What must be subtracted from $x^{4} + 4 x^{2} - 3 x + 7$ to get $3 x^{3} - x^{2} + 2 x + 1$ ?
Answer: $x^{4} - 3 x^{3} + 5 x^{2} - 5 x + 6$

True

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

False

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A True
Let $p (x)$ be the polynomial which must be subtracted from $x^{4} + 4 x^{2} - 3 x + 7$ to get $3 x^{3} - x^{2} + 2 x + 1$ .
So, $x^{4} + 4 x^{2} - 3 x + 7$ $- p (x)$ = $3 x^{3} - x^{2} + 2 x + 1$ .
So, $p (x) = x^{4} + 4 x^{2} - 3 x + 7 - (3 x^{3} - x^{2} + 2 x + 1)$ .
$\Rightarrow p (x) = x^{4} - 3 x^{3} + 5 x^{2} - 5 x + 6$
So, given answer is $T r u e$

Suggest Corrections

Similar questions

x^{4} + 4 x^{2} - 3 x + 7

3 x^{3} - x^{2} + 2 x + 1

x^{4} + 3 x^{3} + 5 x^{2} + 26 x + 56

x^{4} + 2 x^{3} - 4 x^{2} - x + 28

x^{2} + 5 x + 7

x^{4} + 2 x^{2} - 3 x + 7

x^{3} + x^{2} + x - 1

- 3 x^{3} + 4 x^{2} - 5 x + 6

3 x^{3} - 4 x^{2} + 5 x - 6

6 x^{3} - 8 x^{2} + 10 x - 12

lim x \to 1 \frac{x^{4} - 3 x^{3} + 2}{x^{3} - 5 x^{2} + 3 x + 1}

Join BYJU'S Learning Program