-2*(w + 1)**4/7
Solve -a**3 + 32*a + 169 - 223*a - 12*a**2 - 4*a + 39*a**2 = 0.
1, 13
Let y(f) be the first derivative of -2*f**3 + 3*f + 0*f**2 + 0*f**4 + 3/5*f**5 + 3. Let y(v) = 0. What is v?
-1, 1
Let t(h) be the first derivative of h**6/24 - h**5/4 + h**4/2 - h**3/3 + 10. Factor t(s).
s**2*(s - 2)**2*(s - 1)/4
Let k be 2/2 - -6*2/6. Let m(a) be the second derivative of 3*a + a**2 + 2/3*a**k + 0 - 1/5*a**5 + 1/5*a**6 - 2/3*a**4. Solve m(s) = 0 for s.
-1, -1/3, 1
Let x(m) be the first derivative of m**5/35 - m**4/14 - m**3/21 + m**2/7 - 3. Factor x(c).
c*(c - 2)*(c - 1)*(c + 1)/7
Let i(g) be the second derivative of -g**5/20 - g**4/3 - 2*g**3/3 + 2*g. What is r in i(r) = 0?
-2, 0
Let g be ((-16)/(-24))/(1/(-3))*-2. Find j such that 1/5*j**g + 1/5*j**3 + 0 - 1/5*j**2 - 1/5*j**5 + 0*j = 0.
-1, 0, 1
Let a = 18 + -16. Suppose 1/2*s**5 + 0*s + 0*s**a - s**3 + 1/2*s**4 + 0 = 0. Calculate s.
-2, 0, 1
Let g(f) be the second derivative of -f**5/90 + f**4/9 - 4*f**3/9 + 8*f**2/9 - 4*f. Let g(r) = 0. What is r?
2
Let i(p) = -p**3 - p**2 + 2*p + 2. Let f be i(-2). Let -4 - 5*x**2 + 6 - x + 3*x**f + x**3 = 0. Calculate x.
-1, 1, 2
Let g be (7 - 5)/(1/1). Let n(a) be the second derivative of a - 1/6*a**4 + a**g + 0 + 0*a**3. Suppose n(b) = 0. What is b?
-1, 1
Let u(r) = -r**2 + 18*r + 117. Let n be u(23). Let -8/5*p + 0 + 36/5*p**4 + 0*p**n + 34/5*p**3 + 2*p**5 = 0. Calculate p.
-2, -1, 0, 2/5
Suppose 1/3*q**3 - 1 + 7/3*q - 5/3*q**2 = 0. Calculate q.
1, 3
Let c be 5*(8/(-10))/(-1). Suppose c*y - 4 = 4. Factor 2/5*n**y - 4/5*n**3 + 0*n + 2/5*n**4 + 0.
2*n**2*(n - 1)**2/5
Suppose -o - 2 + 4 = 0. Factor h**o - 2*h**3 + h - h**2 + h**3.
-h*(h - 1)*(h + 1)
Let w(r) = r**2 - 4*r. Let m = -8 + 6. Let i(j) = j. Let a(q) = m*w(q) - 6*i(q). Factor a(o).
-2*o*(o - 1)
Let u(z) be the first derivative of -2*z**5/45 - z**4/18 + 2*z**3/27 + z**2/9 + 4. Determine c so that u(c) = 0.
-1, 0, 1
Let a = 3213/5 - 641. Let a*l**4 + 0 + 2/5*l**2 + 0*l + 2*l**3 = 0. Calculate l.
-1, -1/4, 0
Factor -308/3*u**4 + 0*u + 128/3*u**3 - 16/3*u**2 + 196/3*u**5 + 0.
4*u**2*(u - 1)*(7*u - 2)**2/3
Let j = 861/4 - 213. Find r, given that -3/4*r**2 - 3/2 + j*r = 0.
1, 2
Factor -25 - 5*j - 1/4*j**2.
-(j + 10)**2/4
Let i(k) be the second derivative of -3*k - 4/3*k**2 + 4/9*k**4 + 1/5*k**5 + 0 - 2/9*k**3. Factor i(a).
4*(a + 1)**2*(3*a - 2)/3
Let j(k) be the second derivative of -3*k**4/26 - 2*k**3/39 - 10*k. Determine q so that j(q) = 0.
-2/9, 0
Suppose -a**3 - 3/4*a + 3/2*a**2 + 1/8 = 0. What is a?
1/2
Let f be (-3)/42*14/(-24). Let k(j) be the third derivative of -2*j**2 + 0*j**6 - 1/30*j**5 - 1/336*j**8 + 1/105*j**7 + f*j**4 + 0*j**3 + 0 + 0*j. Factor k(t).
-t*(t - 1)**3*(t + 1)
Let o(j) be the third derivative of 0*j**4 + 0*j**3 - 1/210*j**7 + 0 + 1/72*j**6 - 1/90*j**5 + 0*j - 4*j**2. Find f, given that o(f) = 0.
0, 2/3, 1
Let h(m) = -m**3 - 9*m**2 - 7*m + 10. Let i be h(-8). Factor -3*q**i + 3*q**3 + 3*q + 2*q**2 + 5*q**2 + 2*q**2.
3*q*(q + 1)**2
Let j(w) be the second derivative of -7*w**5/30 + w**4 + 4*w**3/3 + 3*w**2/2 - 2*w. Let g(r) be the first derivative of j(r). Factor g(i).
-2*(i - 2)*(7*i + 2)
Factor -14*r + 8*r**3 + 6*r - 2*r**4 - 52 + 29 + 29 - 4*r**2.
-2*(r - 3)*(r - 1)**2*(r + 1)
Suppose 3*f + 4 = 4*f. Find v such that f*v**3 - 3*v**4 - 10*v**3 + 3*v**4 - 3*v**4 = 0.
-2, 0
Let k(w) be the third derivative of 1/120*w**5 - 1/360*w**6 + 0 + 1/6*w**3 + 0*w**4 + 0*w + 3*w**2. Let s(m) be the first derivative of k(m). Factor s(y).
-y*(y - 1)
Let j(m) be the second derivative of 3*m + 2/3*m**2 - 1/60*m**5 - 1/12*m**4 + 0 + 0*m**3. Factor j(h).
-(h - 1)*(h + 2)**2/3
Let f be (-4)/14 - 214/(-14). Suppose 6*b - 10 = 2*b - 2*r, -b - 4*r - f = 0. Find m, given that -2/7*m**3 + 2/7*m**b + 0 + 0*m**4 + 0*m + 0*m**2 = 0.
-1, 0, 1
Let b = 32 + -28. Let d(c) be the third derivative of -3*c**2 - 1/20*c**6 + 1/168*c**8 + 0*c**3 + 2/105*c**7 + 1/3*c**b - 2/15*c**5 + 0 + 0*c. Factor d(p).
2*p*(p - 1)**2*(p + 2)**2
Let u(m) = m**2 + m + 2. Let q be u(0). Suppose q*y = 5*y. Factor i - 1 - i**2 + y*i - 3*i.
-(i + 1)**2
Let j = 621/2 - 310. Determine t, given that -1/4*t**2 + j*t + 3/4 = 0.
-1, 3
Let x(h) be the second derivative of -h**5/60 + h**4/12 - 2*h**2/3 + 14*h. Factor x(c).
-(c - 2)**2*(c + 1)/3
Let y(x) = -10*x + 94. Let b be y(9). Let 0*s**3 + 0*s**2 + 2/11*s**5 + 0*s + 0 - 4/11*s**b = 0. Calculate s.
0, 2
Suppose -1 = 2*r - 3*r, 2*r = -4*j + 10. Let w(d) be the second derivative of 0*d**2 - 1/9*d**3 - 1/6*d**4 - j*d + 0. Solve w(h) = 0 for h.
-1/3, 0
Factor -8/5*x**2 + 24/5*x**3 + 0 + 2/15*x.
2*x*(6*x - 1)**2/15
Let z(y) be the third derivative of y**5/30 + 5*y**4/3 + 100*y**3/3 - 23*y**2. Factor z(w).
2*(w + 10)**2
Let -4*n**3 + 16/9 + 15*n**5 + 176/9*n**2 - 32/3*n - 21*n**4 = 0. What is n?
-1, 2/5, 2/3
Let t = 10 - 8. Factor -2*o**3 - o - 4*o**2 - t*o**2 + o**3 + 4*o**2.
-o*(o + 1)**2
Let c = -56 + 170/3. Find l, given that -c - 2*l + 4/3*l**4 - 2/3*l**2 + 2*l**3 = 0.
-1, -1/2, 1
Factor 0 + 0*v - 3*v**3 + 1/2*v**2.
-v**2*(6*v - 1)/2
Let b(d) be the third derivative of d**7/1890 + d**6/270 - d**5/270 - d**4/18 + d**3/6 + 4*d**2. Solve b(x) = 0.
-3, 1
Let i(f) be the second derivative of f**5/70 - 4*f**3/21 - 4*f - 3. Let i(k) = 0. Calculate k.
-2, 0, 2
Let t = 11 - 7. Suppose -t*p = 4*q + 8, -4*q - 4*p - 4 = -p. Factor 2*o**3 + 1 - q*o + 9*o**2 - 3 - 7*o**2.
2*(o - 1)*(o + 1)**2
Let x(y) = y**2 + 7*y + 9. Let q be x(-6). Suppose 2*v - 5*v + 17 = 4*m, 4*m + 1 = q*v. Suppose 0 - 1/4*k - 1/4*k**4 + 1/4*k**m + 1/4*k**3 = 0. What is k?
-1, 0, 1
Let u(o) be the first derivative of -1/9*o**3 + 3*o - 1/36*o**4 + 0*o**2 - 2. Let t(m) be the first derivative of u(m). Factor t(c).
-c*(c + 2)/3
Let y be (-16)/20*(-16 + 1). Factor y - 12 - 2*f**2 - 2*f.
-2*f*(f + 1)
Let a(c) be the third derivative of c**2 + 0*c**4 - 1/560*c**8 + 3/350*c**7 + 0*c**5 + 0 - 1/100*c**6 + 0*c**3 + 0*c. Factor a(u).
-3*u**3*(u - 2)*(u - 1)/5
Let i(m) = 3*m**3 - 2*m**2. Let z(x) = -7*x**3 + 5*x**2. Let g(a) = -5*i(a) - 2*z(a). Determine u so that g(u) = 0.
0
Let h(r) be the third derivative of 1/360*r**6 + 0*r**5 - 1/72*r**4 + 0*r - 3*r**2 + 0 + 0*r**3. Factor h(y).
y*(y - 1)*(y + 1)/3
Let z be (